Hierarchical Kernel and Sub-kernels

This paper shows the theoretical development of hierarchy by kernels and an algorithm used to obtain an interesting class or partition from a hierarchy. Also shown is the theorem about the Kernels Optimal Criterion and how it is expressed as a function of the masses of the points of the vector space and product scale points, the inertia of the cloud formed by those two points or hierarchical nodes, which are called subcores or sub-kernels. The application is made on the terminal efficiency of postgraduate degrees at ESIA, IPN Mexico, along its first 48 years of academic and scientific life and the development of students´ graduation

Math Words and Their Dendrograms

A hierarchical clustering algorithm based on graph theory is presented, which, from generation of a path from a given vertex, builds a math word and calculates clusterization under an index. This is possible due to modification of Tarry’s algorithm, through exchange of path elements. The unidimensional clustering index applied to σ gives us what I have called Tarry’s hierarchy. From the definition of net word, cycle, tree, tree word, and vertex, a theorem on the relationship between vertices, lines, and letters of a labyrinth is shown, which allows the generation of words and their dendrograms with the application of the Euclidean distance. Practical use of these concepts provides possibilities of connections in arrangements for telephone centrals and robotic arms’ paths

Dimensioning of Fractal Fracture on a Concrete Slab

What is presented here is a methodology that allows to study fractures in any material, especially in concrete elements. The importance lies in the moment in which the fracture that occurs in a structural element (slab in our case study) causes a negative effect on its structural behavior. Traditionally, its study is developed from the perspective of fracture mechanics, with which the energy at the tip of the crack or fracture is calculated, and it cannot go further. But the combination of the theories of fracture mechanics and fractal geometry allows us to obtain the patterns of its behavior in the future. Thus, the research was based on tests made on structural elements of concrete, from a slab led to structural failure and choosing a fracture. This was vectorized in order to obtain a fractal axis, which was called state 0, taking three parts or sections of that state and repeating them on a smaller scale. Subsequently, the research was based on five of the methods used for the study and calculation of the fractal dimension: box dimension, perimeter-area dimension, information dimension, mass dimension, and ruler dimension. Most of the fractal dimensions obtained under these methods were similar to each other

Construction of an Artificial Neural Network-Based Method to Detect Structural Damage

This chapter shows the framework used to obtain data with which the artificial neural network (ANN) was developed. It describes its geometry, properties of the material, sections of structural elements, and loads used. Then, the numerical model of the framework under study is developed in structural analysis using SAP2000® software in order to obtain its modal parameters. In addition, a program made in MATLAB® is shown, from which data with and without damage to the framework under study were obtained, and with which the ANN was developed. Data from the numerical model were used to corroborate data obtained with MATLAB®. The neural model used in this work to detect structural damage is described. Data on damage were obtained simulating a plastic hinge in various elements of a test framework, varying the position of the hinge. The above resulted in obtaining various damage conditions for the same framework, which data thus obtained were used to develop the network. Damage conditions were hierarchized based on their fundamental periods in order to know where is more damage, depending on location of the hinge within the framework. Upon completion of the research, we have concluded that the methodology implemented to detect structural damage is rather simple. It was carried out in four steps

La enseñanza de las matemáticas en el siglo XXI / The Teaching of Mathematics in the 21st Century

Este trabajo hace una contribución académica basada en el fortalecimiento del quehacer docente en el nivel superior de las escuelas de ingeniería, con el objetivo de lograr un creciente aprovechamiento en los estudiantes de Ingeniería Civil. Para ello modificamos los elementos usuales de aprendizaje, llevando tal aprendizaje al desarrollo de las aptitudes y la confianza de los alumnos. Se fomentaron estrategias de aprendizaje diferentes a las tradicionales que dieron como resultado que los estudiantes crearan acrósticos, cuentos, historietas, juegos y canciones, con temas basados en las asignaturas afines a las matemáticas: Estática, Física, Estructuras Isostáticas y Resistencia de Materiales, logrando mejorar el entorno educativo de los estudiantes y al mismo tiempo apoyando el aprendizaje mediante el trabajo en equipo y adquiriendo el alumno un conocimiento más profundo de la asignatura.

La enseñanza de las matemáticas en el siglo XXI / The Teaching of Mathematics in the 21st Century

Este trabajo hace una contribución académica basada en el fortalecimiento del quehacer docente en el nivel superior de las escuelas de ingeniería, con el objetivo de lograr un creciente aprovechamiento en los estudiantes de Ingeniería Civil. Para ello modificamos los elementos usuales de aprendizaje, llevando tal aprendizaje al desarrollo de las aptitudes y la confianza de los alumnos. Se fomentaron estrategias de aprendizaje diferentes a las tradicionales que dieron como resultado que los estudiantes crearan acrósticos, cuentos, historietas, juegos y canciones, con temas basados en las asignaturas afines a las matemáticas: Estática, Física, Estructuras Isostáticas y Resistencia de Materiales, logrando mejorar el entorno educativo de los estudiantes y al mismo tiempo apoyando el aprendizaje mediante el trabajo en equipo y adquiriendo el alumno un conocimiento más profundo de la asignatura.

Haloalkalitolerant Actinobacteria with capacity for anthracene degradation isolated from soils close to areas with oil activity in the State of Veracruz, Mexico

The use of native strains of microorganisms from soils is an excellent option for bioremediation. To our knowledge, until now there has been no other group working on the isolation of Actinobacteria from contaminated soils in Mexico. In this study, samples of soils close to areas with oil activity in the State of Veracruz, Mexico, were inoculated for the isolation of Actinobacteria. The strains isolated were characterized morphologically, and the concentrations of NaCl and pH were determined for optimal growth. Strain selection was performed by the detection of a phylogenetic marker for Actinobacteria located at the 23S rRNA gene, followed by species identification by sequencing the 16S rRNA gene. Several haloalkalitolerant Actinobacteria were isolated and identified as: Kocuria rosea, K. palustris, Microbacterium testaceum, Nocardia farcinica and Cellulomonas denverensis. Except for C. denverensis, the biomass of all strains increased in the presence of anthracene. The strains capacity to metabolize anthracene (at 48 h), determined by fluorescence emission, was in the range of 46–54%. During this time, dihydroxy aromatic compounds formed, characterized by attenuated total reflectance Fourier transform infrared spectroscopy bands of 1205 cm–1 and 1217 cm–1. Those Actinobacteria are potentially useful for the bioremediation of saline and alkaline environments contaminated with polycyclic aromatic hydrocarbon compounds