Conhecimento prévio de números complexos em Engenharia

This paper's objective is to identify the previous mathematical knowledge that computer systems engineering students have before taking the course of complex numbers through the development of cognitive processes of the theory of mathematics in the context of science. For this purpose, an instrument based on these cognitive processes has been designed. This instrument has been applied to convenience sample of students. The data was analyzed quantitatively, and the results show the difficulties that students have on the basic previous knowledge of education.El presente artículo tiene como objetivo identificar los conocimientos matemáticos previos que tienen los estudiantes de Ingeniería en Sistemas Computacionales antes de tomar el curso de números complejos mediante el desarrollo de los procesos cognitivos de la teoría de la Matemática en el Contexto de las Ciencias. Para lo cual se muestra el diseño de un instrumento con base en estos procesos cognitivos, el cual se aplica a una muestra por conveniencia de estudiantes.  Los datos se analizan cuantitativamente y los resultados muestran las dificultades que tienen los estudiantes en los conocimientos previos básicos de la educación.  Este artigo tem como objetivo identificar os conhecimentos matemáticos prévios que os estudantes da Engenharia em Sistemas Computacionais têm antes de fazer o curso de números complexos através do desenvolvimento dos processos cognitivos da teoria da Matemática no Contexto das Ciências. Para isso é mostrado o desenho de um instrumento baseado nesses processos cognitivos, que é aplicado a uma amostra por conveniência de estudantes. Os dados são analisados quantitativamente e os resultados mostram as dificuldades que os estudantes têm nos conhecimentos prévios básicos da educação

Disjointness Graphs of segments in R^2 are almost all Hamiltonian

Let P be a set of n >= 2 points in general position in R^2. The edge disjointness graph D(P) of P is the graph whose vertices are all the closed straight line segments with endpoints in P, two of which are adjacent in D(P) if and only if they are disjoint. In this note, we give a full characterization of all those edge disjointness graphs that are hamiltonian. More precisely, we shall show that (up to order type isomorphism) there are exactly 8 instances of P for which D(P) is not hamiltonian. Additionally, from one of these 8 instances, we derive a counterexample to a criterion for the existence of hamiltonian cycles due to A. D. Plotnikov in 1998

On the packing number of 3 3 -token graph of the path graph Pn P_n

In 2018, J. M. Gómez et al. showed that the problem of finding the packing number $\rho(F_2(P_n))$ of the 2-token graph $F_2(P_n)$ of the path $P_n$ of length $n\ge 2$ is equivalent to determining the maximum size of a binary code $S'$ of constant weight $w = 2$ that can correct a single adjacent transposition. By determining the exact value of $\rho(F_2(P_n))$, they proved a conjecture of Rob Pratt. In this paper, we study a related problem, which consists of determining the packing number $\rho(F_3(P_n))$ of the graph $F_3(P_n)$. This problem corresponds to the Sloane's problem of finding the maximum size of $S'$ of constant weight $w = 3$ that can correct a single adjacent transposition. Since the maximum packing set problem is computationally equivalent to the maximum independent set problem, which is an NP-hard problem, then no polynomial time algorithms are expected to be found. Nevertheless, we compute the exact value of $\rho(F_3(P_n))$ for $n\leq 12$, and we also present some algorithms that produce a lower bound for $\rho(F_3(P_n))$ with $13\leq n\leq 44$. Finally, we establish an upper bound for $\rho(F_3(P_n))$ with $n\geq 13$

Conocimientos previos de números complejos en Ingeniería

This paper's objective is to identify the previous mathematical knowledge that computer systems engineering students have before taking the course of complex numbers through the development of cognitive processes of the theory of mathematics in the context of science. For this purpose, an instrument based on these cognitive processes has been designed. This instrument has been applied to convenience sample of students. The data was analyzed quantitatively, and the results show the difficulties that students have on the basic previous knowledge of education.Este artigo tem como objetivo identificar os conhecimentos matemáticos prévios que os estudantes da Engenharia em Sistemas Computacionais têm antes de fazer o curso de números complexos através do desenvolvimento dos processos cognitivos da teoria da Matemática no Contexto das Ciências. Para isso é mostrado o desenho de um instrumento baseado nesses processos cognitivos, que é aplicado a uma amostra por conveniência de estudantes. Os dados são analisados quantitativamente e os resultados mostram as dificuldades que os estudantes têm nos conhecimentos prévios básicos da educação.El presente artículo tiene como objetivo identificar los conocimientos matemáticos previos que tienen los estudiantes de Ingeniería en Sistemas Computacionales antes de tomar el curso de números complejos mediante el desarrollo de los procesos cognitivos de la teoría de la Matemática en el Contexto de las Ciencias. Para lo cual se muestra el diseño de un instrumento con base en estos procesos cognitivos, el cual se aplica a una muestra por conveniencia de estudiantes.  Los datos se analizan cuantitativamente y los resultados muestran las dificultades que tienen los estudiantes en los conocimientos previos básicos de la educación. 

La tecnología en eventos contextualizados para la construcción del conocimiento de números complejos en ingeniería

La investigación tuvo como objetivo determinar cómo favorece la tecnología en eventos con-textualizados la construcción del conocimiento de números complejos en los alumnos. Este trabajo se fundamentó en la teoría de la Matemática en el Contexto de las Ciencias (MCC). Los resultados mos-traron que la didáctica de la Matemática en Contexto contribuye a que los alumnos construyan su co-nocimiento. Esto es, los alumnos de Ingeniería en Sistemas Computacionales construyen su conoci-miento de los números complejos cuando la matemática se vincula con el objeto principal de estudio de su carrera, dado que ellos tuvieron que desarrollar, en un lenguaje de programación de alto nivel, una calculadora para números complejosThe purpose of this research is to determine how technology in contextualized events, helps students to construct their knowledge of complex numbers. This work is based on the theory of Mathe-matics in the Context of Sciences(MCS). The results showed that the didactic of mathematics in con-text, helps students to construct their knowledge. Thus, computer systems engineering students con-struct their knowledge on complex numbers when mathematics is related to the study’s main aim of students’ career, since students were asked to develop a calculator for complex numbers in high-level programming language.Fil: Mbe Koua Ndjatchi, Christophe. Instituto Politécnico Nacional. Unidad Profesional Interdisciplinaria de Ingeniería Campus Zacatecas. Zacatecas; Méxic

On the connectivity of the disjointness graph of segments of point sets in general position in the plane

Let $P$ be a set of $n\geq 3$ points in general position in the plane. The edge disjointness graph $D(P)$ of $P$ is the graph whose vertices are all the closed straight line segments with endpoints in $P$, two of which are adjacent in $D(P)$ if and only if they are disjoint. We show that the connectivity of $D(P)$ is at least $\binom{\lfloor\frac{n-2}{2}\rfloor}{2}+\binom{\lceil\frac{n-2}{2}\rceil}{2}$, and that this bound is tight for each $n\geq 3$.Comment: 13 pages, 5 figure

An Upper Bound Asymptotically Tight for the Connectivity of the Disjointness Graph of Segments in the Plane

Let P be a set of n≥3 points in general position in the plane. The edge disjointness graph D(P) of P is the graph whose vertices are the n2 closed straight line segments with endpoints in P, two of which are adjacent in D(P) if and only if they are disjoint. In this paper we show that the connectivity of D(P) is at most 7n218+Θ(n), and that this upper bound is asymptotically tight. The proof is based on the analysis of the connectivity of D(Qn), where Qn denotes an n-point set that is almost 3-symmetric

A Performance Comparison of CNN Models for Bean Phenology Classification Using Transfer Learning Techniques

The early and precise identification of the different phenological stages of the bean (Phaseolus vulgaris L.) allows for the determination of critical and timely moments for the implementation of certain agricultural activities that contribute in a significant manner to the output and quality of the harvest, as well as the necessary actions to prevent and control possible damage caused by plagues and diseases. Overall, the standard procedure for phenological identification is conducted by the farmer. This can lead to the possibility of overlooking important findings during the phenological development of the plant, which could result in the appearance of plagues and diseases. In recent years, deep learning (DL) methods have been used to analyze crop behavior and minimize risk in agricultural decision making. One of the most used DL methods in image processing is the convolutional neural network (CNN) due to its high capacity for learning relevant features and recognizing objects in images. In this article, a transfer learning approach and a data augmentation method were applied. A station equipped with RGB cameras was used to gather data from images during the complete phenological cycle of the bean. The information gathered was used to create a set of data to evaluate the performance of each of the four proposed network models: AlexNet, VGG19, SqueezeNet, and GoogleNet. The metrics used were accuracy, precision, sensitivity, specificity, and F1-Score. The results of the best architecture obtained in the validation were those of GoogleNet, which obtained 96.71% accuracy, 96.81% precision, 95.77% sensitivity, 98.73% specificity, and 96.25% F1-Score