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In this paper we propose an algebraic model for a modal epistemic logic. Although it is known the existence of algebraic models for modal logics, considering that there are so many different modal logics, so it is not usual to give an algebraic model for each such system. The basic epistemic logic used in the paper is bimodal and we can show that the epistemic algebra introduced in the paper is an adequate model for it.

The logic PM4N was introduced by Jean-Yves Beziau as a modal and 4-valued system. In this introductory paper, the author presented the system from a matrix logic with four values disposed in a Boolean algebra with a modal operator for the notion of necessity. From that matrix semantics, the paper shows some valid results and stresses some motivations of the matrix semantics and of the system PM4N. In this paper we develop some additional aspects of that logic and present two deductive systems for it, a simple system of tableaux and a sequent calculus.

This paper characterizes the use of qualitative data analysis software in doctoral theses about Mathematics Education developed in Brazil, from 2010 to 2019, to support the choices of these software from paths already followed by other researchers. For this, a mapping was made to identify the theses and the aspects related to the use of these software in the field. The investigation retrieved 651 doctoral theses available in the Brazilian Digital Library of Thesis and Dissertations in which only 31 of them compose the corpus of this paper. This number evidences the little use of these software in the analyzed area. In the corpus, it was observed the predominance of the qualitative approach and the identification of nine different software, being three the most used: Atlas.ti, NVivo and CHIC, in that order. The adoption of software, as described by the authors, is linked to their potential regarding categorization, organization, visualization, data handling, time optimization and analysis facilitation and the possibility of enabling exploration of large volumes and diversity of data.

El presente artículo interpreta teóricamente cómo la competencia real capitalista internacional presiona a que en las sociedades periféricas los balances comerciales dependan de ventajas absolutas de costo basadas en una sobreexplotación laboral-natural, lo que crea dinámicas cíclicas en dichas sociedades. Para reforzar tal interpretación, el artículo toma como caso de estudio al capitalismo periférico ecuatoriano, sobre el que se presentan tendencias histórico-cíclicas de mediano y largo plazo, ejemplos de actividades económicas que al parecer sustentan sus superávits comerciales desde la sobreexplotación laboral-natural, y evidencia estadística de tendencias cíclicas de corto plazo a nivel sectorial, estimando un modelo PVAR sobre un panel de datos compuesto por 43 actividades económicas observadas en el período 2007-2016. Todos los resultados empíricos muestran la importancia de las ventajas absolutas de costo basadas en la sobreexplotación sobre los balances comerciales y el surgimiento de ciclos que refuerzan la condición dependiente del capitalismo ecuatoriano. || This paper theoretically interprets how international real capitalist competition pressures trade balances of the peripheral countries to depend on absolute cost advantages based on the super-exploitation of labor power and nature; dependence which creates cyclical dynamics within those countries. To reinforce such an interpretation, the paper takes as a study case the Ecuadorian peripheral capitalism, about which some historical-cyclical trends are presented as well as some examples of economic activities that seem to obtain their trade surplus through super-exploitation. Also, the paper estimates a PVAR model over a panel data of 43 economic activities observed during the period 2007-2016; from that estimation, it is found evidence of short-run cyclical dynamics among Ecuadorian economic activities. All the empirical results evidence the importance of the absolute cost advantages gained through super-exploitation of labor power and nature on the determination of trade balances and on the rise of cycles that reinforce the dependent condition of Ecuadorian capitalism.

The generalized Kronecker graph product was introduced by Figueroa-Centeno et al. (2008). Later, Baca et al. (2018) used it for obtaining solutions of the n-queens problem on larger boards from solutions on smaller boards. In this paper, we generalize the graph product and the recent results by Baca et al. (2018), obtaining a larger class of solutions by knowing solutions on lower size boards in advance. We finalize the paper stating a couple of conjectures regarding conditions for obtaining composite solutions via graph product.

This paper aims to identify how historical information can contribute to teacher education regarding to the Golden Ratio content. Therefore, in the theoretical framework, the relevance of the teacher's investigative stance and the contributions that the use of the History of Mathematics provides for the training of this professional are discussed, as well as about some aspects of the Golden Ratio. For this purpose, an implementation was carried out that involved the use of the History of Mathematics, in order to work on the Golden Ratio content with 4th year students of the Mathematics Degree course at a public educational institution. In this paper, the focus was directed to the study of myths and truths concerning the Golden Ratio during the planning of the implementation, as well as to the discussions of the students later. The research is qualitative in nature, based on participant observation for data collection and mixed categorization, for analysis of what had been constituted. We concluded that the use of historical information about the Golden Ratio content led to critical manifestations, so that the research teachers and students in initial training had the opportunity to deconstruct certain beliefs impregnated and disseminated in history.

In this paper we address CLOSEST STRING problem that arises in web searching, coding theory and computational molecular biology. To solve it is to find a string that minimizes the maximum Hamming distance from a given set of strings. CLOSEST STRING is an NP-hard problem. This paper proposes two linear-time algorithms, one for the general case, a kernelization algorithm, and the other for three-strings, a linear-time algorithm called Minimization First Algorithm (MFA). A formal proof of the correctness and the computational complexity of the proposed algorithms are given.

In the present paper we study episodes of the life and work of the German-Danish mathematician Werner Fenchel from the perspective of the significance of the Second World War. On the one hand, we will see how the mathematical society, in particularly the mathematician Harald Bohr, helped Fenchel to set up an academic life in Copenhagen, Denmark. On the other hand, we will see how the organisation of scientists’ contribution to the war effort in the USA during the war, and the post war military financing of academic research in the post war period interfered with some of Fenchel’s mathematical work, especially his contribution to duality theory in nonlinear programming. As such, the study presented is this paper contributes to our understanding of how mathematics and conditions of a particular place and time interfere in the history of mathematics

The purpose of the present paper is to show how some current researches – published in papers and books – approach the difficulties in Mathematics learning. We intend to reflect on teaching and learning Mathematics by analysing some aspects that have been pointed out, especially about learning difficulties some students have in Mathematics area. We used the research qualitative approach with procedures of document analysis. At first, we described the meaning of the word ‘difficulty’, passing through learning difficulties and learning difficulties in Mathematics. The latest researches point the urgent need of a didactic overhaul in Mathematics teaching and maturation of all school communitiy, regardless the teaching level, concerning learning difficulties.

In this paper, we explore the interconnection and existing relationships between the Sovereign Credit Default Swaps (henceforth, CDS) and the stock markets of the main European countries. Thus, the goal of this paper is to test if the CDS premia can predict the stock market returns of the most relevant economies within the Eurozone, so that, they serve as advanced indicators like mechanisms of price transmission. For this purpose, we apply the Granger Causality test to analyze ten main European stock markets from 2004 to 2016 by using daily data. Our hypothesis is proved to work for the largest economies with liquid CDS markets, whereas the transmission mechanism between CDS and stock prices is not so evident for the smallest ones. || En este documento, exploramos la interconexión y las relaciones existentes entre los Soberanos Credit Default Swaps (en adelante, CDS) y los mercados bursátiles de los principales países europeos. Por lo tanto, el objetivo de este documento es comprobar si las primas de CDS pueden predecir los rendimientos del mercado de valores de las economías más relevantes dentro de la zona euro, de modo que sirvan como indicadores avanzados como los mecanismos de transmisión de precios. Para este propósito, aplicamos la prueba de Causalidad de Granger para analizar los diez principales mercados bursátiles europeos desde 2004 a 2016 mediante el uso de datos diarios. Se ha demostrado que nuestra hipótesis funciona para las economías más grandes con mercados de CDS líquidos, mientras que el mecanismo de transmisión entre los CDS y los precios de las acciones no es tan evidente para los más pequeños.

A problem of practical interest is the determination of the reachability sets of ordinary differential equations with an external perturbation, or with a control. This problem can be extended to non-Newtonian spaces generated by continuous and injective functions α. This paper presents the problem of determining the reachability tube of a family of non-Newtonian first-order linear differential equations with an external perturbation, or with a control, that belongs to a set of functions that are α-continuous and α-bounded. The reachability tube is determined explicitly in three non-Newtonian spaces that are associated with three α-generators. The results obtained are illustrated numerically.

For over twenty years, Frege tried to find the foundations of arithmetic through logic, and by doing this, he attempted to establish the truth and certainty of the knowledge. However, when he believed his work wasdone, Bertrand Russell sent him a letter pointing out a paradox, known as Russell‟s paradox. It is often considered that Russell identified the paradox in Frege‟s theories. However, as shown in this paper, Russell, Frege and also George Cantor contributedsignificantly to the identification of the paradox. In 1902, Russell encouraged Frege to reconsider a portion of his work based in a paradox built from Cantor‟s theories. Previously, in 1885, Cantor had warned Frege about taking extensions of concepts in the construction of his system. With these considerations, Frege managed to identify the precise law and definitions that allowed the generation of the paradox in his system. The objective of this paper is to present a historical reconstruction of the paradox in Frege‟s publications and discuss it considering the correspondences exchanged between him and Russell. We shall take special attention to the role played by each of these mathematicians in the identification of the paradox and its developments. We also will show how Frege anticipated the solutions and new theories that would arise when dealing with logico-mathematical paradoxes, including but not limited to Russell‟s paradox.

In this paper we discuss the professional activity of Leopoldo Nachbin (1922-1993) in the period in which he worked at National Faculty of Philosophy of the University of Brazil (FNFi/UB, in Portuguese) until his retirement by Institute of Mathematics of the Federal University of Rio de Janeiro (IM/UFRJ, in Portuguese). We identify the influence played by some mathematicians such as G. Mammana (1893-1980), L. Schwartz (1915-2002), A. Monteiro (1907-1980), A. Weil (1906-1998), J. Dieudonné (1906-1992), M. Stone (1903-1989), and A. A. Albert (1905-1972) in the professional training of L. Nachbin. We also address the serious difficulties he encountered in the Mathematics Department of FNFi when he was entered in the competition, opened in 1950, for the post of full Professor (Professor Catedrático) of Mathematics and Superior Analysis of FNFi. We emphasize in the paper, that the period from 1947 to the 1960s marks the most creative and productive phase in terms of scientific research in the academic life of L. Nachbin.

In this paper, we consider a method of constructing isothermic surfaces in S3 based on Ribaucour transformations. By applying the theory to the flat torus, we obtain two family of complete isothermic surfaces in S3. One four-parameter family of complete isothermic surfaces that contains n-bubble surfaces inside and outside of the torus. We also get another four-parameter of complete isothermic surfaces which are Dupin surfaces. As aplication we obtain explicit solutions of the Calapso equation.

In this paper, we provide a class of surfaces called ϵ-isothermic surface in the pseudo-Euclidean 3-space and we introduce the pseudo-Calapso equation. We prove that for each ϵ-isothermic surface, we can associate two solutions to the pseudo-Calapso equation. In particular, we associate solutions to the Calapso, Zoomeron and Davey-Stewartson III equations. In sequence, we classify the Dupin surfaces in pseudo-Euclidean 3-space having distinct principal curvatures and provide explicit coordinates for such surfaces. As application of the theory, we obtain explicit solutions to the pseudo-Calapso equation and from these solutions, we provide new explicit solutions of the Zoomeron and Davey-Stewartson III equations. Moreover, we also provide explicit solutions to these equations that depend on ϵ2−holomorphic functions.

El objetivo de este trabajo es contrastar el efecto de contagio en el fracaso empresarial como consecuencia de la proximidad geográfica entre empresas del mismo sector. Para ello, desarrollamos una aplicación empírica basada en el análisis de los estadísticos espaciales join-count sobre una muestra de empresas del sector servicios en el municipio de Murcia (España). Los resultados muestran un patrón de autocorrelación espacial significativo, de tal forma que la probabilidad de fracaso de una empresa no solo depende de sus características internas sino también de su proximidad a otras empresas fracasadas. Estos resultados pueden ser un interesante punto de partida para el desarrollo de análisis que incluyan los efectos de la proximidad geográfica entre empresas en la literatura de fracaso empresarial. || This paper aims to contrast the spillover effects in business failure derived from the geographic proximity among firms of the same sector. To get this purpose, we develop an empirical application based on the analysis of the join-count statistics on a sample of firms of service sector located in the municipality of Murcia (Spain). Our results show significant spatial autocorrelation pattern, therefore, the probability of failure in a firm not only depends on its internal characteristics, but also on the situation of failure of its vicinity peer companies. These results can be an interesting starting point in the development of papers which consider the interdependence effects among closer peer companies in business failure literature.

La normativa contable internacional ofrece con la Norma Internacional de Contabilidad 40 (NIC 40) "Inversiones inmobiliarias" un caso referente para investigar la decisión que toman las empresas cuando se les ofrece el valor razonable o el coste histórico como criterios alternativos de valoración. En este trabajo aprovechamos la oportunidad que ofrece esta norma para aportar evidencia adicional en un contexto multinacional y multisectorial sobre cuáles son los motivos que explican la elección contable. Además, en este trabajo introducimos y comparamos el uso de las redes neuronales artificiales y los árboles de decisión, con el objetivo de evaluar la capacidad predictiva de estas metodologías, frente a la tradicionalmente utilizada regresión logística para la resolución de problemas de clasificación en este área. Los resultados de la clasificación indican que tanto las redes neuronales como los árboles de decisión pueden ser una alternativa interesante a los métodos clásicos estadísticos como la regresión logística. En particular, las dos metodologías mostraron una mayor capacidad predictiva frente a la regresión logística aunque no se encontraron diferencias significativas entre ambas. || International Accounting Standard 40 (IAS 40 - Investment properties) offers an ideal setting for research on accounting choice as it represents a paradigmatic case choosing between the fair value and the historical cost as the measurement criteria. In this paper, we take the opportunity of this standard to provide additional evidence in a multinational and multi-context on the determinants that explain the accounting choice. Furthermore, in this paper, we introduce and compare the use of artificial neural networks and decision trees in order to assess the predictive capability of these methodologies, compared to other techniques commonly used to solve classification problems in this area such as the logistic regression. The classification results indicate that both neural networks and decision trees can be an interesting alternative to classical statistical methods such as the logistic regression. In particular, both methods outperformed the logistic regression in terms of predictive ability, although no significant differences were found between both.

Following the recent work of Gómez-Déniz and Pérez-Rodríguez (2014), this paper extends the results obtained there to the normal-exponential distribution with dependence. Accordingly, the main aim of the present paper is to enhance stochastic production frontier and stochastic cost frontier modelling by proposing a bivariate distribution for dependent errors which allows us to nest the classical models. Closed-form expressions for the error term and technical efficiency are provided. An illustration using real data from the econometric literature is provided to show the applicability of the model proposed. || Continuando el reciente trabajo de Gómez-Déniz y Pérez-Rodríguez (2014), el presente artículo extiende los resultados obtenidos a la distribución normal-exponencial con dependencia. En consecuencia, el principal propósito de este artículo es mejorar el modelado de la frontera estocástica tanto de producción como de coste proponiendo para ello una distribución bivariante para errores dependientes que nos permitan encajar los modelos clásicos. Se obtienen las expresiones en forma cerrada para el término de error y la eficiencia técnica. Se ilustra la aplicabilidad del modelo propouesto usando datos reales existentes en la literatura econométrica.

This paper introduces a filtering strategy for addressing optimization problems arising in binary Support Vector Machine classification. The training optimization problem aims to solve the dual formulation which involves a quadratic objective function subjected to a linear and box constraints. Our approach employs a Filter algorithm with Sequential Quadratic Programming iterations that minimize the quadratic Lagrangian approximations. Notably, we utilize the exact Hessian matrix in our numerical experiments to seek the desired classification function. Moreover, we present a Filter algorithm combined with the Augmented Lagrangian method aiming to accelerate the algorithm convergence. To substantiate our method's effectiveness, we conduct numerical experiments through MATLAB, comparing outcomes with alternative methodologies detailed in existing literature. Numerical experiments shows that the Filter--SQP combined with Augmented Lagrangian method is competitive and efficient method compared with an interior-point based solver and LIBSVM software in relation of classification metrics and CPU-time.

This paper gives a survey over the existence of uniform L∞ a priori bounds for positive solutions of subcritical elliptic equations (P)p -\Delta_p u =f(u), in \Omega, u = 0, on \partial\Omega widening the known ranges of subcritical nonlinearities for which positive solutions are a-priori bounded. Our arguments rely on the moving planes method, a Pohozaev identity, W1,q regularity for q > N, and Morrey’s Theorem. In this part I, when p = 2, we show that there exists a-priori bounds for classical, positive solutions of (P)2 with f(u) = u2∗−1/[ln(e + u)]α, with 2∗ = 2N/(N − 2), and α > 2/(N − 2). Appealing to the Kelvin transform, we cover non-convex domains. In a forthcoming paper containing part II, we extend our results for Hamiltonian elliptic systems (see [22]), and for the p-Laplacian (see [10]). We also study the asymptotic behavior of radially symmetric solutions uα = uα(r) of (P)2 as α → 0 (see [24]).

El artículo tiene por objetivo determinar las variables que pueden condicionar la decisión observable de un individuo con respecto a escuchar música grabada en Colombia. Para ello, se estiman modelos probit usando microdatos de la Encuesta de Consumo Cultural 2008. Los resultados muestran que individuos con educación superior, que toman cursos y talleres culturales y se sitúan en los niveles medios y altos de estrato socio-económico presentan la mayor probabilidad de escuchar música grabada. Igualmente, se encuentra que individuos que se auto-reconocen como afro-descendientes se asocian con una menor probabilidad de escuchar música grabada. El artículo contribuye a la escasa literatura empírica sobre los determinantes de la participación cultural en países de América Latina. || This paper purpose is to determine the variables that could influence the individual observable decision of listening to recorded music in Colombia. To do so, probit models are estimated using micro-data from the Encuesta de Consumo Cultural 2008 [Cultural Consumption Survey 2008 ]. Empirical results show that individuals with higher education that take cultural courses and workshops, and belong to medium and high socio-economic strata, are those with the highest probability of listening to recorded music. Additionally, self-identied individuals as African-Colombian-descendent present the lowest likelihood. This paper contributes to the scarce empirical literature on the determinants of cultural participation in Latin America.

This paper describes an emerging approach to the design of task sequences and the theory that undergirds it. The approach aims at promoting particular mathematical concepts, understood as the result of reflective abstraction. Central to this approach is the identification of available student activities from which students can abstract the intended ideas. The approach differs from approaches in which learning to solve the problem posed is the intended learning. The paper illustrates the approach through data from a teaching experiment on division of fractions.

In this paper we first explore how Wittgenstein’s philosophy provides a conceptual tools to discuss the possibility of the simultaneous existence of culturally different mathematical practices. We will argue that Wittgenstein’s later work will be a fruitful framework to serve as a philosophical background to investigate ethnomathematics (Wittgenstein 1973). We will give an overview of Wittgenstein’s later work which is referred to by many researchers in the field of ethnomathematics. The central philosophical investigation concerns Wittgenstein’s shift to abandoning the essentialist concept of language and therefore denying the existence of a universal language. Languages—or ‘language games’ as Wittgenstein calls them—are immersed in a form of life, in a cultural or social formation and are embedded in the totality of communal activities. This gives rise to the idea of rationality as an invention or as a construct that emerges in specific local contexts. In the second part of the paper we introduce, analyse and compare the mathematical aspects of two activities known as string figure-making and sand drawing, to illustrate Wittgenstein’s ideas. Based on an ethnomathematical comparative analysis, we will argue that there is evidence of invariant and distinguishing features of a mathematical rationality, as expressed in both string figure-making and sand drawing practices, from one society to another. Finally, we suggest that a philosophical-anthropological approach to mathematical practices may allow us to better understand the interrelations between mathematics and cultures. Philosophical investigations may help the reflection on the possibility of culturally determined ethnomathematics, while an anthropological approach, using ethnographical methods, may afford new materials for the analysis of ethnomathematics and its links to the cultural context. This combined approach will help us to better characterize mathematical practices in both sociological and epistemological terms.

There are bottom-up movements imbued with different praxis into mathematics education, which promotes the combination of heterogeneous values – inserted in social participation, cultural diversity, and reconnection with the Pachamama. Such movements have been developed by collectives of thinkers constituted by members with the most diverse knowledge. Embedded in a counter-colonization resistance by a persistence of the horizontality into the educational process, this paper aims to dialogue around sociocultural-ecological connections experienced in processes of critical ethnography developed in community mathematics education of ascending movements in Brazil and Portugal. The aim is to promote a path in which an old necessity to share the human topological ontology constructed and reconstructed in five different ethnographic fields, in which both the humanscapes and the equal liberty, sea-ing in indissociable lines, evidenced the oppression of schooling mathematics knowledge over the sociocultural-ecological human relations. Such sea-ing motion is proposed as an alternative path to demystify, re-signify, or only complement, the how human being perceives itself in its surroundings and brings for the most diverse mathematics education processes – formal_informal_non-formal, the importance of the situationality of the apprentice as well as the relevance of the intellectual justice towards equitable societies.

This paper is part of a wider study focused on divisibility. Participants were prospective elementary teachers. One of the aims of the research is to characterize the meanings of multiple shown by prospective teachers. In this paper, we present the results concerning this aim. We analyse the productions of 37 prospective elementary teachers collected in a practice session, designed and developed in the context of a teaching experiment. We characterize the meanings through the following elements of the didactic analysis: conceptual structure, representation systems and phenomenology. Prospective teachers showed mostly three meanings of multiple: product, relationship and dividend in an exact division.

This paper presents the results of a survey conducted in a public university in the country, which aimed to identify the presence elements ordinarily related to subjective phenomena, in the works published in National Symposium of Physics Education, an event that provides meeting between teachers, researchers and students from around the country. The elements to which we have referred are found in contemporary didactic and pedagogical proposals, because it is identified that purely cognitive or even cultural rights are not sufficient to understand the phenomena that happen in the classroom, or more broadly, in education as a whole. The analysis contemplated the publications of the past 3 symposia, and the results infer a small increase of citations of these elements. However, this growth must be questioned because the quotes are made in isolation, not being taken to support the analysis of the authors. In addition, this research also shows that the presence of these elements is very small compared with the total number of papers published in the events.

Marketing effectiveness has been accepted as one of the most important parts in corporate performance system. It is due to dynamical changes in business environment in after-crisis times. The goal of this paper is the definition of used possible indicators in measuring marketing effectiveness. The paper presents advance in usable indicators, especially financial and non-financial metrics. Selected studies, focusing on different branches and different indicators, were analysed by the author. The author of article puts the question, which classification is the most statistical explaining the difference of stake- holders in term of evaluation their impact on business management. There were made cluster analysis for data mining including its graphic presentation through dendogram and two-sample t-test by statistical software IBM SPSS Statistics 22 to obtain relevant answer on defined research question. Such limitation of the paper is possible to signify focusing only on domestic (Czech) industrial market. || La eficacia de la comercialización se ha aceptado como una de las partes m ́as importantes del sistema del funcionamiento corporativo. Es debido a los cambios dinámicos en el ambiente de negocio en tiempos después de la crisis. El objetivo de este artículo es la definición de indicadores posibles usados en la medición de eficacia del marketing. El artículo presenta avance en indicadores usables, especialmente métricas financieras y no financieras. Los estudios seleccionados, centrándose en diversas ramas y diversos indicadores, fueron analizados por el autor. El autor del artículo pone la pregunta: ¿cuál es la clasificación más estadística que explica la diferencia de las partes interesadas en función de la evaluación de su impacto en gestión empresarial? Se realizaron análisis clúster para minería de datos, incluyendo su representación gráfica a través de dendograma y t-test para dos muestras usando el software estadístico IBM SPSS Statistics 22 para obtener respuesta pertinente a la pregunta definida en la investigación. Tal limitación del artículo es posible significar centrarse solamente en el mercado industrial doméstico (checo).

Este texto apresenta o contexto de problematização do Curso de Pedagogia do Programa de Formação de Professores para Educação Básica do Plano de Ações Articulada- PARFOR, da Universidade Federal do Maranhão - Campus de Imperatriz, com a inserção de alunos indígenas nas suas demandas de matrículas. Na problematização feita, professores e alunos do curso situam e discutem o atendimento às peculiaridades que os índios requerem em seus processos formativos. Tivemos como objetivo neste trabalho apresentar a sistemática de ações que o curso tomou, em busca de garantir uma aprendizagem signifi cativa a esses alunos. Partimos de um mapeamento feito com os alunos e de grupo de estudos realizados pelos professores, no ano de 2013. Como resultados, apresentamos falas dos alunos, que destacam as difi culdades e contribuições do curso, e falas dos professores refl etindo sobre a proposta curricular do curso e de suas metodologias. Palavras-chave: Formação de professores. Alunos. Indígenas. Abstract This paper presents the context of questioning the School of Education Program Teacher Training for Basic Education Action Plan articulated-PARFOR, Federal University of Maranhão - Campus Empress, with the inclusion of indigenous students in their enrollment demands. In questioning made, teachers and students of the course lie and discuss the compliance with peculiarities that require the Indians in their formative processes. Our objective in this paper provide a systematic course of actions taken in pursuit of ensuring meaningful learning for these students. We start from a mapping done with students and group studies conducted by teachers in 2013. As results we present students ‘ speech when contributions and highlight the diffi culties of the course, and speeches from teachers when they reflect about the course curriculum proposal and methodologies. Keywords: Teacher education. Students. Indigenous.

Este artigo apresenta um relado de tutoria no PET Conexões de Saberes de Imperatriz-MA e uma pesquisa realizada na Universidade Federal do Maranhão, no Centro de Ciências Sociais, Saúde e Tecnologia (CCSST) em Imperatriz, numa proposta de discutir as dificuldades vivenciadas pelos estudantes de graduação relacionadas à elaboração dos trabalhos de conclusão de curso, intitulados TCCs. A pesquisa bibliográfica foi baseada na utilização de aportes teóricos de autores que tratam da temática da metodologia voltada à pesquisa, tais como Pedro Demo, Antonio Chizzotti, Maria Cecília de Souza Minayo, Maria Cecília Maringoni de Carvalho. A perspectiva que adotamos foi, a partir de uma situação concreta, levar o estudante a refletir, estudar e apresentar soluções para um fato concreto. Foram relacionados os aspectos problemáticos comuns à realidade brasileira com a experiência de estudantes de graduação na realidade específica da Universidade Federal do Maranhão. A pergunta de pesquisa é: como levar o estudante a refletir sobre o fazer acadêmico de forma autônoma? Partimos da dificuldade em elaborar projetos de pesquisa e TCCs: que fatores os estudantes apontam como os que representam dificuldades importantes para a realização do projeto para o TCC e a pesquisa propriamente dita? Afinal, que dificuldades existem nesse processo de elaboração do trabalho de conclusão de curso? E a hipótese que demonstramos é de que as condições institucionais combinadas a outros fatores, com destaque para a orientação, perfazem os mais importantes que representaram as principais dificuldades dos estudantes. Palavras-chave: Tutoria. Metodologia. Trabalho de conclusão de curso. Abstract This paper presents the report of a research conducted at Universidade Federal do Maranhão, in the Center of Social Sciences, Technology and Health (CCSST) in Imperatriz, Maranhão, in a proposal to discuss the diffi culties experienced by undergraduated students in terms of producing fi nal papers called TCCs. The literature research was based on theoretical contribuitions of authors on the metodological subject related to research such as Pedro Demo, Antonio Chizzotti, Maria Cecília de Souza Minayo e Maria Cecília Maringoni de Carvalho. The perspective adopted from a real situation lead the student to think, study and fi nd a solution to a real fact. The troublesome aspects comom to the brazilian reality were related with the experience of undergraduated students in a specifi c reality of the University of Maranhão. The question is: which factors students point as the most important diffi culties to make a resarch or a project? After all, are there diffi culties in this process of producing the fi nal paper? The hypothesis we demonstrate is that the institutional conditions combined with other factors, especially the orientation were the most important factors that represented de main diffi culties students have. Keywords: Tutoring. Metodology. Final paper.

In this paper, we study the uniqueness of two difference polynomials of entire functions sharing one value, polynomial and small function. Our results of this paper are improvement of the previous theorems given by Chen and Chen [2], Liu, Liu and Cao [22] and Li et al. [19].

Some mathematics educational reform policies indicate that mathematics education should be connected to learners‟ cultures. However, teaching in schools rarely brings the interconnection between mathematics and culture in pedagogically informed ways. Connections are often done superficially; the curriculum in schools lacks content and specific strategies that enable the making of the connections explicit in the context of teaching. The qualitative study from which this paper emerges worked with three mathematics teachers in an attempt to teach mathematics in ways that connect key concepts with culture. Through mathematizing culturally-based activities performed at a cultural village2, two Grade 9 mathematics topics in the South African curriculum were indigenised. A teaching unit on the indigenised topics was designed and implemented in five Grade 9 classes at the same school. The paper demonstrates that the experience of designing, implementing, and reflecting on the intervention study had some positive contribution to the participating teachers‟ pedagogical repertoire. Teachers saw the possibility of using cultural villages as instructional resources for connecting mathematics education to learners‟ cultures in the South African curriculum. I argue that cultural villages can be used as contexts for mediating culture and mathematics education.

Beginning from the reflections about a methodology used in a research project with an indigenous Colombian community, this paper outlines some possibilities for ethnomathematical research. Issues like intellectual property and social relevance are discussed in order to propose a broader concept of “academic instance”, trough the acknowledgement and legitimation of alternative scenarios of generation, transmission and transformation for mathematical knowledge. This paper has five sections: a) preliminaries about the indigenous community, b) description of the research process and its products (for their very nature, it will be written in a first-person plural voice), c) individual thoughts, treating the harmony between the ethnomathematical methodology and its theoretical, humanistic and political foundations, d) final remarks, sharing insights for further development, e)an epilogue or a review about the experience, to discuss the spirit which aims the analysis made.

Ethnomathematics is the mathematics of cultural groups, but often those cultural groups are “others” and “elsewhere”. However, it is also valuable to look inward to see the interaction of mathematics and one’s own culture. An assignment in a graduate course offers this opportunity to students. The assignment is to find an area of the student’s personal “culture” (sometimes defined rather broadly) and find its use of mathematics. Students are asked to write about (a) the cultural area; (b) how they are personally tied to it; and (c) how and where it uses mathematics. In addition to the paper, students make an oral presentation. Thus, all students learn (often surprising) aspects of their classmates’ non-professional life, and the presenter digs into areas of family and heritage that may not have been reviewed before. Since all students are classroom mathematics teachers, finding their own cultural mathematics is not only enlightening for themselves, but also offers opportunities to include new mathematics applications in their teaching. This paper includes much personal background that led to this assignment and is a report on more than a decade of using it, including brief student examples.

This paper aims to recover, develop, explore and expand the cultural practices of the ethnic group Nyanekankhumbi from southwestern Angola from an ethnomathematical perspective evidenced in the construction of houses of cob wall, keeping in mind the social multiculturalism of schools that exists, in part, almost everywhere, and in particular, in Portugal with a considerable and growing number of immigrants from Africa and other parts of the world. It becomes increasingly relevant to preserve the cultural memory of these people. This paper presents an introduction to the ethnomathematics studies in Africa by various authors usnig a methodology based on informal conversation with group members, participant observation, and interviews, supported by photographic records and written field notes. The results of the research developed in Huíla (Angola) registered much important mathematical knowledge about building the traditional houses of the Nyaneka-nkhumbi that can be understood in the creation of tasks in a context of formation, a topic of interest in the first author‟s doctoral project.

The method of ordinary differential equations in the context of calculating the special functions of wave catastrophes is considered. Complementary numerical methods and algorithms are described. The paper shows approaches to accelerate such calculations using capabilities of modern computing systems. Methods for calculating the special functions of wave catastrophes are considered in the framework of parallel computing and distributed systems. The paper covers the development process of special software for calculating of special functions, questions of portability, extensibility and interoperability.

We introduce in this paper the spinor differential and integral calculus from q- lorentzian algebra, differential spinor equation and lorentzian q− spinor differential equation. Finally a few comments.

The main objective of this paper is to determine the local and global Zeta function of B(C_{p^3}) the Burnside ring for cyclic groups of order p^3 and to study some relations that fulfill this Zeta function.

Entre los factores determinantes de la actuación exportadora de las empresas, numerosos estudios han subrayado la relevancia del mix de marketing. Generalmente, la mayoría de los estudios abordan el análisis de las variables centrado en estrategias específicas, en particular fenómenos de estandarización-adaptación. El presente estudio analiza si existe un efecto interactivo de fortalezas generadas en las diferentes variables del mix de marketing que pueda asociarse a diferentes perfiles exportadores. Para ello, se ha empleado el algoritmo Extreme Learning Machine (ELM) dentro de los procedimientos Perceptrón Multicapa (MLP) de Redes Neuronales Artificiales (RNA). Asimismo, el análisis se combina con un novedoso procedimiento de análisis de sensibilidad desarrollado ad hoc para este estudio, el cual permite conocer los efectos individuales e interactivos de las variables predictoras sobre la variable dependiente en problemas clasificatorios de naturaleza dicotómica. Los resultados obtenidos nos permiten corroborar la existencia de los efectos interactivos postulados, poniendo al mismo tiempo de manifiesto la utilidad de las RNA y del análisis de sensibilidad propuesto para la investigación en el área de marketing y, específicamente, para los estudios de internacionalización de empresas. || Among the determining factors in export activity, many studies have highlighted the relevance of the marketing mix. Generally, the majority of them use a variables analysis to focus on specific strategies, in particular, standardized-adaptations. This paper analyzes if there is an interactive effect of strength generated in different variables of the marketing mix that can be associated with different export profiles. The Extreme Learning Machine (ELM) algorithm has been used within the Multilayer Perceptron (MLP) of Artificial Neural Networks (ANN). In addition, the analyses combine a novel approach for sensitivity analysis developed ad hoc for this paper to determine the individual and interactive effects of predictable variables on the dependent variable in classification problems of a dichotomous nature. The results obtained allow us to confirm the existence of the postulated interactive effects, simultaneously revealing the usefulness of ANN and of the sensitivity analysis proposed for research in the area of marketing and, specifically, in firms' internationalization studies.

This paper examines the sample proportions estimates in the presence of univariate missing categorical data. A database about smoking habits (2011 National Addiction Survey of Mexico) was used to create simulated yet realistic datasets at rates 5% and 15% of missingness, each for MCAR, MAR and MNAR mechanisms. Then the performance of six methods for addressing missingness is evaluated: listwise, mode imputation, random imputation, hot-deck, imputation by polytomous regression and random forests. Results showed that the most effective methods for dealing with missing categorical data in most of the scenarios assessed in this paper were hot-deck and polytomous regression approaches. || El presente estudio examina la estimación de proporciones muestrales en la presencia de valores faltantes en una variable categórica. Se utiliza una encuesta de consumo de tabaco (Encuesta Nacional de Adicciones de México 2011) para crear bases de datos simuladas pero reales con 5% y 15% de valores perdidos para cada mecanismo de no respuesta MCAR, MAR y MNAR. Se evalúa el desempeño de seis métodos para tratar la falta de respuesta: listwise, imputación de moda, imputación aleatoria, hot-deck, imputación por regresión politómica y árboles de clasificación. Los resultados de las simulaciones indican que los métodos más efectivos para el tratamiento de la no respuesta en variables categóricas, bajo los escenarios simulados, son hot-deck y la regresión politómica.

En el presente trabajo mostramos los resultados más relevantes obtenidos en un proceso de encuestación a 300 usuarios de la estación “Pablo de Olavide" del metro de Sevilla. El objetivo del trabajo es doble: por un lado, analizar el perfil del usuario (motivaciones por las que usan el metro, intermodalidad y flujos); mientras que, por otro lado, a partir de las disposiciones a pagar con respecto a posibles incrementos en el precio del servicio, estimamos parcialmente la elasticidad precio de la demanda para esta población objetivo tan concreta. El perfil tan específico de los usuarios de dicha parada así como las características propias del metro de Sevilla explican algunos de los resultados obtenidos esperando ayuden a los gestores y administradores de Metro de Sevilla en la toma de decisiones. || In this paper the most relevant results obtained in a survey conducted by 300 users of the “Pablo de Olavide" Seville metro stop are presented. The aim of the paper is twofold. On the one hand, the user profile is analysed: motivations for using the subway, intermodality and ows, whereas, on the other hand, the price elasticity of demand is partially computed by means of the willingness to pay for that specic user profile. In fact, both the particular user profile and Seville metro's characteristics explain some of the obtained results that hopefully will help managers of Seville Metro in making decisions.

In the present paper, the SIR epidemiological model was used to study the behavior of the spread of the COVID-19 Pandemic in the Tacna Region. To determine the parameters of the model, the information published through social networks by the Regional Health Directorate of the Tacna Region of Peru was used, which was systematized in an EXCEL matrix and then exported to process the information in the System of Scientific Computing Mathematica. As a result, the graphs corresponding to the model referred to the Susceptible, Infected, Recovered and Deceased individuals from the COVID-19 Pandemic in the Tacna Region were obtained and then the graphs were interpreted in the time interval of the study.

A linear rank inequality is a linear inequality that holds by dimensions of vector spaces over any finite field. A characteristic-dependent linear rank inequality is also a linear inequality that involves dimensions of vector spaces but this holds over finite fields of determined characteristics, and does not in general hold over other characteristics. In this paper, using as guide binary matrices whose ranks depend on the finite field where they are defined, we show a theorem which explicitly produces characteristic-dependent linear rank inequalities; this theorem generalizes results previously obtained in the literature.

In this paper we prove a result on 0-cycles on surfaces as an application of the theorem on the kernel of the Gysin homomorphism of Chow groups of 0-cycles of degree zero induced by the embedding of a curve into a surface, and we study the connection of this result with Bloch’s conjecture and constant cycles curves.

This paper proposes a simple mathematical model that represents the dynamics of youth play for adolescents from 11 to 18 years. This model is defined by a system of 3 differential equations, which are based on continuous processes. The specification of the classes of our model is based on the group classification of the state of gravity of the problem given in [10]. Then we proceed to find the equilibrium points of the system and its analysis. For our numerical simulation we estimate all the parameters of the model using the research work [6] and we apply the Runge kutta algorithm of order 4. As a result and conclusion it is determined that the problem with the game is endemic among young people. In addition, the prevalence of problems with the game is lower in students aged 15 to 18 than in students aged 11 to 14.

In this paper, we show a way to characterize the R-automorphisms of formal power series on several indeterminates and with coefficients over a commutative ring with identity, R. We show this characterization, as an extension of existing result for the R-automorphisms of the formal power series in an indeterminate, given by O’Malley, M. and Wood, C. in [12].

In this paper, a modified Leslie-Gower type predator-prey model introducing in prey population growth a delayed strong Allee effect is studied. The Leslie-Gower model with Allee effect has none, one or two positive equilibrium points but the incorporation of a time delay in the growth rate destabilizes the system, breaking the stability when the delay cross a critical point. The existence of a Hopf bifurcation is studied in detail and the numerical simulations confirm the theoretical results showing the different scenarios. We present biological interpretations for species prey-predator type.

En el presente documento realizamos una recopilación bibliográfi- ca de las principales investigaciones acerca de la enseñanza y el aprendizaje de la demostración, con el ánimo de aportar fuentes de consulta a la comunidad de educadores en matemáticas interesados en el tema. Planteamos una estructura organizativa que incluye las siguientes líneas de investigación: Consideraciones histórico-epistemológicas, La demostración en el currículo, Concepciones y dificultades de los estudiantes al demostrar, Relaciones entre argumentación y demostración y Propuestas didácticas para la enseñanza de la demostración. Abstract. In this paper we present a synthesis of main research publications on the teaching and learning of proof. Our aim is to provide a reference to the mathematics educators interested in this topic. The paper is organized based on the following research topics: Historic-epistemological issues, Proof in curriculum, Students’ conceptions and difficulties, Relationship among argumentation and proof, Teaching units to teach proof.

In this paper we analyze the effects of physical exercise on the brain, on cognitive/school performance and on mental health from a Neuroscience perspective, in association with Mathematical Anxiety (MA). Physical exercise promotes structural and functional benefits to the nervous system, improves cognitive performance and anxiety. The evidence provide support to the effects of physical exercise on decreased matemathical anxiety in school-age children. We address discussion to improve viable educational strategies for the improvement of students physical, cognitive and mathematical performance.

In this paper, teachers’ knowledge regarding statistical competences and curriculum documents, mobilized in the Collaborative Group for the Training of Teachers in Statistical Education (MoSaiCo Edu) is highlighted. Considering the Discourse of the collective subject technique, the audio transcription of seven group meetings was analyzed. As a result, one can describe signs of mobilization of professional teaching knowledge related to the insertion of statistics in documents and textbooks. This was noticeable with regard to learning and skills developed by students, with regard to statistical competences, such as educational goals and with regard to the specificities and importance of context and the conceptual and procedural domain of Statistics. In this way, spaces for collaborative work among teachers provide opportunities for sharing and building teaching practices and understanding, favoring the proposition of categories and the legitimization of a specific basis for professional practice and teaching of Statistics.

This paper discusses the possibilities of adequacy or the obstacles presented in the Brazilian National Curriculum (Base Nacional Comum Curricular — BNCC, in portuguese) for the development of Socioscientific Issues (SSI) in science education for Elementary School. Therefore, our main objective is to understand which are the elements, perspectives and formative aspects present in the text of the document that indicate possibilities or obstacles for the development of practices aligned with the perspectives of Socio-Scientific Issues. To this end, we focus our discussion on three broad axes: General conceptions of formation and (mis) alignment with the SSI perspective; Formative itineraries for science education centered on SSI; Relevant contents and topics in SSI treatment. Based on the analysis, we understand that, at a discursive level, there are openings from which it is possible to undertake practices based on the perspectives of SSI, although not without an explicit investment in the production of appropriate conditions for such.