Search

Copyright of Colloquium Exactarum is the property of Asociacao Prudentina de Educacao e Cultura (APEC) 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 Em Extensao is the property of Em Extensao 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 Colloquium Humanarum is the property of Asociacao Prudentina de Educacao e Cultura (APEC) 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 an engine, the valve train is responsible for approximately 6% to 35% of the total friction losses, with the value varying with the design and operating conditions. Even a 1% improvement in the fuel economy of a vehicle model is of great economic and environmental relevance. One of the engine systems subject to considerable friction is the control system and actuation of gas admission and discharge valves, the valve control system. Friction efforts and wear between the cam and the tappet depend on the relative speeds of the parts, the state of the surfaces in contact, the lubrication and temperature conditions, and the materials and geometries of the cam and tappet. A carefully project of the cam-tappet system is needed to preserve parts integrity and system functionality. This work presents some important experiments carried out with various cam-tappet systems, measured on engines or constructed using parts of an engine. Several important quantities are measured and analyzed by the reported experiments. The main objective of this paper is to promote a better understanding of these quantities that can be useful to engine designers to minimize energy losses or for optimize desirable mechanical characteristics of the system. Also, this paper allows researchers to plan new experiments and/or rapidly identify typical experimental results. It was possible to conclude that typical friction coefficients between cam and tappet varies from 0.05 to 0.15, that the force between valve stem-valve guide represents only about 1.5 -2% of the force acting on the valve stem, that the cam-follower friction was low for viscous oil SAE 50, compared with other lubricants, whereas camshaft bearing friction was low for lubricant SAE 5W-40 in the same engine, that the friction at the cam-follower interface decreases with increasing engine speed, that viscous oil gave greater oil film thickness as compared to the low-viscosity lubricant at the cam-follower interface, among others.

Copyright of Revista Espacios is the property of Talleres de Impresos Oma 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 object of this paper is to evaluate some finite double summations relations for the multivariable $A$-function using the summation of a double hypergeometric series. The formulas derived in this paper are most general in character, we also provide a few particular cases for derived summation formulas.

The aim of this paper is to introduce a new class of mappings called almost nonexpansive mappings in a $b$-metric space. Some characteristics of this class of mappings are discussed. Fixed point and common fixed point results for such mappings are obtained. An application to the Cauchy problem in a Banach space is also shown in this paper.

In this paper, we discuss the implementation and numerical aspects of the Matlab solver designed for the solution of Low Protein Model (LPD). In this paper, we study the existence and uniqueness of the weak solution and we try to write some codes in Matlab which are based on Euler’s Method and several technics of programmation. subject to an initial condition dM dt = µL − δM, (2) L(0) = 0 and M (0) = 0. (3) The code is based on Euler’s Method and several technics of programmation.

Let S be a commutative semiring with unity. In this paper, we introduce the weakly nilpotent graph of a commutative semiring. The weakly nilpotent graph of S, denoted by 􀀀w(S) is defined as an undirected simple graph whose vertices are S and two distinct vertices x and y are adjacent if and only if xy 2 N(S), where S = Sn f0g and N(S) is the set of all non-zero nilpotent elements of S. In this paper, we determine the diameter of weakly nilpotent graph of an Artinian semiring. We prove that if 􀀀w(S) is a forest, then 􀀀w(S) is a union of a star and some isolated vertices. We study the clique number, the chromatic number and the independence number of 􀀀w(S). Among other results, we show that for an Artinian semiring S, 􀀀w(S) is not a disjoint union of cycles or a unicyclic graph. For Artinian semirings, we determine diam(􀀀w(S)). Finally, we characterize all commutative semirings S for which 􀀀w(S) is a cycle, where 􀀀w(S) is the complement of the weakly nilpotent graph of S. Finally, we characterize all commutative semirings S for which Γw(S) is a cycle.

In this paper we establish in first the existence of strong optimal solutions of a control problem for dynamics driven by a linear forward-backward doubly stochastic differential equations of mean-field type (MF-FBDSDEs), with random coefficients and non linear functional cost. Moreover, we establish necessary as well as sufficient optimality conditions for this kind of control problem. In the second part of this paper, we establish necessary as well as sufficient optimality conditions for existence of both optimal relaxed control and optimal strict control for dynamics of nonlinear mean-field forward-backward doubly stochastic differential equations.

We show that integration by parts formulas based on Malliavin-Skorohod calculus techniques for additive processes help us to compute quantities like ${\E}(L_T h(L_T))$ for different suitable functions $h$ and different models for the cumulative loss process $L_T$. These quantities are important in Insurance and Finance. For example they appear in computing expected shortfall risk measures or stop-loss contracts. The formulas given in the present paper, obtained by simple proofs, generalize the formulas given in a recent paper by Hillairet, Jiao and Réveillac using Malliavin calculus techniques for the standard Poisson process, a particular case of additive process.

In this paper, we introduce a viscosity-type extragradient algorithm for finding a common point of the solution of a pseudomonotone equilibrium problem and a fixed point problem of an infinite family of multi-valued quasi-nonexpansive mappings in real Hilbert space. Using our algorithm, we state and prove a strong convergence result of our iteration sequences. An application to variational inequality problem was considered. Lastly, we give a numerical example of our main result. The result presented in this paper extends and complements some recent results in literature.

This paper introduces a class of rings called left nil zero semicommutative rings ( LNZS rings ), wherein a ring R is said to be LNZS if the left annihilator of every nilpotent element of R is an ideal of R. It is observed that reduced rings are LNZS but not the other way around. So, this paper provides some conditions for an LNZS ring to be reduced and among other results, it is proved that R is reduced if and only if the ring of upper triangular matrices over R is LNZS. Furthermore, it is shown that the polynomial ring over an LNZS may not be LNZS and so is the case of the skew polynomial over an LNZS ring. Therefore, this paper investigates the LNZS property over the polynomial extension and skew polynomial extension of an LNZS ring with some additional conditions.

Let $K$ be a pure number field generated by a complex root of a monic irreducible polynomial $F(x)=x^{2^r\cdot7^s}-m\in \mathbb{Z}[x]$, where $m\neq \pm 1$ is a square free integer, $r$ and $s$ are two positive integers. In this paper, we study the monogenity of $K$. We prove that if $m\not\equiv 1\md{4}$ and $\overline{m}\not\in\{\pm \overline{1},\pm \overline{18},\pm \overline{19}\} \md{49}$, then $K$ is monogenic. But if $r\geq 2$ and $m\equiv 1\md{16}$ or $s\geq 3$, $\overline{m}\in\{ \overline{1}, \overline{18}, -\overline{19}\} \md{49}$, and $\nu_7(m^6-1)\geq 4$, then $K$ is not monogenic. Some illustrating examples are given at the end of the paper.

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.

Copyright of Revista Alea: Estudos Neolatinos is the property of Programa da Pos-Graduacao em Letras Neolatinas Fac de Letras - UFRJ 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 identify and analyze the theme of Financial Education (EF) in academic research in the latest editions of ENEM, CIBEM and SIPEM. The methodological approach is qualitative of the bibliographical. We believe that the SBEM electronic database enabled a bibliographic survey of academic production. The results pointed to the need to promote discussions about EF in the school environment, recognizing its contribution to the integral and critical formation of the subject, its articulation with social, political, economic, environmental and cultural problems, making education a progressively active social force. They also highlighted the urgent need to implement continuing education programs that enable the planning and implementation of more assertive teaching practices in this area.

Since the publication of the Base Nacional Comum Curricular (National Common Curricular Base), Financial Education has become a topic to be developed in the classroom, mainly related to the mathematics curriculum. In this sense, teachers are in charge of addressing it. In view of this, in this paper we aim to discuss understandings of Financial Education aimed at Basic Education and produced by mathematics undergraduates, mobilized in two training meetings. Based on Critical Mathematics Education and the qualitative research paradigm, we identified five topics using content analysis procedures. The results of the analysis of these topics indicate that the future teachers have knowledge of School Financial Education, although they relate the subject to economic aspects and Financial Mathematics.

In this paper, we investigate the tensions and interferences between philosophy and mathematics in the context of the emergence of pure mathematics in Prussia in the 19th century. In historiography the occurrence of an epistemological turn in mathematics in that century is well known. Such occurrence came to restructure the internal conceptions of its objects, in detriment of a quantitative notion and instead from a relational conception. We argue here that this change was facilitated, precisely, by the Kantian understanding that mathematics, by dealing with synthetic a priori judgments, would conceive itself as the foundation of thinkability. Our approach resides upon investigating how these notions were addressed and conceived of in the works of two authors: Jakob Fries, philosopher of science and mathematics at the beginning of the 19th century, and Hermann Grassmann, mathematician whose work would influence new conceptions by the second half of that century. Our research identifies, in the perspectives and practices of Fries and Grassmann, a conceptual unity, regarding the foundational reflection of mathematics from abstract structures of thinking. This finding reveal, on the other hand, the intervention of philosophical practices and references within the mathematical practice, producing tensions and encompassing a relevant role in the epistemological change in question. [ABSTRACT FROM AUTHOR]

The undoubted benefits and intrinsic virtues of mathematics should not blind us to potential collateral damage as the huge juggernaut of mathematics rolls over education and society towards a reshaped future. Because of its great power and influence across the whole of society we need to undertake an ethical audit. This paper conducts an ethical critique that considers four interrelated aspects of mathematics in education and society and their negative impacts. 1. The overvaluation of mathematics and the effects this power has in maintaining privileges. 2. The powerful negative impacts of mathematical studies have on many individual learners. 3. Visible but problematic applications of mathematics within society that are shielded from criticism because mathematics continues to be viewed as neutral. 4. The profound and performative effects of the hidden applications of mathematics that reformat society and change our everyday lives but remain unchecked in every sense. Most of the paper is devoted to revealing these damaging effects. The solutions proposed are for ethical awareness to be fostered in mathematical study at all levels, as well as challenging the widespread stereotype of mathematics as ethically neutral.

In this paper, we present the results of a new approach to the splitting factor preconditioner, which is a preconditioner based on the Incomplete Cholesky factorization and the splitting preconditioner. In previous work for small linear programming problems, the preconditioner was applied in all iterations of the interior point method and compared with the splitting preconditioner also applied in all iterations. In this paper, we will do a hybrid approach, in which in the first iterations the preconditioner is the Incomplete Cholesky Factorization, and in the last iterations, the preconditioner used is the splitting factor preconditioner or the splitting preconditioner. The results obtained show that even in the hybrid approach, the splitting factor preconditioner achieved better performance.

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 proposes a family of line--search methods to deal with weighted orthogonal procrustes problems. In particular, the proposed family uses a search direction based on a convex combination between the Euclidean gradient and the Riemannian gradient of the cost function. The non--monotone line--search of Zhang and Hager, and an adaptive Barzilai--Borwein step--size are the chosen tools, in order to speed up the convergence of the new family of methods. One of the extremes of that convex combination is reduced to well--known spectral projected gradient method, while the another one can be interpreted as a Riemannian steepest descent method. To preserve feasibility of all the iterates, we use a projection operator based on the singular value decomposition, which can be computed efficiently via the spectral decomposition of an appropriate matrix. In addition, we prove that the entire uncountable collection of search directions satisfies a descent condition. Some numerical experiments are provided in order to demonstrate the effectiveness of the new approach.

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 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

In this paper, we introduce and study a system of set-valued Cayley type inclusions involving Cayley operator and (H; )-monotone operator in real Banach spaces. We show that Cayley operator associated with the (H; )-monotone operator is Lipschitz type continuous. Using the proximal point operator technique, we have established a fixed point formulation for the system of set-valued Cayley type inclusions. Further, the existence and uniqueness of the approximate solution are proved. Moreover, we suggest an iterative algorithm for the system of set-valued Cayley type inclusions and discuss the strong convergence of the sequences generated by the proposed algorithm. Some examples are constructed to illustrate some concepts used in this paper.

In their paper [1], Shahzad Ahmad et al. given a characterization on any pure sextic number field Q(m1/6) with square-free integers m satisfying m 6 ±1 (mod 9) to have a power integral bases or do not. In this paper, for these results, we give a new easier proof than that given in [1]. We further investigate the cases m 1 (mod 4) independently to the satisfaction of m2 1 (mod 9), m 1 (mod 9), and the number fields defined by x2r3t −m, where r, t are two non-negative integers, and m is a square free integer are investigated. The proposed proofs are based on Dedekind’s criterion and on prime ideal factorization.

In this paper we establish Hyers-Ulam-Rassias stability of a generalized functional equation in fuzzy Banach spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc. 72 (1978), 297-30.

Copyright of EduSer: Revista de Educação is the property of EduSer: Revista de Educacao 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 aim is to present an integer linear programming model to the problem of the designation of didactical assignments in a university that maximizes professor's abilities and preferences. To validate and evaluate the effectiveness of the model, a preliminary case study was carried out at the Department of Mathematics of the Federal Technological University of Paraná - Cornélio Procópio Campus. In this context, the results obtained are promising, with improvements in indexes related to satisfaction, skill and teacher workload compared to the manual designation adopted by the department and also with another formulation for the problem presented in the literature. [ABSTRACT FROM AUTHOR]

This paper aims to describe and analyze an instrumental orchestration which aimed to apply the double integral in determining the center of mass of a variable density blade and the electrical charge in a given region. The study, qualitative in nature, involved undergraduate mathematics and engineering students of a public university in Amazonas, and the data were collected by observation of classroom activities and recorded through video recording and an electronic form questionnaire. The theoretical framework is composed of Luc Trouche's Theory of Instrumental Orchestration and Guy Brousseau's Theory of Didactic Situations. The results show, among other things, that the stages of action, formulation, validation, and institutionalization when used in the instrumental orchestration performance mode are important elements of didactic situations and that, through them, the teaching and learning processes contribute to the construction of knowledge. [ABSTRACT FROM AUTHOR]

In this paper, a set of conditions under which the absolute Nörlund summability method include in the absolute weighted mean method have been established. Three non-trivial examples to show that this inclusion holds have been given, and other three examples to show that even if both and are regular, the inclusion fails to holds have been constructed. The paper give two non-trivial examples to show that the equivalence of these two methods may holds. Finally, we give two examples to show that inclusion may holds in only one way without the other.

In this paper the linear representation of a graph is defined. A linear representation of a graph is a subgroup of $GL(p,\mathbb{R})$, the group of invertible matrices of order $ p $ and real coefficients. It will be demonstrated that every graph admits a linear representation. In this paper, simple and finite graphs will be used, framed in the graphs theory's area

In this paper, we develop a new numerical method, game theory and option pricing to compute a bankruptcy triggering asset value. we will draw our attention to determining a the numerical asset value, or price of a share, at which a bankruptcy is triggered. This paper develops and analyze a cubic spline collocation method for approximating solutions of the problem. This method converges quadratically. In addition, this article also provides with a real-life case study of the investment bank, and the optimal bankruptcy strategy in this particular case. As we will observe, the bankruptcy trigger computed in this example could have served as a good guide for predicting fall of this investment bank.

The aim of this paper is to investigate the stability problem for the pexiderized trigonometric functional equation f₁(xy)+f₂(xσ(y))=2g₁(x)g₂(y), x,y∈G, where G is an arbitrary group, f₁,f₂,g₁ and g₂ are complex valued functions on G and σ is an involution of G. Results of this paper also can be extended to the setting of monoids (that is, a semigroup with identity) that need not be abelian.

Various families of generating functions have been established by a number of authors in many different ways. In this paper, we aim at establishing (presumably new) a generating function for the extended second Appell hypergeometric function $F_{2} (a, b, b'; c, c'; x, y; p)$. Further we derive a relation in terms of the Laguerre polynomials and differentiation formulas. We also present special cases of the main results of this paper.

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.

Trends in Computational and Applied Mathematics is a new journal published by the Brazilian Society for Computational and Applied Mathematics (SBMAC). SBMAC was established in 1978 as a scientific organization aimed at developing and promoting Computational and Applied Mathematics in Brazil. It is a leading environment for researchers, professionals and students working in Applied Mathematics and related fields. Currently, SBMAC has over 300 members and it organizes the largest scientific event in t his field in Latin America, the National Congress of Computational and Applied Mathematics (CNMAC), an annual congress that attracts around 700 attendees. Furthermore, SBMAC organizes regional events and co sponsors many other events in Brazil. In 1999, SBMAC created the journal Tendências em Matemática Aplicada e Computacional (TEMA), which was originally devoted to papers presented at CNMAC and to the dissemination of Applied Mathematics in Portuguese. With the publication of 21 volumes, the jornal has grown and has become a leading Brazilian journal in the field. In the past few years, the great increase in the number of submissions in English, by Brazilian and foreigner researchers alike, shows that TEMA has attracted an international audience and is recognized as an important publication in Computational and Applied Mathematics. The new journal, Trends in Computational and Applied Mathematics, marks the rebirth of TEMA as a truly international journal, yet one that preserves its history and the high profile that it has achieved. Our goals are to publish original research, theoretical developments and case studies on promising themes; to offer an interdisciplinary and reliable international forum; to provide an efficient peer review system, leading to a fast response time to the first decision. For forthcoming issues of TCAM, we invite researchers in Applied Mathematics and related fields to submit papers with innovative and/or relevant contributions to Computational and Applied Mathematics. We hope you enjoy reading the first issue of the new TCAM. We are looking forward to receiving your future contributions, as well as any comments and suggestions you may have. We will try our best to adjust to the expectations of our readership.

Physical activity provides numerous benefits to physical and mental health, even affecting learning. Despite this, one of the main modern problems is represented by sedentariness. Children and adolescents spend most of their time at school. Therefore, a valid teaching methodology to benefit from the positive effects of physical activity and reduce sedentary moments could be interdisciplinary learning, which integrates physical education into various curricular subjects. Specifically, this paper proposes a systematic literature review of some protocols (n = 11) to investigate whether an elementary school’s integrated physical education and mathematics curriculum can improve learning in the logic-cognitive domain. From all the studies reviewed, the strong importance of interdisciplinary teaching, linking mathematics to physical education, was confirmed to reduce sedentary moments and enable a better attitude toward this discipline, breaking down the many stereotypes that often paint it as a complex and abstract subject.

Grounded on the philosophy of language of Wittgenstein and some of his commentators, this paper aims to discuss the calculation and the mathematical writting in situations of teaching and learning. In different contexts, learners must mobilize different techniques: in everyday life, on the market, for example, the student solves "calculations in his head" in their commercial relations; in school, students must learn to do calculations on paper and they learn to objectify/formalize the calculations using mathematical writing, learning, thus, a new skill. This fact shows that when the student has success with calculations in your everyday life and do not perform well in school, this means he lacks skills to work with mathematical writing. We seek to show also that in both situations, both in the calculation in the head as in the calculation on paper, it is not an internal mental process, once the student applies rules in the public domain that are learned. [ABSTRACT FROM AUTHOR]

Copyright of Psicologia: Reflexão e Critica is the property of Springer Nature 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 this paper‎, ‎we introduce and investigate a subclass‎ of analytic and bi-univalent functions which both $f(z)$ and $f^{-1}(z)$ are m-fold symmetric in the open unit disk U‎. Furthermore‎, ‎we find upper bounds for the initial coefficients $|a_{m‎ + ‎1}|$ and $|a_{2m‎ + ‎1}|$ for functions in this subclass‎. ‎The results presented in this paper would generalize and improve some recent works‎.

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 article we reflect on the representation records that intervene in the study of curves and surfaces, as reference mathematical objects, exploring the Sieve-Geometric technique. For this, we analyse the GeoGebra software and the practices of the students of a Master course in Mathematics Education to solve a problem using the paper/pencil environment. The results show that students have mastery of their geometric thoughts in the treatment of objects in the two-dimensional plane, but present difficulties in the representation of geometric objects in three dimensions, which are manifested in the inadequate mobilization of geometric thoughts on the curved and surface sieve, delimiting the geometric object involved in the problem, both in Spatial and Analytical Geometry. [ABSTRACT FROM AUTHOR]

Copyright of Educação Matemática Pesquisa is the property of Pontificia Universidade Catolica de Sao Paulo, Programa de Estudos Pos-Grad. em Educacao Matematica 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.)