Change points in the hazard function of survival models

In this work, a chronological presentation of the main results and applications of the different investigations that analyze the problem of the change point in the hazard function of survival models is made, these include the constant hazard function by parts and Cox-type regression models with change points.

Level of competence on the concept of basis of vector space using SOLO taxonomy

The purpose of this research paper is to determinate the level of competence on the concept of basis of a vector space on college level students who finished the Linear Algebra course, providing complementary information to the various studies from a different perspective through the SOLO taxonomy (Structure of the Observed Learning Outcome). An instrument was designed to address the concept of basis from different perspectives and difficulty degrees; it was applied through individual video-recorded interviews. Their answers were analyzed, and it was found that they average level 3 (multistructural) of the taxonomy: the students know the basis definition from an algorithmic or methodological perspective, and they can reproduce some procedures, but they are unable to understand the basis concept.

A virtual learning environment for a remedial differential calculus course

Information and communication technologies have led to the development of new learning modalities and techniques. This research is based on the design of a remedial course for the subject of Differential Calculus and its corresponding method of evaluation in a virtual learning environment, which allows the student practical and autonomous learning. Its elaboration consists of two parts: the instructional design associated with the learning topics identified as necessary for the learning of the Differential Calculus and the evaluation method for the achievement of the learnings. This course is expected to assist the student in the possible learning lags of the Differential Calculus to successfully complete the Integral Calculus learning unit.

Production optimization by using integer linear programming under a practical approach

This paper addresses the problem of production scheduling under a practical approach, which seeks to find out what would be the product mix to ensure the company to obtain the most useful, also requires that these combinations of products obtained from quickly and efficiently contributing thus to achieve lower costs associated with production. A specific mathematical model based on integer linear programming applied specifically to the product mix is presented, as well as the results obtained from the practical problem from the use of the model in integer linear programming, the use of the software and considering the own conditions of the problem addressed here.

Knowledge friction in universities, approach from game theory

In today's market economies, organizations see knowledge as one of their most valuable and strategic resources and seek to properly manage it so that it becomes a competitive advantage (Teece, 1988; Hamel and Prahalad, 1990, Drucker, 1994; Nonaka and Takeuchi, 1995; Boisot, 1998; Spender, 1996; Senge, 1990). Although many organizations make significant investments in technology and tools to promote knowledge sharing, cultural, behavioral, and structural aspects are the main determinants of success (Sharma and Bhattacharya, 2013). Organizational knowledge processes are, by their nature, generally social and complex. The behaviors related to sharing knowledge of organizational agents are full of situations of conflict of interest or dilemmas in which they receive different payments based on their strategic decisions. Such situations can be modeled as games. This article presents the approach to a particular dilemma, that of the knowledge friction in an Institution of Higher Education through Game Theory, describing a non-cooperative game model that allows showing the scope of said situation according to the decisions considered to be done by employees and employer and their related payments, exploring different decision-making scenarios.

Imitation as a social norm that influences the choice of career and labor participation of women

In Latin America, labor market indicators still show large gender gaps in access to opportunities and rights. These inequalities persist despite various policy efforts because they emanate from a social system that reproduces stereotypes and gender roles. This contradicts the development vision of the United Nations and the ILO: “Without gender equality, sustainable development is neither development nor sustainable”. This contribution focuses on the impact of social norms on women's decisions, regarding career choice and labor participation. To this end, we have built and simulated an agent-based model. The model assumes that gender roles are acquired and reproduced through the environment that surrounds women. The results of this social simulation suggest that the environment greatly influences the perception of women about the roles they must assume and the areas in which they must play, so it is pertinent to design policies aiming to change the conceptions of identity and traditional gender roles, since the construction and adoption of new and more equitable values is in part acquired through the imitation of the behavior observed in a woman's environment.

Learning the parabola through semiotic records in university students

Learning achieved by students in their first course of mathematics at the university reflects a low achievement, which is especially observed in the topic of the parabola. Due to this problem, the objective of improving the academic achievement of students in that topic, through a didactic strategy based on semiotic representations, was proposed. To this end, a quantitative inquiry was carried out, with a pre-test post-test design, on both a control group and an experimental group. There, a total of 44 students, of an average age of 19 years who were taking the subject of Mathematics Foundations, participated. It was found that the gain between the post-test and pre-test measurement was significantly higher (p<0.01) in the experimental group with respect to the control group, where the conventional strategy for the course was being used. It is concluded that it is possible to improve the learning of the parabola in students through the strategy based on semiotic representations, and that it is highly recommended to apply it for the learning of other mathematical objects in the basic sciences courses of the engineering division.

Fractal algorithm for the modeling of consumption in COVID-19

We present an analysis of the exogenous factors of consumption, we simulate it in a fractal algorithm whose objective is the Brownian equilibrium through the iterative multiplication of assumptions of an initial function at current prices whose values are constant and positive that will derive in the final solution that is characterized by non-negativity and does not denote absolute convergence, only relative to their economies of scale compared to iterative methods, we find other procedures derived from the stochastic method but formulated strictly as mathematical developments, they are fractal optimization algorithms, which are based on search of an objective function that minimizes the distance between the initial function and the expected iterations of the candidate functions to be a solution, verifying the corresponding restrictions.

Memetic algorithm used in a flow shop scheduling problem

Scheduling activities in flow shops involves generating a sequence in which the jobs must be processed. To generate the sequence, some criteria are taken into account, such as the completion time of all the jobs, delay time in delivery, idle time, cost of processing the jobs, work in process, among others. In this case, completion time of all jobs and idle time are taken as the objective function. To generate the sequence, a Memetic Algorithm (MA) is used that combines Simulated Annealing (SA) and Genetic Algorithms (GA) to solve the problem. A permutation type decoding was used for the vectors that make up the MA population. The SA was used for the generation of the initial population. Selection, recombination and mutation processes are generated in a similar way to GA. In this case there are 6 parameters to be set; temperature, z parameter, recombination probability, mutation probability, cycles and initial population. To set these parameters, the Response Surface Methodology is used for two objectives. Achieving improvements in the algorithm result of at least 2%. These results help to minimize processing times which impacts with the economics of the enterprise. Using the MA in an interface that helps the user to make a decisión about the Schedule of the Jobs.

Analytical proofs of expected value and variance of the main functions of continuous probability distributions, with examples of their applications

The present work proposes the design of mathematical problems, which allow the adequate understanding of mathematical concepts of probability for its correct interpretation and later application in the resolution of probabilistic problems. For the development of this work we rely on the theory of didactic situations of Brousseau (1997) and Sadovsky (2005). We believe that new materials and didactic models of this type have great educational potential because they encourage the analysis and understanding of various probability problems (Panizza, 2003). Accurate communication between teachers and students in the approach, interpretation, resolution, and testing of probability problems is of vital importance. The software used for this purpose is the MATHEMATICA program, a tool that facilitates the writing of formulas and calculations, as well as the construction of graphs, through a friendly interface, facilitating the self-taught work of the student and encouraging the development of analysis skills and problem solving. We believe that these materials will contribute to the teaching and learning processes of probability at higher education levels.