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Este artigo teve o intuito de responder o seguinte questionamento: quais materiais didáticos podem ter sido lidos em artigos da Revista de Ensino do estado do Rio Grande do Sul e utilizados para o ensino de frações entre os anos de 1930 e 1960? Como esses materiais foram apresentados e organizados? Para tanto, foram utilizados os pressupostos de uma pesquisa histórica que se debruçou acerca do periódico Revista do Ensino do Estado do Rio Grande do Sul. Observou-se artigos que tratavam da metodologia de ensino de fração com materiais didáticos. Ao fim da pesquisa identificou-se, nas mais diversas apresentações, o uso de elementos do cotidiano das crianças para a construção dos mesmos, tais como folhas de papel e madeira. São citados os jogos, quadro de frações, etc. Os materiais didáticos tinham o intuito de que o aluno descobrisse por si os conceitos envolvidos nesse conteúdo pela manipulação e/ou acompanhamento e direcionamento do professor em relação aos procedimentos propostos para trabalhar com as frações nas atividades. Palavras-chave: Operações aritméticas. Ensino primário. Periódico. História da educação matemática. The teaching of fractions through Revista do Ensino do Estado do Rio Grande do Sul: the use of didactic materials from the years of 1930 to 1960 Abstract In this article we had the intention of answering the following question: what didactic materials from the Revista de Ensino do Estado do Rio Grande do Sul magazine’s articles might have been used for the teaching of fractionsbetween the years of 1930 and 1960? How were they presented and organized? The presupposition of an historical research was used, leaning on the periodic Revista de Ensino do Estado do Rio Grande do Sul. The observed articles used the methodology of fraction teaching with didactic materials. Towards the end of the research, it was identified in many presentations, the use of the children’s everyday elements for the construction of these materials, such as sheets of paper and wood. Games, fractions board and etc were indicated. The didactic materials had the purpose of the student figuring out by him or herself the concepts involved on this subject by the manipulation and/or support and guidance from the teacher regarding the proposed procedures to work with fractions on the activities. Keywords: Arithmetic operations. Primary school. Periodic. History of mathematics education.

This article aims to analyze the evaluations made by the teachers of the participation of elementary school teachers in the research project entitled “Professional Development of Teachers who Teach Mathematics” (Project D-Estat), in the year of 2018. The Project aims to investigate the statistical learning experiences of teachers who teach mathematics in elementary school, within the scope of a collaborative group, aiming at professional development during the training process. The research uses qualitative methodology in an action research perspective. The paper presents theoretical reflections on professional development and teacher education, considerations on Teaching Sequence and Investigative Cycle. As a methodological resource, the narrative interview was used, in the format of a conversation circle. The analysis of the results gives evidence of a path taken by the teachers towards professional development and a better understanding of how to work the statistical thinking of their students. The teachers' oral and written narratives demonstrate the importance of participation in training processes for professional development.

In this article, our objective was to identify and analyze what and how the texts of the Mathematical Modeling discourse can be developed in the pedagogical practice and its implications in the formation of teachers. To this end, we selected scientific papers from the last three editions of two events in the country, the National Conference on Modeling in Mathematics Education and the International Research Seminar in Mathematics Education, which specifically bring together the entire community that researches on Mathematical Modeling. The research has a qualitative approach, inspired by Basil Bernstein's model of description language. From the analyzed texts, we observed that there are different possibilities to develop modeling activities and these different possibilities have different approaches: focus on content, focus on technology, focus on ethnomodelling, which allows the teacher to create different opportunities for learning students.

Considering the need for differentiated pedagogical practices enabling the association of student’s reality and other areas of knowledge, so that scientific/school concepts/content have greater meaning, this paper presents the approximation between methodologies Mathematical Modeling and STEAM. Such discussion is indispensable, because when researching the Catalog of Theses and Dissertations of the Coordination for the Improvement of Higher Education Personnel (CAPES), no studies involving both methodologies were identified. With this, research presents elements associating similarities in the stages/phases indicated by each methodology, which allow the student, mediated by the teacher, to develop mathematical and physical models to solve current problem situations. Based on the theoretical studies carried out, it is possible to consider that the two methodologies have similarities and can be inserted into the process of Mathemathics teaching and learning, allowing the student to be the protagonist in the construction of his knowledge, not only of mathematical concepts, but also in an interdisciplinary approach.

Given a list L(v) for each vertex v, we say that the graph G is L-colorable if there is a proper vertex coloring of G where each vertex v takes its color from L(v). The graph is uniquely k-list colorable if there is a list assignment L such that jL(v)j = k for every vertex v and the graph has exactly one L-coloring with these lists. In this paper, we characterize uniquely list colorability of the graph G = Kn2 + Om. We shall prove that if n = 2 then G is uniquely 3-list colorable if and only if m >= 9, if n = 3 and m >=1 then G is uniquely 3-list colorable, if n >=4 then G is uniquely k-list colorable with k =[m/2]+1, and if m>=n-1, entonce G es UnLC.

The goal of this paper is to show explicitly the construction of a Cartan-Eilenberg system for the twisted equivariant K-theory groups of a finite G-CW complex, with G a finite group. Such a system defines a spectral sequence, whose second page is given by the Cˇech cohomology of a presheaf associated to projective representations of isotropy groups.

In this paper, we present a characterization of the convergence on the n-th order Grassmannian that permits us to show in a direct way that this set is compact and every vector bundle is measurable. Finally, we obtain a criterion to induce measurable bundles.

In this paper, we present the results of an investigation of Arithmetic textbooks written in the late 19th and early 20th centuries containing the topic “decimal metric system”. Among the textbooks published in the State of Pará, Brazil, we highlight the work of Tito Cardoso de Oliveira: “Arithmetica Complementar para os cursos primário complementar, normal e commercial”. We present a description and an analysis of the decimal metric system topic present in the 8th edition of his textbook, which was probably published in the 1920s. The proposals metric system's teaching and learning have reflections on classroom practices. We verify that the determinations established by the legislation are partially followed by Oliveira. He presents the metric system clearly and objectively, includes several illustrations and contextualized arithmetic problems related to this topic. However, he does not include other principles of the intuitive method, propagated since the last decade of the nineteenth century in Brazil and prescribed by school legislation

The present research is derived from State of Art and it aims to highlight what is being produced in academic researches, in the form of dissertations and theses, from 2006 to 2016, regarding the teaching of the themes Origin of Life and Biological Evolution. the analysis was performed using pre-printed descriptors based on Megid Neto (1999) and Teixeira (2008). 78 articles were found, being 65 dissertations and 16 theses. Half of the papers are dissertations on teaching Biological Evolution, and only one thesis investigates the teaching of the Origin of Life. We found three issues that were not well investigated in the researches: Curriculum and Programs, Non-Formal Education and School Organization. These results, as well as the researches focused on the analysis of academic production, can contribute to the deployment of more specific proposals of teaching formation and improvements in the teaching-learning of this theme.

This paper sought to discuss the extent to which cultural issues allied with Mathematical Modeling can contribute and provide students with Meaningful Learning. Students from elementary schools in the countryside of Rio Grande do Sul participated in the research. Interventions were carried out in the school environment and classroom observations with the purpose of verifying the subsumers of the students, making a data survey and analyzing the school context. This survey made it possible to list three themes of interest to the students: Livestock, Fisheries and Agriculture. In this work we present an activity that addresses the topic of Fisheries as a basis for studying statistical concepts and analyze whether the learning of these concepts was significant. From the analysis of the results it was possible to infer that learning becomes significant when we insert cultural issues as a central theme, because these can underpin the learning of new concepts; strengthen and mean concepts already known.

This paper aims to analyze the evidence that constitutes the professional identity of future mathematics teachers when participating in a study group within the scope of the Supervised Curricular Internship. The qualitative research was carried out in 2019 at a public school in Formiga (MG), and included the participation of two students from a Mathematics Degree course and their Internship supervisors. The data discussed in this text were produced through written narratives of the interns, audio and video recordings of the meetings, evaluation and self-evaluation made by the undergraduate students. The formative experiences, experienced by the graduates in the internships and in the study group, contributed to the manifestation of aspects of the teacher identity, such as: emotion, self-knowledge, autonomy and political commitment. The results show the importance of formative contexts for the development of professional identity.

This paper presents the partial results of a Master's-degree-level research project on the contribution of employing the teaching-learning-assessment methodology through problem solving using GeoGebra, in connection with the different registers of representations, in teaching and learning the maxima and minima of functions. The educational product derived from this research was a didactic booklet, developed using the online GeoGebraBook tool, composed of several applications that seek to assist in the resolution of function optimization problems. Adopting a qualitative and interpretative approach, data were collected on the solutions of an activity tested in two pilot classes, one in high school and another in an undergraduate program. In the results, we will point out the potential regarding the use of technology that favored the resolution of the problem due to the interactive approach and the possibility of transition between different representations, as well as some challenges in certain stages of the adopted methodology.

Most important features of the earth structure can be studied through the analysis of Rayleigh wave dispersion. This consists on its filtering and inversion to obtain shear wave velocity distribution with depth. I have applied this analysis to show lithospheric structure of South Iberia, by means of a set of 2D images of shear velocity for depths ranging from 1.5 to 46 km. The data used to obtain Rayleigh wave dispersion are the traces of 44 earthquakes, occurred on the neighbouring of Iberia. These earthquakes have been registered at 3 WWSSN stations located on Iberia. These stations have been considered because period range of best registration for WWSSN seismograph is the more suitable to explore the elastic structure of the Earth, for the depth range which is the objective of this study. I have proceeded to group all seismic events in source zones to obtain a dispersion curve for each path source-station. Dispersion curves are obtained by digital filtering with a combination of MFT and TVF filtering techniques. Thus, a set of source-station averaged dispersion curves was obtained. This set of dispersion curves is inverted according to generalized inversion theory, to obtain shear wave velocity models for each source-station path. These models can be interpolated to obtain a 2D mapping of the elastic structure of South Iberia, by kriging method. This mapping reveals the principal structural features of South Iberia and surroundings zones. Such features, as the existence of lateral and vertical heterogeneity in the study area, also can be seen in Moho depth mapping presented in this paper. Finally, I want to remark that no shear velocity models have been obtained for intermediate depths (5 to 30 km), up to date, for the Iberian area. For this reason, this is the goal of the study presented in this paper.

This paper aims to reflect on the practice of Mathematical Modeling in the sociocritical perspective articulated to the model of investigative cooperation that deals with dialogical communication. It is part of a master's thesis whose theme for the development of modeling is water scarcity, a problem that emerged from the students' reality. The research is qualitative whose instruments used in the production of data were the researcher's logbook, students' textual production and recordings. Data were collected at a school located in Castelo, Espírito Santo, with students from the 8th grade of Elementary School. The results reveal that the Mathematical Modeling in the sociocratic perspective is par excellence, an environment that favors dialogical acts; in addition to bringing mathematical content closer to social problems, it promotes the collective investigation of perspectives through dialogue, favoring the teaching and learning process and the citizens' education of students.

Pese a la reconocida importancia sobre la explicitación del conocimiento dentro de la gestión del conocimiento, este proceso ha sido mayormente estudiado desde la perspectiva interna. Es decir, considerando únicamente a los trabajadores como actores de la explicitación, dejando de lado que con frecuencia las fuentes de conocimiento son actores externos. El objetivo de este trabajo es evaluar si existen diferencias significativas entre las empresas que hacen explicitación del conocimiento de forma interna, versus las que incluyen actores externos en este proceso. Para ello, se aplicó un modelo de red en el que los nodos representan actores internos y externos y los vínculos dirigidos dan cuenta de quién es la fuente del conocimiento y quién es quién es responsable de la explicitación del conocimiento. Se aplicó el modelo a 21 pequeñas empresas de servicios colombianas y con base en los resultados obtenidos se encontró que es posible clasificar a las empresas en cuatro categorías según su tendencia a mostrar más o menos explicitación interna, y más o menos explicitación abierta. Los resultados sugieren que existen perfiles de explicitación con mejor desempeño que otros. || Despite of the recognized importance on the explicitation of knowledge within knowledge management, this process has been mainly studied from the internal perspective. That is, considering only the workers as explicit actors, leaving aside that the sources of knowledge are often external actors. The objective of this paper is to evaluate if there are significant differences between companies that make knowledge explicit internally, versus those that include external actors in this process. For this, a network model was applied in which the nodes represent internal and external actors and the directed links give an account of who is the source of knowledge and who is who is responsible for the disclosure of knowledge. The model was applied to 21 small Colombian service companies and based on the results obtained it was found that it is possible to classify companies into four categories according to their tendency to show more or less internal explicitness, and more or less open explicitness. The results suggest that explicitation profiles exist with better performance than others.

This paper aims to recognize the research carried out on the theme Mathematical Modeling and Continuing Education and to understand from them the professional development (DP) of the participating teachers. For this, we used as a methodological approach qualitative research, of bibliographic type, based on the search for data in the Brazilian Digital Library of Theses and Dissertations. We found fourteen surveys, between 2010 and 2019 using the advanced search field and the title option, among which we selected eleven for analysis. The analysis procedures are based on thematic content analysis. From the unit of analysis professional development we present two categories in which we discuss that: 1) the research deals with continuing education with modeling from the perspective of the teachers DP and the spaces/time constituted for the training favor the DP and 2) the transition from continuing education to the classroom is a DP movement situated in the teaching profession.

SS (Strategic Scanning) is unique, partially subjective, inconsistent, interdisciplinary, vague and multidimensional process. Its description and optimisation suffers from IS (Information Shortage) and heterogeneity. IS eliminates straightforward application of traditional statistical methods. Heterogeneity problems are caused by heterogeneous nature of scanned information structures. Artificial Intelligence has developed some tools to solve such problems. Qualitative reasoning is one of them. It is based on the least information intensive quantifiers i.e. trends. There are four different trends i.e. qualitative values and their derivatives: plus/increasing; zero/constant; negative/decreasing; any value / any trend. The paper studies SS models based on ELEs (Equationless Heuristics). An example of ELE is – If novelity is increasing then confidence is decreasing. A solution of a qualitative model is represented by a set S of scenarios and a set T of time transitions among these scenarios. The key information input into an ELE model is subjective knowledge of experts. A consensus among SS experts is often not reached because of inconsistencies of experts’ knowledge. The SS case study is 12 dimensional (e.g. Freshness, Relevance) and based on 12 ELEs. There are 29 scenarios. || SS (Strategic Scanning) es un proceso único, parcialmente subjetivo, inconsistente, interdisciplinario, vago y multidimensional. Su descripción y optimización adolece de IS (escasez de información) y heterogeneidad. IS elimina la aplicación directa de los métodos estadísticos tradicionales. Los problemas de heterogeneidad son causados por la naturaleza heterogénea de las estructuras de información escaneadas. La Inteligencia Artificial ha desarrollado algunas herramientas para resolver tales problemas. El razonamiento cualitativo es uno de ellos. Se basa en los cuantificadores que requieren menos información, es decir, las tendencias. Hay cuatro tendencias diferentes, es decir, valores cualitativos y sus derivados: más / creciente; cero / constante; negativo / decreciente; cualquier valor / cualquier tendencia. El artículo estudia los modelos SS basados en ELE (heurística sin ecuaciones). Un ejemplo de ELE es: si la novedad aumenta, la confianza disminuye. La solución de un modelo cualitativo está representada por un conjunto S de escenarios y un conjunto T de transiciones de tiempo entre estos escenarios. La entrada de información clave en un modelo ELE es el conocimiento subjetivo de los expertos. A menudo no se llega a un consenso entre los expertos en SS debido a inconsistencias en el conocimiento de los expertos. El estudio de caso de SS es de 12 dimensiones (por ejemplo, Frescura, Relevancia) y se basa en 12 ELE. Hay 29 escenarios.

Los indicadores multivariantes de capacidad han sido muy utilizados en la industria manufacturera y en entornos similares en tanto que proporcionan medidas cuantitativas sobre el potencial y rendimiento de un proceso descrito por múltiples características de calidad susceptibles de evaluación y correlacionadas simultáneamente. En este artículo se presenta una evaluación empírica de múltiples enfoques de análisis de capacidad multivariante en el sector manufacturero cartagenero, a saber: uno basado en la relación del volumen la región de tolerancia y el volumen de la región del proceso, otro fundamentado en el análisis de componentes principales y adicionalmente, se propone la aplicación de otros indicadores que incluyen dentro su mecánica interna de análisis factorial la proporción de observaciones fuera de los márgenes de especificación y su variabilidad en el largo y corto plazo. Los resultados suministrados indican que el proceso productivo analizado no es marginalmente capaz para cumplir con las especificaciones técnicas predefinidas y que existe un vasto margen de mejoría. || Multivariable capacity index have been used frequently in the manufacturing industry and similar environments, since they provide quantitative measurements of the potential and performance of a process described by multiple quality characteristics susceptible to evaluation and correlated simultaneously. In this paper, we present an empirical evaluation of several approaches to analyze a multivariate industrial process. In the firs approach we study relationship of the volume of the tolerance region and the volume of the process region. In the second approach, we propose the application of principal components technique and, finally, we propose the application of other indicators that analyze the proportion of observations located outside the specification margins and their variability in the long and short term. The results provided indicate that analyzed production process is not marginally capable for satisfying predefined technical specifications and that there is a high margin of improvement.

In this paper, a theoretical relationship is obtained to measure the effect that inefficiency has on marginal costs, degree of economies of scale and technical change. It is shown that when the relationship between inefficiency and output level is ignored, the estimation of marginal costs and the degree of economies of scale are incorrect. The measurement of technical change is also wrongly calculated if one does not consider the variation of inefficiency over time. This could lead to incorrect pricing decisions that would transfer inefficiency to the consumer via prices and non-optimal investments in productive capacity. In addition, the effect of technical change on costs could be erroneously estimated. The empirical application of this theoretical model to Spanish port authorities during the period 2008-2016 shows that marginal costs of port services were overestimated, the degree of economies of scale was underestimated and the time variations of the inefficiency were interpreted erroneously as technical change when the relationship between inefficiency and output and time is not considered. || En este trabajo se obtiene una relación teórica para medir el efecto que la ineficiencia tiene sobre los costes marginales, el grado de economías de escala y el cambio técnico. Se muestra que cuando se ignora la relación entre la ineficiencia y el nivel de producción, las estimaciones de los costes marginales y del grado de economías de escala son incorrectas. La medición del cambio técnico también es errónea si no se considera la variación temporal de la ineficiencia. Esto podría llevar a que se tomen decisiones de fijación de los precios que transferirían la ineficiencia al consumidor vía precios y a que las decisiones de inversión en capacidad productiva no fuesen óptimas. Además, el efecto del cambio técnico sobre los costes se podría valorar erróneamente. La aplicación empírica de este modelo teórico a las autoridades portuarias españolas durante el periodo 2008-2016 muestra que los costes marginales de los servicios portuarios se sobreestimaron, el grado de economías de escala se infraestimó y las variaciones temporales de la ineficiencia se interpretaron erróneamente como cambio técnico cuando la relación entre la ineficiencia y los outputs y el tiempo no fue considerada.

Este trabajo prueba la existencia de contagio financiero entre los mercados de acciones de la región de América Latina y el mercado de acciones de Estados Unidos basado en el análisis del comportamiento de las correlaciones en periodos de estabilidad y crisis. El estudio emplea un modelo GARCH de correlaciones condicionales dinámicas multivariado para estimar las correlaciones cambiantes en el tiempo, y utiliza la prueba estadística-t bajo un procedimiento bootstrap para analizar los posibles canales de efectos de contagio financiero en los mercados de acciones emergentes. Los resultados muestran que las correlaciones estimadas se incrementaron en el periodo de la turbulencia financiera, como consecuencia de la presencia de cambios estructurales fuertes. Asimismo, el estudio proporciona evidencia de que los mercados de acciones de Brasil, Chile, Colombia, México y Perú son fuertemente contagiados durante la crisis financiera global. Sin embargo, el mercado de acciones de Argentina muestra evidencia de interdependencia con respecto al mercado de acciones de Estados Unidos. Los hallazgos tienen importantes implicaciones para los inversionistas y diseñadores de la política económica que buscan apropiados mecanismos para evitar los efectos negativos del contagio financiero en los mercados de acciones emergentes. || This paper tests the existence of financial contagion between US and Latin America stock markets based on the analysis of pattern of the correlation coefficients during crisis and stable periods. The study applies a dynamic conditional correlation multivariate GARCH model to estimate time-varying correlations and adopts the t-statistics test under a bootstrap procedure to examine the potential channels of financial contagion effects on emerging stock markets. The empirical results confirm that the estimated correlations has increased significantly in the period of financial turmoil as result of the presence of strong structural changes. Moreover, the study provides evidence that Brazil, Chile, Colombia Mexico and Peru stock markets are significantly affected by the contagion effects from the global financial crisis. However, Argentina stock market exhibits strong evidence of interdependence with the USA stock market. The findings have important implications for investors and policy makers, which seek preventive mechanisms to avoid negative effects of the financial contagion in emerging stock markets.

This paper aims to analyze the use of Mathematics grammar in teaching and learning situations. Such analysis is made on the basis of Wittgenstein's second language philosophy and some of his commentators. To do so, our theoretical text, we discuss the universality of mathematical language; the need to translate mathematical language into natural language; and the use of mathematical grammar and some of its developments. The mathematical grammar is the set of rules that determine the correct use of symbols and words of the mathematical vocabulary and it is in the application of these rules that the apprentice understands the meaning of the mathematical concepts.

In this paper, we establish a comparison between one of the most traded financial derivatives in the markets, the so-called catastrophe bonds (abbreviated as cat bonds) and the corporate bonds. In the first section, we start from a brief definition as well as some basic concepts. In section two, we will enumerate the type of investors to whom these products might interesting and how to price them. Afterwards, in section three we move onto the analysis of the trading rule proposed, that is, the comparison with Corporate bonds, our benchmark, in terms of expected returns. In sections four and five, we will point out some key issues on how the credit risk associated to these products can be reduced and, finally, in the last section, we will conclude with some discussions and remark the state-of-the-art research on this field. || En este artículo establecemos una comparación entre uno de los derivados financieros más negociados en los mercados, los llamados bonos catástrofe (abreviados como bonos CAT) y los bonos corporativos. En la primera sección comenzamos con una breve definición y algunos conceptos básicos. En la sección dos, enumeraremos el tipo de inversores para quienes estos productos pueden ser interesantes y cómo se podría fijar el precio. Posteriormente, en la sección tres, pasamos al análisis de la regla de negociación propuesta, es decir, la comparación con los bonos corporativos, nuestro punto de referencia, en términos de rentabilidad esperada. En las secciones cuatro y cinco señalaremos, respectivamente, algunas cuestiones clave sobre cómo se puede reducir el riesgo de crédito asociado a estos productos y, finalmente, en la última sección, concluiremos con algunas discusiones y comentaremos las investigaciones más recientes sobre este tema.

En Ecuador el crédito comercial actúa como fuente de financiación entre las pequeñas empresas, sin embargo, existe evidencia acerca del bajo acceso y uso de este tipo de crédito por parte de las pertenecientes al sector de manufacturas, además de que provoca un efecto positivo en la producción de las mismas. El presente trabajo revisa datos secundarios de fuentes oficiales analizando la evolución de la relación entre la producción, medida por sus ventas, y las cuentas por pagar a proveedores e instituciones financieras (2007-2017) de las pequeñas empresas manufactureras ecuatorianas. Se observó que existe una relación directa-positiva de los ingresos y el uso del crédito de proveedores. A través de una modelación econométrica que postula una extensión a la función de producción Cobb-Douglas de carácter modificada, se consideró como argumento adicional la variable “S” crédito de proveedores. Mediante entrevistas en profundidad a gerentes de pequeñas empresas, se exploraron los factores que determinan el uso de crédito de proveedores como alternativa de financiamiento. De esta manera se pudo caracterizar el crédito comercial acorde con la facilidad de obtención, orígenes, fidelidad, mecanismo de pago, que son aspectos que influyen en la decisión del volumen del crédito y el plazo a convenir para tal operación. Así mismo se pudo evidenciar las limitaciones que los empresarios tienen para el acceso hacia el crédito bancario. || In Ecuador the commercial credit acts as a financing source between the small companies, however, exists evidence about the low access and uses of this type of credit by firms belonged to manufacturing sector, furthermore it causes a positive effect on the production of them. In this paper, a review of secondary data from official sources was developed in which series of evolution data about the relationship between production, measured by sales, and accounts payable to suppliers and financial institutions were analyzed. (2007-2017) of the small Ecuadorian manufacturing companies, it was observed that there is a direct-positive relationship between income and the use of credit from suppliers. Through an econometric modeling that postulates an extension to the Cobb-Douglas production function of a modified nature, the variable "S" supplier credit was considered as an additional argument. Through in-depth interviews with managers of small companies, the factors that determine the use of credit from suppliers as an alternative to financing were explored. In this way, commercial credit could be characterized according to the ease of obtaining, origins, loyalty, payment mechanism, that they are aspects that influence in the decision of the volume of the credit and the term to agree for such operation; Likewise, it was possible to demonstrate the limitations that entrepreneurs have for access to bank credit, such as guarantees, high interest rates and non-competitive conditions.

In this paper, we describe a convenient categorical structure with respect to a class of monomorphisms M and epimorphisms E for any topological category. We show in particular that the structure that we introduce here, which is induced by topological functors and their initial liftings, allows the study of some M−coreflective subcategories of a topological category. We pay special attention to projective structures.

In this paper, we use the smoothing Jacobian strategy to propose a new algorithm for solving complementarity problems based on its reformulation as a nonsmooth system of equations. This algorithm can be seen as a generalization of the one proposed in [18]. We develop its global convergence theory and under certain assumptions, we demonstrate that the proposed algorithm converges locally and, q-superlinearly or q-quadratically to a solution of the problem. Some numerical experiments show a good performance of this algorithm.

The importance of good mastery of specialised mathematics knowledge for mathematics teachers and prospective teachers is now recognised internationally. This paper presents an exploratory study aimed at investigating how mathematics education courses affect the Mathematics Teachers’ Specialised Knowledge (MTSK) of prospective primary teachers. A questionnaire was administered to a sample of 118 future teachers, and an analysis of their answers was carried out with the MTSK model. The research highlights positive feedback on the effectiveness of the mathematics education laboratory that was staged, and provides an outline of the beliefs and the knowledge of the prospective teachers.

In this paper we present a research whose objective was to verify the effectiveness of the active methodology of Learning Based on Problems in the teaching of Probability in High School, with a view to developing the competences and abilities foreseen in the Common National Curricular Base. For that, we proceeded to a qualitative research through a case study, applying a didactic sequence to a class of 2nd year High School students from a public school in Maceió (AL). In order to verify the effectiveness of the didactic sequence and the development of competences and skills provided for in the National Common Curricular Base, we created analysis tools to identify the types of errors and skills and competences developed. The results demonstrated the need for teachers to know the PBL to use it in classes, in addition to understanding that its application differs in several aspects from application in Higher Education, with the need to adapt it Basic Education.

The Differential and Integral Calculus (DIC) course is taught in six of the nine undergraduate courses of the Federal Institute of Education, Science and Technology of the North of Minas Gerais (IFNMG), campus Januária and has a high failure rate compared to other subjects. This paper shows the results of a research which sought to find answers to the main difficulties faced by students and teachers of the DIC course, in relation to the teaching and learning process. In order to obtain the data, questionnaires were applied to the students of the course and to the teachers who teach or have already taught this course on the Campus, as well as monitoring for a group of students. The results show the reality of DIC teaching and learning at Campus Januária and opens the door for discussions about this issue that covers not only the IFNMG, but also other higher education institutions in Brazil.

This paper presents an analysis of a chapter of Luiz Roberto Dante's high school textbook “Mathematics: Context and Applications” on the content of functions, based on some assumptions of the Semiotic Representation Records Theory. The work chosen for the analysis is volume 1 of a collection approved by the National Textbook Program (PNLD 2018). For this, a qualitative study was carried out from Raymond Duval's Theory of Semiotic Representation Records, which aimed to identify and analyze the representation records that the book brings in the explanatory text of the chosen chapter and how it occurs the coordination between them. In the end, we conclude that the way the articulation between the representation records displayed in the book occurs favors the understanding of the mathematical object functions, since the various representation records are used simultaneously when approaching each part of the explanation.

Acoustic Emission (AE) is a proven successful Non-Destructive Testing (NDT) method to assess the state of storage tank floors. Traditional AE source location in tanks floors is performed using only the wavefronts that have traveled directly from the source to the sensor (direct hit). The wavefronts captured after reflected from the tank walls are identified and discarded. This paper proposes a new AE source location algorithm in tanks that considers a combination of reflections and direct hits. The proposed algorithm is based on time symmetry acoustics and ray theory. The methodology uses the concept of time symmetry acoustics in which a wave detected at any location can be directed back to the source when re-created at the detection place. Therefore, the developed approach takes the time at which each wave arrives to the sensor and sends it back as if time had reversed. Ray theory is used in the methodology to account for the way in which the wavefront is reflected when encounters an obstacle such as the walls of the tank. Then, the point of intersection of all wavefronts is identified using an optimization algorithm. This point where all wavefronts intersect is considered the location of the source. The location algorithm considers the first path or direct hits from the source to the sensors combined with reflections obtained by wavefronts bouncing from the tank walls. The proposed location algorithm was validated using numerical data from 176ft diameter tank and experimentally using AE data from a tank 55ft diameter.

This paper aims to analyze academic research that addresses the inclusion of deaf students and focuses on problem solving. For this, mapping in educational research was used as a methodological procedure. Searches were conducted in Qualis A1 to B2 journals, CAPES thesis and dissertations portal, Academic Google and Scielo, using the keywords 'inclusion of deaf people', inclusion and problem solving. 'and' problem situations'. After filtering the results were found six articles that were part of the corpus of analysis. The results showed that inclusion is not occurring effectively, because the teacher is not yet prepared to attend deaf students and, consequently, teaching Mathematics for these students. It is also worth noting the limited number of researches that deal with the inclusion of deaf people, focusing on problem solving.

In this paper, we report the experience gained in Teaching Internship, an academic discipline required for our doctoral training in progress, with the aim of highlighting the contributions of metacognitive strategies in initial Science teacher training in the early years. Considering the qualitative research approach, we analyzed the records in the field diaries of the students who attended Practicum II in the Education course to identify and discuss, in the light of Textual-Discursive Analysis (TDA), the results of the strategies used in the building and implementation of Natural Science lessons taught by students. The records reveal moments of reflection and self-knowledge, showing important notes about teacher training which has been adjusted to a scientific culture. At this, we realized that we need to promote spaces for discussion and collective knowledge construction necessary for Science education in the early years, allowing students to look at themselves in a process of self-knowledge by reframing their memories, beliefs and perceptions as a way to expand their knowledge for the scientific and socially committed teaching practice.

Este trabajo identifica factores explicativos de la supervivencia de flujos de comercio argentinos utilizando como método de identificación la combinación del método de Análisis de Árbol de Clasificación y Regresión (CART, con sus siglas en inglés) y econometría de corte transversal. Mientras que el primero determina los mejores predictores, el segundo ofrece una función global que vincula a la variable dependiente con aquellos. La combinación de estos métodos permite reducir el número de variables potencialmente explicativas en problemas en los que no existe consenso teórico, o salvar situaciones en las que existen relaciones no lineales, datos faltantes u observaciones anómalas. La aplicación al caso de estudio permite observar que existe una diferencia significativa entre flujos de exportaciones preexistentes y nuevos flujos, a pesar de que las variables explicativas de su duración resulten ser las mismas. || This paper identifies factors that explain the survival of Argentine trade flows using the combination of the Classification And Regression Tree analysis (CART) method and cross-section econometrics as the identification method. While the first determines the best predictors, the second offers a global function that links the dependent variable with those. The combination of these methods allows to reduce the number of potentially explanatory variables in problems in which there is no theoretical consensus, or to resolve situations in which there are non-linear relationships, missing data or anomalous observations. The application to the case study allows us to observe that there is a significant difference between pre-existing export flows and new flows, e

This article will focus on the research for the strategic allocation of reserve fund of the Moroccan pension scheme in order to ensure and improve its solvency. The first aim of this paper is to construct and test an Economic Scenario Generator (ESG) based on a model inspired of the Ahlgrim approach (2005) and adapted to the specificities of asset-liability management (ALM) and liability-driven investing (LDI). In our study, we will also develop the ALM technique based on the maximization of the reserve under the criterion of maximization of solvency ratio (since the fund is in deficit).To do this, we consider a recent strategic asset allocation approach based on the "constant weight" strategy, or Fixed-Mix, Kouwenberg (2001). Indeed, we will implement the LDI strategies based on the Sharpe and Tint model (1990). For that, we will first try to find the desired weightings of the asset classes in an asset context only. Afterwards, we try to build a hedge portfolio (LHP) and a performance research portfolio (PSP). || Este artículo se centrará en la investigación para la asignación estratégica del fondo de reserva del plan de pensiones marroquí para garantizar y mejorar su solvencia. El primer objetivo de este documento es construir y probar un generador de escenarios económicos (ESG) basado en un modelo inspirado en el enfoque Ahlgrim (2005) y adaptado a las especificidades de la gestión de activos y pasivos (ALM) y la inversión basada en pasivos (LDI) En nuestro estudio, también desarrollaremos la técnica ALM basada en la maximización de la reserva bajo el criterio de maximización de coeficiente de solvencia (ya que el fondo está en déficit). Para hacer esto, consideramos un enfoque de asignación estratégica de activos reciente basado en el "peso constante "estrategia, o Fixed-Mix, Kouwenberg (2001). De hecho, implementaremos las estrategias LDI basadas en el modelo de Sharpe y Tint (1990). Para eso, primero intentaremos encontrar las ponderaciones deseadas de las clases de activos solo en un contexto de activos. Luego, tratamos de construir una cartera de cobertura (LHP) y una cartera de investigación de rendimiento (PSP).

En este artículo se analiza la exportación de México hacia la Unión Europea y China para conocer las probabilidades, en el caso de que las políticas comerciales de los Estados Unidos de América (EE.UU.) obligaran a cambiar el rumbo de los productos mexicanos hacia esos mercados. El trabajo se inicia con una síntesis de las políticas económicas de México hasta llegar a los acuerdos en materia comercial que tiene suscritos, con énfasis en el Tratado de Libre Comercio con la Unión Europea (TLCUEM) así como también esbozando la dinámica comercial de bienes con China. Posteriormente se describe trimestralmente la exportación mexicana de bienes y sus principales destinos, para después analizar los valores de la exportación desde el año 2012 y hasta el 2015, verificando que los datos se ajusten a distribuciones gamma y normal, estimando probabilidades para distintos ensayos, que contemplan los promedios exportados, los máximos e inclusive importes aún mayores para conocer las posibilidades que tendría México para sustituir distintas cantidades que eventualmente no pudieran colocarse en el mercado estadounidense.|| This article analyses the Mexican exports to China and the European Union along with the effects of a possible shift of Mexican products to the above markets due to a change within the US-Mexico trade agreements. Beginning with a review of Mexican trade agreements with the European Union and China, the article describes the quarterly Mexican exports of goods and products and their primary destinations to these countries. Later, the paper analyses the exports of Mexican products from years 2012-2015 fitting their values to Gamma and Normal distributions. Probabilities for different scenarios, which include the average and maximum exports, are given in order to quantify the possibilities that Mexico has to replace the goods and products that can not be positioned in the American market.

En este trabajo se presenta un análisis de las implicaciones que tiene sobre los modelos de crecimiento estándar asumir una hipótesis alternativa al crecimiento exponencial de la población y cómo la forma de modelizar el tiempo puede alterar el comportamiento dinámico de estos modelos. Se estudia también una extensión (en tiempo continuo y en tiempo discreto) del modelo de crecimiento de Mankiw-Romer-Weil al apartarse del supuesto estándar de la tasa de crecimiento de la población constante. Más concretamente, se asume que esta tasa es decreciente en el tiempo y se introduce una ley general de crecimiento de la población que verifica esta característica. Con esta especificación, el modelo puede ser representado por un sistema dinámico de dimensión tres, que admite una única solución para cualquier condición inicial. Se muestra que existe un único equilibrio no trivial que es un atractor global. Además, se caracteriza a la velocidad de convergencia hacia el estado estacionario, mostrando que en este modelo la velocidad es inferior a la del modelo original de Mankiw-Romer-Weil. || This paper presents an analysis of the implications it has on standard growth models assume an alternative hypothesis to the exponential growth of the population and how modeling time can alter the dynamic behavior of these models. An extension (in continuous time and discrete time) of the Mankiw-Romer-Weil growth model is also studied by departing from the standard assumption of the constant population growth rate. More concretely, this rate is assumed to be decreasing over time and a general population growth law verifying this characteristic is introduced. In this setup, the model can be represented by a three dimensional dynamical system which admits a unique solution for any initial condition. It is shown that there is a unique nontrivial equilibrium which is a global attractor. In addition, the speed of convergence to the steady state is characterized, showing that in this framework this velocity is lower than in the original model.

Ante un hipotético, pero cada vez más real, caso de riesgo de impago de una hipoteca o ante una caída en los tipos de interés, un asunto importante que se plantea el prestatario es el de la posibilidad de minimizar ese riesgo mediante la selección de la mejor opción de refinanciación. En el presente trabajo se presenta un modelo de refinanciación de hipotecas desarrollando un método de programación puramente cuantitativa, con una simulación basada en un algoritmo creado especialmente para este caso y que puede ser útil para deudores hipotecarios. Así, se comienza explicando la base teórica sobre la que se asienta la investigación, para pasar a desarrollar el problema, continuando con su implantación. Finalmente, se analizan los resultados y se comentan las conclusiones más relevantes. || Facing an hypothetical, but increasingly, case of default risk on a mortgage or a fall in interest rates, an important issue raised by the borrower is the possibility of minimizing that risk by selecting the best refinancing option. In this paper, a mortgage refinancing model is presented, developing a purely quantitative programming method with a simulation based on an algorithm created especially for this case and that can be useful for mortgage debtors. Thus, we begin by explaining the theoretical basis on which the research is based, to proceed to develop the problem, continuing with its implementation. Finally, the results are analyzed and the most relevant conclusions are commented.

In this work, we present some numerical results about the problem of a rising hot solid sphere immersed in a Newtonian fluid which viscosity depends on the temperature. The model formulated to solve the problem considers two dimensionless parameters: The Peclet number, Pe and a parameter related with the viscosity, e. Small and large variations on e lead to interesting results segregated into two regimes which exhibit an asymptotic structure. To carry out the computations to solve the proposed model, the element finite method was used along with a non-slip boundary condition for the contact surface between the sphere and the fluid and the results obtained were compared to those shown recently in papers related wherein contact surface has a slip-boundary condition prescribed.

Explicit Finite Diferences Methods (FDM) are used for numerical simulations in seismic problems. In these cases the medium is heterogeneous and for the guarantee of a precise and stable solution there is the need to use refined discretizations for spatial and temporal variables, resulting in large- scale problems. In this paper we present the explicit FDM for the wave equation in a heterogeneous domain and show the results through computer simulations.

In this paper we study the effect of vaccination control, medical treatment and spraying to malaria epidemic model. Firstly the non-control malaria epidemic model is generated and the equilibrium point is determined. Afterward, the stability of equilibrium point in previous model is investigated. The research is continued by deciding the optimal control of malaria epidemic model and minimizing the cost. The results show that the control effect can reduce the subpopulation of infected human and mosquitoes.

Jean Piaget's theory has given many contributions to the teaching of several areas of knowledge over the last decades. The interactionist, critical, and progressive perspectives that have been commonly adopted have given the constructivist movement an interpretive potential capable of analyzing the didactic-pedagogical processes by overcoming individual concepts of common sense. Despite this, through our experience in our daily teaching activities, we hypothesize that it is not uncommon to understand the Piagetian theoretical contribution as a theoretical reference capable of dealing only with situations that eminently involve children and the beginning of adolescence. The textbooks that have the objective of disseminating Piagetian contributions mainly describe the concepts and analyzes that point to or are related to early childhood education, which hinders their introduction as a theoretical reference for investigations of situations that lead to High School and Higher Education. his paper makes an analysis of an empirical research done with students of a public university in Brazil that sought to confirm or refute our hypothesis. Finally, we suggest for initial teacher training or teacher training, materials that relate to research using this epistemology in order to extend it and make it accessible to the teacher in his daily work.

This paper, made in qualitative approach built from literature review and the audiovisual records retrieval from the research of a mathematics teacher in a unit specialized on deaf education in the city of Belem/PA, in 2008, aims to reflect on the recognition and acknowledgment importance of individuality and the need to find a new form of communication that allows an interaction for the socio-educational process from a situation in mathematics class involving deaf students and one deaf-blind student. The text consists on three parts that present reflections on mathematics education and the inclusion of excluded students from a minority group generally excluded by society itself, with the example of Ana, a deaf-blind student, in a deaf student class. The results on the reflections show that it is necessary to know about communication and to build an interaction, in order for the inclusion to happen in any social and educational environment, especially in mathematics classes.

Las escalas cualitativas formadas por términos lingüísticos son utilizadas por diversas disciplinas para determinar preferencias y diversos aspectos de la vida de los individuos. Aunque es habitual asignar números a las categorías de respuesta de estas escalas, no es adecuado utilizar codificaciones numéricas cuando los individuos perciben proximidades psicológicas distintas entre las categorías consecutivas de la escala, es decir, cuando las escalas cualitativas no son uniformes. En este trabajo se propone un procedimiento ordinal para jerarquizar un conjunto de alternativas a partir de las valoraciones mostradas por un grupo de individuos mediante una escala cualitativa no necesariamente uniforme. Dicho procedimiento está basado en las proximidades ordinales entre las categorías de respuesta de las escalas. El procedimiento propuesto se ilustra con un ejemplo tomado del Barómetro del Centro de Investigaciones Sociológicas (CIS) de mayo de 2011. || Qualitative scales formed by linguistic terms are used by different disciplines to determine preferences and different aspects of individuals’ lives. Although it is usual to assign numbers to the response categories of scales, it is not suitable when individuals perceive different proximities between the consecutive categories of the scale, that is, when scales are not uniform. In this paper, an ordinal procedure is proposed to order a set of alternatives from the assessments given by a group of individuals through a qualitative scale not necessarily uniform. This procedure is based on ordinal proximities between the response categories of scales. The proposed procedure is illustrated with an example taken from the Barometer of the Center for Sociological Research of May 2011.

A network is an acyclic directed graph in which there are sources that have some messages and want to transmit to receivers through the combination of messages in intermediate nodes. The goal is to find a collection of functions that allow to combine messages in order to satisfy the demand of the receivers. In this paper, we study the fractional solvability problem of a network using an extension of the solvability problem in closure operators given by Gadouleau in 2013. We define linear programming problems via the desired extension in order to study capacities; using some information inequalities and characteristic-dependent linear rank inequalities, we obtain upper bounds on linear capacity of some networks and closure operators over some fields.

The research paper presents a computational model by Cellular Automata (Cell-DEVS) applied to the transmission of Dengue disease, spread by mosquitoes to a susceptible population. This model will have a multilevel approach to consider exogenous interactions such as temperature. This will allow to be able to visualize the critical points where the mosquito reproduction is much greater, and thus carry out control strategies.

In this paper we introduce the generalized Helmholtz equation and present explicit solutions to this generalized Helmholtz equation, these solutions depend on three holomorphic functions. As an application we present explicit solutions to the Helmholtz equation. We note that these solutions are not necessarily limited to certain domains of the complex plane C.

In this paper, we determine list-chromatic number and characterize chromatically unique of the graph G = Kr2+k. We shall prove that ch(G) = r + 1 if 1

In this paper we obtain some upper bounds for the minimum of the Weber function on a strongly convex ball in a Riemannian manifold with positive sectional curvature; where the minimum is reached on the weighted geometric median of “m” given points in the strongly convex.

This paper describes a study of mathematical argumentation in primary school. The principal aim is to explore the nature of complex argumentation at a structural level. The context of the study was a teaching experiment involving nine tasks that promoted argumentation among fifth graders. We use the framework and method of reconstructing complex argumentation in the classroom proposed by Knipping (2008). The findings show that complex argumentation at a structural level in the context of refuting conclusions is characterized by a source-like structure with the addition of a new refutation argument element.

This paper presents a regression model for discrete time data with cure fraction. For this purpose, we considered a mixture model, in which times are modeled through the discrete Weibull distribution and the cure probability modeled with covariates by using the logit link function. Considering that the model is a mixture, the estimation of the parameters was performed by EM algorithm. The behavior of the estimating algorithm was tested with Monte Carlo simulation experiments and an application for real data was added.