Table of contents

H M Parra-López¹, J P Rojas Suárez¹, and E D V-Niño²

¹Universidad Francisco de Paula Santander, San José de Cúcuta, Colombia

²Foundation of Researchers in Science and Technology of Materials, Colombia

E-mail: deydannv@gmail.com, matematicasyestadistica@ufps.edu.co

These proceedings present the written contributions of the participants of the XIV Applied Mathematics Meeting and XI Statistics Meeting (XIV AMM and XI SM), which was held from 7 to 8 December, 2018, at the San José de Cúcuta city, Colombia, organized by the "Departamento de Matemáticas y Estadística" of the Universidad Francisco de Paula Santander.

Accordingly, the fundamental objective of this meeting (XIV AMM and XI SM), was to create and promote a space of reflection and discussion about mathematics and statistics (history, evolution, teaching, and application). Likewise, the XIV AMM and XI SM conference was a scenery where researchers and teachers in the area of mathematics to interact, socialize research results and consolidate networks for the exchange of ideas. In this way, it was searched strengthen mathematics and statistics as a science, the pedagogical principles that tend to disseminate science, innovation, as well as encourage the creation of other learning scenarios, enhance the application of mathematics in various areas of knowledge and arouse the interest of the students through research in these sciences.

List of Organizing Committee, International Committee, National Committees, Photo-Mathematics Contest Coordinators; Fractal-light are available in this pdf.

All papers published in this volume of Journal of Physics: Conference Series have been peer reviewed through processes administered by the proceedings Editors. Reviews were conducted by expert referees to the professional and scientific standards expected of a proceedings journal published by IOP Publishing.

The role of computational mathematics on the study of the fundamental properties of neutrinos and axions and their impact on the energy loss within stellar structure is illustrated in this work. The theoretical predictions, done with the aid of a numerical code for simulating stellar evolution, are used in three cases of interest: the number of neutrinos reaching our planet from the closest stellar system, calculated by modelling its two main stars and their corresponding neutrino spectrum; the magnitude of the neutrino magnetic dipole moment and the axion-electron coupling constant is estimated by comparing stellar models to the tip-RGB of fifty globular clusters; and, finally, the survival of the Earth, after the Sun becomes a red giant is tested for an scenario in which axions and neutrinos are being simultaneously produced within the solar core.

Alzheimer's disease is a degenerative neurological disorder that comes with the aging process characterized by cognitive, affective and behavioral deficits. a possible method that can support the diagnosis and treatment of Alzheimer's disease is called fractal geometry, given that the brain has fractal structure, therefore, Alzheimer's disease is an observed progressive process of alterations within the groups of topographic voxels, which means that a geometrical fractal analysis can support the diagnosis of the disease. For this purpose, a double blind clinical trial study was designed, calculating the fractal dimension and the lagunarity of magnetic resonance imaging of the cerebral cortex of patients with the neurological report of Alzheimer's disease, implementing the box-counting method or "entropy of kolmogorov", by means of a software with logarithm FracLac (p=1.029). As a relevant result, a characteristic fractal pattern was evidenced in the images of patients with Alzheimer's disease, which allowed to postulate the mathematical method as a possible analysis to complement the clinical order in the diagnostic assessment.

Urban population growth, together with the industrial advances, leads to consider time as one of the most precious goods and therefore, an indicator of quality of life. Larger cities usually have mobility challenges due to inefficient or insufficient transport means or inadequate design of the road layout. Therefore, people may spend large portions of their daytime moving around places. It is precisely in this type of cities, where it is more complicated to find solutions that really solve the problem because it would be harder to change the already existing infrastructure. Two roads compositions, from the cities of Barcelona, Spain, and La Plata, Argentina, were selected to incorporate a fractal analysis in order to relate it with homogeneity. This was performed using a box counting methodology which determines the fractal dimension. As a complement, fractal lagunarity was calculated to get a value of the existing voids in the magnetic resonance images. The results show that the images have similar fractal dimension regarding the differences in road structure. However, the lagunarity is not the same, La Plata, Argentina, has a lower value than Barcelona, Spain, which indicates more coherence in the road structure.

The objective of this research was to analyze the characteristics of the bells and dynamic particularities of the bell tower of the cathedral of San José de Cúcuta, Norte de Santander, Colombia. The research had a mixed methodological approach, using a simplified numerical model of the structure. The spectrum of structural response is determined, analyzing according to the bells, magnitudes of the function of variable forces, with the time that they introduce on the structure with their own weight, speed of rotation and inertia; the most unfavorable dynamic amplification factor and response for quasi-static analysis for forces is determined. It is concluded that the bell of greater weight introduces greater efforts in the tower, being the location of the bell a direct incident factor.

The objective of this investigation was to determine the styles of reasoning according to the taxonomy structured of observed learning objectives of John Biggs in the students of geometry of the specialty of mathematics of the "Universidad Pedagógica Experimental Libertador", Venezuela. The stated problem is that teachers of mathematics must know the problems of teaching mathematics; besides, they should know how their students learn, since according to the reasoning styles of John Biggs, one can determine how and with what depth a person learns. The methodology is quantitative, not experimental, and descriptive at the field level, where specialized literature was reviewed, and the results obtained from the application of the test with the super-item, as a data collection instrument, were analyzed by objectives based on the construction of the database in statistical package for the social sciences, the statistical analysis and the detailed interpretation of the procedure performed for each item, which allowed the analysis and interpretation of the results. These results reach the uni-structural level catalogued by Biggs as inferior or superficial. Therefore, recommendations are offered to improve the learning level of the students in question.

In this article, we present some research results whose objective was to analyze the growth of Duranta plants, under the influence of sprinkling foliage and CO₃Cu concentrations. The methodology followed a quantitative approach, field-type experimental design, data are taken during 30 days of cultivation, length of root, dry weight, and stem diameter and height are measured. The results show an increase of dry weight, harmonic growth of the root related to the height of the plant. It is concluded that a solution of 140 g of CO₃Cu liter of latex-1 generates increase in dry weight of Duranta.

The objective of this study is to perform an analysis on the effect of the increase in temperature under the context of climate change on the dynamics of a population of ectothermic organisms, which are highly susceptible to these changes, as their body temperatures depend crucially on the environmental temperature. In our modelling approach, population abundance is governed by a logistic growth, where the intrinsic growth rate is affected by the change in temperature. The relationship between environmental temperature and the intrinsic rate of increase will be represented by a thermal performance curve type. In order to facilitate analytical simplicity but also novelty, a cubic expression is proposed to represent the thermal performance curve, the intensity of intraspecific competition is considered to remain constant and the tendency of temperature increase follows a linear expression. Finally, consequences on the trends of population abundance curves are assessed.

In this project, a descriptive research was carried out in order to analyze, evaluate and detail the behavior of buildings between 4 and 18 floors of residential use in the City of San José de Cúcuta, Colombia, at the moment they are subjected to forces produced by earthquakes. For this purpose, a sample of 40 buildings framed in the above-mentioned characteristics was used by means of the SAP 2000 software. The seismic analysis of each building was made and the displacements of these were obtained when they are submitted before an earthquake. With this information, it was possible to calculate the drifts and evaluate them based on the requirements that determine the stiffness conditions present in the buildings. Finally, a document was drawn up identifying those buildings that are susceptible to significant damage in the event of a seismic movement and recommendations, due to the fact that they represent a social risk.

The automobile is the main means of transportation in most cities of the world, however, its excessive use has generated several environmental and social problems, one of them is the lack of control over parking on public roads, affecting vehicle traffic, disturbing the image of the city, increasing the rate of accidents and causing negative effects on the mood of drivers and pedestrians. There are different alternatives to reduce these indicators, highlighting the effectiveness of the implementation of parking meter systems, which seek to regulate parking on public roads through a fee and a time limit. This article demonstrates the design, feasibility and impact (economic, social and environmental) of an implementation of the parking meter system in the center of the city of San José de Cúcuta, Colombia, with data from the Secretariat of Transit of the metropolitan area of the city of San José de Cúcuta, Colombia and the national institute of roads, achieving a solution to the problem of traffic congestion in the city and also contributing to create citizen culture among its inhabitants.

An experimental investigation was made in search of the improvement of the material used for the conformation of the subgrade in pavements. Three separate excavations were carried out 150 m apart in a 510 m stretch located in the Guayabal environmental technology park in the city of San José de Cúcuta, Colombia. In each excavation 2 samples were taken at depths of 0.50 m and 1 m. The soil samples extracted were analyzed in accordance with the regulations of the "Instituto Nacional de Vías" of Colombia in its update of 2013. It was collected material, not superior to 20 mm, of biosanitary residues treated by the Ecosterile machine series 250C located in the environmental technological park Guayabal. Five experimental mixtures were carried out partially substituting 2%, 6%, 8%, 10% and 14% of the weight of the excavated soil with treated biosanitary residues, random percentages taken as initial reference in the experimentation due to the characteristics of the substitute material. The California bearing ratio test was performed on experimental mixtures whose data were tabulated and compared with those obtained in similar tests carried out on the material conventionally used for the improvement of the subgrade in pavements according to Colombian regulations. The tests provided interesting information that concluded in the substitution of 2% of the conventional material to improve the performance of the subgrade in the intervened section, a value that obtained better results in the California bearing ratio test, yielding 79.2% with respect to the result obtained by the conventional material. The exposed results are convenient for the economy of road projects due to the partial substitution of traditional material by residual material, at the same time the use of a hospital waste is implemented as construction material, bringing with it positive environmental and social benefits as far as its final disposition.

This investigation analyzes the propagation of the uncertainty of the number of life cycles to fatigue failure, taking into account the strain life method, considering as random variables some parameters of the material and loading in a steel plate under fatigue, with constant and variable loading through multidimensional Hermite polynomials. The application of series of multidimensional Hermite polynomials allowed the prediction of the randomness of the output vector. This research has shown that a multidimensional Hermite polynomial adequately estimates the propagation of the uncertainty of the input random variables. The results showed that variations in material and loading parameters can generate important failure probabilities and allowed quantifying the variability in the number of life cycles for fatigue failure steel parts

The objective of the article is to evaluate emotional intelligence in the initial teacher training of the mathematics bachelor program at the "Universidad Francisco de Paula Santander", San José de Cúcuta, Colombia. The methodology is framed in the qualitative approach with some complementary aspects of the quantitative approach, the applied technique is the interview and the trait meta-mood scale instrument. The results describe that the impacts of integrating the emotive dimension in the learning strategies of mathematics is a greater resilience in the teachers in formation, since thanks to the contact with their emotions through introspection and reflection they manage to draw plans and alternatives that help them to devote more time, ask more and study better, especially in those aspects that cause them difficulty.

The objective of the research work, was to analyze the curriculum of the programs from "Universidad Francisco de Paula Santander" in San José de Cucuta, Colombia. The sample was participatory non-probability, with the participation of 200 students from Catatumbo and university student's, both from the different semesters and documents curriculums. A mixed study of sequential explanatory design was applied. In the first quantitative phase, the results were obtained by applying a digital questionnaire to the students. The data were analyzed using the observation guide for their respective analysis. The results of both phases were merged by the contrasting method. The conclusions demonstrate the importance of curriculum for training in research and innovation and critical thinking, curriculum for the creation, adaptation and/or use of communication and information technologies, curriculum for social inclusion in the university.

The research aimed to design a teaching strategy and analyze benefits of its implementation in the use of technologies like GeoGebra and interactive materials that offers the web as enabling tools and teaching as mediation is aimed at students in grade 11 middle education. Tests pre-test and post-test and two experimental groups were applied control. It was verified that the teaching strategy has a positive influence on learning the experimental group improved the level of understanding of the concept of derivative and thus academic performance, in contrast to the control group to which is applied the traditional methodology.

The objective of this research was to create a structural model able to explain the profile of student leaders during their youth stage, by implementing the pedagogical model form national university organization, in order to develop skills from a cognitive approach using an event-based learning trend. The research had a quantitative methodological approach, addressing differences in the students' cognitive abilities for oral expression and textual production, along with a correlational method of factorial design analysis, as a field type. The beneficiary population was made up of students from private educational institutions with an average age of 17 years. According to the model, it was found that among the factors associated with leadership are, the ability to lobby, strategies, critical reading, intensity of the debate, discourse analysis, quality of presentation, decision making, characteristics that determine the profile of a ruler.

Geometric thinking is a process in which competences are developed to understand three-dimensional space. The experience arises from the need to implement teaching methodologies that allow to optimize both the potential of teachable that has the geometry as the potential of learnability of the student with the purpose of deepening in the learnings so that, by means of the construction of models and the mathematical principle of reconstruction and invention of mathematics, emphasizing spatial thinking and leading the student to recognize geometric objects, geometric spaces and associated transformations to develop mathematical skills while strengthening their geometric thinking.

The present study is aimed at promoting the use of pedagogical guidelines to strengthen the practice of the teacher of mathematics, through the use of specific competences of the area, in this sense the present research focuses on what happened in the process of teaching mathematics from pedagogical approaches proposed by the "Ministerio de Educación Nacional", Colombia, as a result, it is proposed as a general objective to promote the use of pedagogical guidelines based on the Singapore model to enhance the teaching of mathematical skills, in order to be able to face the challenges of new educational spaces thought as transforming elements of the educational reality. On the other hand, this research is contextualized in the educational institutions "Lucio Pabón" in Ocaña and "Confanorte" in Los Patios, Norte de Santander, Colombia, to achieve such purposes, a qualitative ethnographic methodology was used, and field since it intends to interact with the object of study and its incidence in reality. For this, three teachers from the area of mathematics in each institution were selected, considered as key informants, since they will be in charge of supplying the diagnostic information and, from there, emphasizing the qualitative method using triangulation as the main method of analysis, from which emerged some categories that ensured the need to transform the praxis of the teacher, for this reason a proposal based on the Singapore method and on mathematical competences has been designed for the teachers of the indicated context.

A time series, also called a time series or chronological series, consists of a set of data, coming from realizations of a random variable that are observed successively in time. Its analysis involves the use of statistical methods to adjust models to explain their behavior and make reliable forecasts. In this article integrated autoregressive models of moving average are adjusted to the studied series, complemented with specific methods of fractal geometry as support for the detection of the existence of random cycles in the series. The present investigation implies the realization of simulations, in a first phase and, later, the analysis of temporal series of economic and social variables of the country and the region.

The study developed, and which is presented succinctly in this report, aimed to implement an intervention plan with the GeoGebra software tool for geometric reasoning in ninth grade students of the San José Educational Institution of the city of San José de Cúcuta. Methodologically, it is a quasi-experimental study of pretest and posttest with control group. The pretest showed flaws in Geometric Reasoning in the students, both in the control and experimental groups. These results led to the design and implementation of a Treatment Plan for the experimental group using the GeoGebra software tool. After applying the posttest, it was demonstrated, through its results, that the Plan was highly significant, since a high percentage of the students of the experimental group correctly answered the questions of the instrument on geometric reasoning.

Mathematics, in populations with Special Educational Needs, must be worked from the context of the students and with problems that they can show leading them to apply the concepts and solutions to everyday life. In this context, the present study is based on the objective of implementing pedagogical strategies based on the use of the Educaplay interactive platform for the learning of mathematics in populations with special educational needs in the "Carmen Teresiano" school in the city of San José de Cúcuta, Colombia. From the theoretical point of view, it is based on humanist theory and the cognitive paradigm; on the other hand, it is based on the manual of the teacher of children with special educational needs of the "Ministerio de Educación", Chile. Methodologically, it is a quasi-experimental study of pre- and post-test with only one group. The results of the pretest reflect deficiencies in the use of basic mathematical contents in the target population, which allowed for the design and implementation of an intervention plan and then to reapply, under the same conditions, the post-test. This resulted in an increase in the execution of the questions posed, which demonstrates the effectiveness of the intervention plan.

Attached to the differential calculus concepts, particularly the of limit and continuity usually difficult environment to its conceptual construction, since it is usually oriented to the domain of algebraic processes, restricting the understanding and thus limiting learning and appropriation of the same. This research was developed by students of the hotbed of research in mathematics education, aiming to promote the correct conceptual apprehension of the themes of the differential calculus, through the design and implementation of various didactic sequences, based on didactic engineering as research methodology. Sequences used different registers of semiotic representation such as graphical, algebraic, natural and tabular. The activities were implemented in students belonging to the "Facultad de Ingeniería, Universidad Francisco de Paula Santander", Colombia. Through the raised situation a better apprehension on the understanding of the infinitesimal of the meaning of the boundary (related to the continuity of this) and a better insight on the graphic understanding of limit and continuity, has strengthened since they had the opportunity to visualize the object of study in a direct way.

Current technological changes have allowed companies to make transformation of business accounting information regardless of distance, time or volume of data, therefore, this research aims to know the current relationship between accounting processes and the use of information and communication technologies in the industrial sector of the city of Ocaña, Colombia, through a quantitative methodological approach of cross-sectional descriptive type, using statistical software SPSS for processing and analysis of information from data obtained from the questionnaire type Likert applied to 83 micro small and medium sized enterprises in the industrial sector; where the results obtained show that local industrial companies face challenges, restrictions and paradigms against the use of information and communication technologies because they do not know many tools, programs and platforms that facilitate the systematization of data, bringing as a consequence the low speed of dissemination and processing, the lack of control of expenses and costs, the relevant errors before the delivery and substantiation of accounting reports and finally to the generation of barriers that prevent them from reducing the participation gap in the world of the information society.