Search

Copyright of HOLOS is the property of Instituto Federal do Rio Grande do norte - IFRN and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper describes the steps to convert a paper-and-pencil English proficiency test for academic purposes, consisting of multiple choice items administered following the Admissible Probability Measurement Procedure [24], adopted by the graduate program at the Institute of Mathematics and Computer Sciences at the University of São Paulo (ICMC-USP), Brazil, to a computerized adaptive test (CAT) based on an Item Response Theory Model (IRT). Despite the fact that the program accepts various internationally recognized tests that attest non-native speakers English proficiency, such as the Test of English as a Foreign Language (TOEFL), the International English Language Testing System (IELTS) and the Cambridge English: Proficiency (CPE), for instance, its requirement is incoherent in public universities in Brazil due to the cost, which ranges from US$ 200.00 to US$ 300.00 per exam. The TAI-PI software (Computerized Adaptive Test for English Proficiency), which was developed in Java language and SQLite, started to be used to assess the English pro?ciency of students on the program from October, 2013. The statistical methodology used was defined considering the history and aims of the test and adopted Samejima's Graded Response Model [21], the Kullback-Leibler information criterion for item selection, the a posteriori estimation method for latent trait [2] and the Shadow Test approach [29] to impose restrictions (content and test length) on the test composition of each individual. A description of the test design, the statistical methods used, and the results of a real application of TAI-PI for graduate students are presented in this paper, as well as the validation studies of the new methodology for pass or fail classification, showing the good quality of the new evaluation system and examination of improvement using the IRT and CAT methods.

Recent advancement in the field of nonlinear analysis and fractional calculus help to address the rising challenges in the solution of nonlinear fractional partial differential equations. This paper presents a hybrid technique, a combination of Tarig transform and Projected Differential Transform Method (TPDTM) to solve nonlinear fractional partial differential equations. The effectiveness of the method is examined by solving three numerical examples that arise in the field of heat transfer analysis. In this proposed scheme, the solution is obtained as a convergent series and the result is used to analyze the hyper diffusive process with pre local information regarding the heat transfer for different values of fractional order. In order to validate the results, a comparative study has been carried out with the solution obtained from the two methods, the Laplace Adomian Decomposition Method (LADM) and Homotophy Pertubation Method (HPM) and the result thus observed coincided with each other. Inspite of the uniformity between the solutions, the proposed hybrid technique had to overcome the complexity of manupulation of Adomian polynomials and evaluation of integrals in LADM and HPM respectively. The methodology and the results presented in this paper clearly reveals the computational efficiency of the present method. Due to its computational efficiency, the TPDTM has the potential to be used as a novel tool not only for solving nonlinear fractional differential equations but also for analysing the prelocal information of the system.

In this paper, considering a wider class of simulation functions some fixed point results for multivalued mappings in α-complete metric spaces have been presented. Results obtained in this paper extend and generalize some well known fixed point results of the literature. Some examples and consequence are given to illustrate the usability of the theory.

Copyright of Revista Philósophos is the property of Revista Philosophos and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Acta Scientiarium: Education is the property of Universidade Estadual de Maringa and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Revista Práxis Educativa is the property of Revista Praxis Educativa and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Veritas is the property of EDIPUCRS - Editora Universitaria da PUCRS and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper aims to analyze how teacher trainer's actively supported the professional agency development of teachers, members of a Community of Practice. Therefore, a qualitative research of their participation in the enterprise Numerical Sets Study, with an interpretative slant, was undertaken. The results show that the teacher trainer fostered the study of ideas and mathematical concepts about irrational numbers; encouraged the teachers to work with challenging mathematic tasks; supported them while planning and with the development of a class planed on inquiry based-teaching about irrational numbers. The closeness among the participants, the former and the teachers of the community, affected their professional identities, by valuing their mathematical practice, in order to foster and reinforce their own professional agency. [ABSTRACT FROM AUTHOR]

This paper has a research that objective to use GeoGebra software in a problem solving approach, for an understanding of the sine and cosine functions. To this end, the use of technological resources in Mathematics classes are discussed, with a view to enabling research. The following is an analysis of an activity, carried out with a second year class in High School, in the area of skills and competences evaluation. The results of the methodology research thus allow the development of autonomy and a collaborative work culture in the construction of concepts, as well as the investigative process would not be possible without the use of technological resources. [ABSTRACT FROM AUTHOR]

The paper approaches the digital technologies use perspectives in the mathematics teacher initial education with emphasis on professional practice in basic education. The analysis was guided by theoretical perspective of technological, pedagogical and contend knowledge of Mishra e Koehler. Thus, we realize the investigation in the course of Mathematics Licentiate of a federal public university of the State of Santa Catarina, Brazil, on which examined institutional curriculum documents and teaching plans of all disciplines. Furthermore, we examined empirical material constituted from questionnaires and interviews realized with teachers and students. The results pointed four perspectives of articulation of the technologies to de pedagogical and content knowledge. The analyses and discussion about these perspectives indicate that the articulation between pedagogical, technological and content knowledge in the formative activities contributes to the teacher initial education in direction to professional practices changes. [ABSTRACT FROM AUTHOR]

The integration of digital games in teaching and learning processes has been assuming a relevant role in terms of contributions that offer. Considering the importance of these resources, this paper analyses the use of two digital games in mathematics classes with 5th grade students from an urban school and with 6th grade students from an indigenous school of the west region of Paraná state. The games were applied in both realities, thus requiring the creation of differentiated strategies to their use. Because of their playful and attractive form, it was verified that the educational digital games serve as stimulus to the students from different contexts and cultures, and as subsidies to improve the teaching and the learning of curricular contents. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the possible influences of the Solidarity Assimilation Pedagogy (SA) in the process of teaching and learning of continuity. The SA is a proposal that aims to break with traditional mathematics teaching, allowing students to receive bonus grades for group learning work unrelated to the assessment grade. The learning work of each class is based on a activity sheets composed of problems on the topic addressed. In this article, we analyze the development of the activity sheets about the continuity of a function, applied in a class of Calculus. The data analyzed through content analysis allowed us to infer that SA allows students to develop autonomy in learning, making them co-responsible for the whole process. [ABSTRACT FROM AUTHOR]

The aim of this article is to present and analyze the trends in digital technologies in Mathematics teaching, pointed out in the XVIII, XIX, XX and XXI editions of the Brazilian Meeting of Graduate Students in Mathematics Education. As a methodological procedure, we use the state of the art and meta-analysis of 141 papers, among abstracts and complete articles, which were published in the annals of the years 2014 to 2017. Results indicate that the master's research predominates, involving mainly students of basic education. Still, in the years 2014 and 2015, the digital technology theme is a research trend. In the year 2016, the highlight was for GeoGebra, followed by the digital technologies theme and the use of videos. Finally, in 2017, GeoGebra remains in the highlight, followed by the use of videos. [ABSTRACT FROM AUTHOR]

This article aims to explain a panorama of research on continuing teacher education for teachers who teach mathematics in basic education with an emphasis on technology and it has a temporal cut from 2013 to 2017. It is a "meta-analysis" study, that is, it has a bibliographic character. The dissertations and theses were collected in the CAPES and BDTD repositories in a total of 44 papers, however, only 15 corresponded to the proposed objective. The results reveal the insertion of several technological instruments in the formative processes, with emphasis on computers. In addition, few dissertations and theses approach in their context the subjective relations existing in the formations, mainly emphasizing the activities developed throughout the formative processes. [ABSTRACT FROM AUTHOR]

This paper reports on an experience in teaching mathematics in a graduate course in public health, intermingled with reflections and concepts. Students enrolled in such courses generally feel uneasy about learning mathematics. Without underrating the usual obstacles and even affinities in developing abstractions, the results suggest that a major portion of the difficulties derives not from mathematics itself, but from an oppressive experience in the past. Difficulties also relate to the construction of space in the classroom. Such a perspective involves understanding experiments and life experiences in which the subjects are involved. In short, the work focuses on how to transmit mathematics in the development of a pedagogical approach.

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.

This paper presents a new iterative method for the simultaneous determination of simple polynomial zeros. The proposed method is obtained from the combination of the third-order Ehrlich iteration with an iterative correction derived from Li's fourth-order method for solving nonlinear equations. The combined method developed has order of convergence six. Some examples are presented to illustrate the convergence and efficiency of the proposed Ehrlich-type method with Li correction for the simultaneous approximation of polynomial zeros.

Sensitivity and uncertainty analysis hold significant importance across a range of applications, spanning from industrial problems to climate change, financial risk assessment, as well as mathematical and computational models. These analyses involve identifying influential input parameters in models to comprehend their impact on the output. Sensitivity analysis can be performed locally, examining parameter effects at a fixed value, or globally, evaluating the model across a range of parameter values. The Sobol method stands as a robust approach for global sensitivity analysis, employing a Sobol sequence to create samples more uniformly within the input parameter space, thus enabling efficient exploration of model inputs. This paper aims to introduce a computational implementation in Scilab to generate the Sobol sequence for utilization in sensitivity analysis through the Sobol method. A test case was applied to generate Sobol sequences and discuss the obtained results.

Copyright of Brazilian Journal of Education, Technology & Society (BRAJETS) / Cadernos de Educação Tecnologia e Sociedade (CETS) is the property of Brazilian Journal of Education, Technology & Society - BRAJETS and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In recent years, lots of papers have been published on module amenability. In this paper, our main aim is to study the homological properties of various module derivations and prove some results about module amenability. So this paper continous a line investigation in [3], [4] for Banach algebras.

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.

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.

In this paper, by employing Ricceri variational principle, we prove the existence of infinitely many weak solutions for fourth-order problems depending on two real parameters. We also provide some particular cases and a concrete example in order to illustrate the main abstract results of this paper.

In this paper, we establish coincidence point and common fixed point theorems involving two pairs of weakly compatible mapping satisfying contraction condition with complex coefficient are proved in complex valued metric space. The presented theorems generalize, extend and improve many existing results in the literature. An example is given at the end of the paper.

Results relating to fractional Fourier transform and their properties in the Lizorkin space are employed in this paper to investigate the Cauchy representation of fractional Fourier transform for integrable Boehmians. An inversion formula for the fractional Fourier transform is addressed. The conclusion remark of the paper spells the initiation for the present investigation.

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.

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.

Copyright of História Unisinos is the property of Universidade do Vale do Rio dos Sinos and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The purpose of this research was to identify and analyze the scientific publications, national and international, about the pedagogical strategy of the flipped classroom in the teaching of Mathematics. The study retrieved 16 papers, covering investigations in the contents of Calculus, Numerical Methods and Linear Algebra. Other searches showed the inversion of the classroom in the reduction of anxiety and also in the use of this proposal by teachers of Mathematics. Such mapping indicated a limited number of publications, from 2014 to 2017, with only five journals. Therefore, it is considered necessary new searches that can discuss the flipped classroom and the influences of this one in the teaching of Mathematics. [ABSTRACT FROM AUTHOR]

Aedes aegypti is the main vector of multiple diseases, such as dengue, yellow fever, Zika, and chikungunya. Diseases associated with mosquitoes have been growing in recent years, with more than one-third of the world population at risk. Control techniques have been studied to prevent the spread of the Aedes aegypti, such that new formula and how to use adulticides and larvicides, among others. This paper proposes a novel approach in the field of partial differential equations and optimization. We consider a two-dimensional diffusion-reaction model that describes the interaction between aquatic and adult female stages spreading across a domain with parameters dependent on rainfall and temperature. We also formulate a mono-objective and multiobjective optimization problem to minimize the Aedes aegypti populations and the control, considering the application of adulticides and larvicides, using actual data from the city of Lavras/Brazil. The operator splitting technique is used to solve the diffusion-reaction system, coupling finite difference and the fourth-order Runge-Kutta method and optimal solutions were searched by using the Real-Biased Genetic Algorithm and Non-dominated Sorting Genetic Algorithm -II. Numerical results show significant reduction of the Aedes aegypti population.

Segmentation is one of the inferential applications for detecting patterns in digital images, which has been widely used in the health area. Thresholding, a type of segmentation, consists of separating the gray groups of an image, through one or more thresholds applied to the histogram. Thus, we used the gray tone with the lowest Fuzzy Divergence found to apply the enhancement method, through membership values. This paper presents a method to assist physicians in interpreting lung radiography images, especially in the pandemic caused by COVID-19, when enhancing lung images. In addition, we consulted with a group of medical experts who saw an improvement in image quality, providing the perception of detail in the enhanced image compared to the original image.

At the end of the 19th century, projective geometry was at the basis of most geometric research in Italy, and of much other research work in Europe. Furthermore, through its close connection with descriptive geometry, it seemed particularly responsive to social and educational needs of the time. In Italy, a reform of the Technical Institutes brought projective geometry into the syllabuses; and Cremona's book Elementi di Geometria Projettiva helped to spread the synthetic method in Italy and in Europe. In this paper we will examine the link between projective geometry and education, from the personal point of view of Luigi Cremona, and from the institutional point of view of technical instruction in schools and universities. Information about the reception of Cremona's book in Europe and some letters from Cremona's estate will help us to understand the scientific climate of that period.

How should we write a history of mathematics education? To answer this question, we have to consider why we should want to study this history. For many mathematics teachers – as in the case of the author- it is simply necessary to explore your own profession to improve your teaching. But in the end it would be useful if some people took a more scientific approach and looked for mainlines in the development, tendencies, patterns or even explanations. To do so we have to consider the initial local history of mathematics education in a wider context both in a nationwide and in an international comparison as well in comparison with other school subjects and the history of pedagogy in general. In this paper we explore the possibility to make a wave model of the development of mathematics education in Denmark in the past two centuries, illustrating periodic changes between times with emphasis on understanding and times with emphasis on drill and skills. To which extent can a model like this be explained?

This paper describes the process through which the Hebrew language, formerly only a liturgical language, became the language of mathematical instruction in Hebrew schools. Around the end of the 19th century and the beginning of the 20th century, Hebrew was not used in daily life by the Jewish community in Palestine. With the foundation of Hebrew schools, the lack of Hebrew mathematical vocabulary became apparent and a systematic creation of Hebrew scientific terminology began. This new terminology enabled the creation of the first Hebrew secondary mathematics textbook.

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 article tackles a thorny issue within the reception of Badiou’s philosophy, i.e., the question of the role of the “social” within the ontological framework it outlines. Acknowledging that the question of the social is underdeveloped in Badiou’s system, the paper argues that there are resources in it to develop a social ontology, and attempos to flesh it out through an original and sustained reading of Badiou’s key formula on the distinction between democratic materialism and materialist dialectic: “there are only bodies and languages, except that there are truths”.

This paper explores the recent updating of Badiou's general philosophical proposal in the specific approach of a "speculative strategy" in his recent book The Immanence of Truths. I hypothesize that the idea of a "speculative strategy" is a third stage in Badiou's project called "philosophy of the event", which fulfills and radicalizes the previous stages of "platonism of the multiple" and "communism of Idea", development whose continuity rests on the internal unity of his project flinking his ontological and meta-ontological wager as a necessarily systematic philosophy. First, I will show the general elements of Badiou's philosophy, explaining its stages and the emergence of what I will call "philosophy of the event and multiple being". Secondly, I will delve specifically into the convergence of the ontological thesis and the meta-ontological one, to characterize the author's enterprise as a systematic project detached from ontotheology thanks to the speculative recourse to mathematics to think infinity. Finally, I will argue that the "strategy" of the author's recent work implies a specification of the role of mathematics within his speculative ontology.

In this paper we introduce and study the notion of d-continuity continuity on mixed fuzzy topological spaces. We have investigated this notion in the light of the notion of q-neighbourhoods, q-coincidence, fuzzy d-closure, fuzzy d-interior. In this paper we have established the relationship between fuzzy continuity and fuzzy d-continuity in mixed fuzzy topological spaces.

The object of the present paper is to derive the solution of generalized kinetic equations of fractional order involving the Wright generalized Bessel function or Bessel–Mitland function. The obtained results in this paper, imply the known results of Chaurasia and Pandey [24] more precisely in terms of K4 –function introduced by Sharma [12] believed to be new. Special case, involving the F- function is considered.

In this paper, we extend the study of $\Psi_\mathcal{H}$ operator introduced and studied in [5] and rectify the errors in the paper. Moreover, characterizations of $\mu-$codense and strongly $\mu-$codense hereditary classes in generalized topological spaces are also given.

This paper will discuss about a new topology, obtained from a grill and a filter on the same set. The Characterizations and open base of the new topology are also aim of this paper. The generalized continuity is also a part of this paper.

Mathematical proofs aim to establish the truth of mathematical propositions by means of logical rules. Some recent literature in philosophy of mathematics alleges that some mathematical proofs also reveal why the proved mathematical propositions are true. These mathematical proofs are called explanatory mathematical proofs. In this paper, I present and discuss some salient problems around mathematical explanation: the existence problem, the normative problem, the explanandum problems of truth value and psychological value, the logical structure problem, the regress problem and the modelling problem. At the end, I sum up two contemporary models for mathematical explanation - the deductive-nomological model and the model of Steiner. I analyse these models against the previous problems. [ABSTRACT FROM AUTHOR]