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Axiomatic Set Theory à la Dijkstra and Scholten

Acosta Gempeler, Ernesto; Aldana Gomez, Bernarda; Bohorquez Villamizar, Jaime Alejandro; Rocha Niño, Hernan Camilo (Springer VerlagAlemania, 2017)

The algebraic approach by E. W. Dijkstra and C. S. Scholten to formallogic is a proof calculus, where the notion of proof is a sequence of equivalencesproved – mainly – by using substitution of ‘equals for equals’. This ...
Between closed and Ig-closed sets

Pachon Rubiano, Néstor Raúl (Business Global LLCNew York, 2018)

The concept of closed sets is a central object in general topology. In order to extend many of important properties of closed sets to a larger families, Norman Levine initiated the study of generalized closed sets. In ...
SOME PROPERTIES OF J -HAUSDORFF, J -REGULAR AND J -NORMAL SPACES

Pachon Rubiano, Néstor Raúl (Vasile Alecsandri UniversityBacau, 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 ...
BUZANO’S INEQUALITY IN ALGEBRAIC PROBABILITY SPACES

Agredo, J.; Leon, Y.; Osorio, J.; Peña, A. (Croacia, 2019)

We obtain a generalization of Buzano’s inequality of vectors in Hilbert spaces , using the theory of algebraic probability spaces. In particular, we extend a result of Dragomir given in [7]. Applications for numerical ...
Negafibonacci Numbers via Matrices

Triana Laverde, Juan Gabriel (Universidad Estatal de TbilisiGeorgia, 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 ...
Modeling the effects of light wavelength on the growth of Nostoc ellipsosporum

Ortiz Moreno, Martha Lucia; Cárdenas Poblador, Jaleydi; Agredo, Julián; Solarte Murillo, Laura Vanessa (Pontificia Universidad JaverianaJuan Carlos Salcedo-Reyes (salcedo.juan@javeriana.edu.co)Bogotá, Colombia, 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 ...
Regularity and normality in ideal bitopological spaces

Pachon Rubiano, Néstor Raúl (Universidad Católica del NorteAntofagasta, Chile, 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 ...
Other forms of continuity modulo an ideal

Pachón Rubiano, Néstor Raúl (Universidad Católica del NorteAntofagasta, Chile, 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 ...
Soluciones de la Ecuación de Smoluchowski caso discreto y caso continuo

Gacharná González, Juan Manuel (Escuela Colombiana de Ingeniería Julio GaravitoMatemáticas, 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 ...

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Axiomatic Set Theory à la Dijkstra and Scholten
...
Acosta Gempeler, Ernesto | 2017

The algebraic approach by E. W. Dijkstra and C. S. Scholten to formallogic is a proof calculus, where the notion of proof is a sequence of equivalencesproved – mainly – by using substitution of ‘equals for equals’. This paper presentsSet, a first-order logic axiomatization for set theory using the approach of Dijk-stra and Scholten. The approach is novel in that the symbolic manipulation offormulas is shown to be an eective tool for teaching axiomatic set theory tosophomore students in mathematics. This paper contains many examples on howargumentative proofs can be easily expressed inSetand points out howSetcanenrich the learning experience of students. These results are part of a larger ef-fort to formally study and mechanize topics in mathematics and computer sciencewith the algebraic approach of Dijkstra and Scholten.

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Between closed and Ig-closed sets
...
Pachon Rubiano, Néstor Raúl | 2018

The concept of closed sets is a central object in general topology. In order to extend many of important properties of closed sets to a larger families, Norman Levine initiated the study of generalized closed sets. In this paper we introduce, via ideals, new generalizations of closed subsets, which are strong forms of the Ig-closed sets, called ρIg-closed sets and closed-I sets. We present some properties and applications of these new sets and compare the ρIg-closed sets and the closed-I sets with the g-closed sets introduced by Levine. We show that I-closed and closed-I are independent concepts, as well as I * -closed sets and closed-I concepts.

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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.

LEER
BUZANO’S INEQUALITY IN ALGEBRAIC PROBABILITY SPACES
...
Agredo, J. | 2019

We obtain a generalization of Buzano’s inequality of vectors in Hilbert spaces , using the theory of algebraic probability spaces. In particular, we extend a result of Dragomir given in [7]. Applications for numerical inequalities for n- tuples of bounded linear operators and functions of operators defined by double power series are also generalized.

LEER
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.

LEER
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.

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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.

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Other forms of continuity modulo an ideal
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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.

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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.

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