Disciplinas de Fundamentos de Matemática: uma discussão à luz dos significados da palavra “fundamentos”

Based on a survey of summaries of courses on the Foundations of Mathematics, from Mathematics Teacher Education programs in the southern part of Brazil, and some remarks on the legislation related to the course syllabuses, we discuss the meaning of the word ""Foundations"" in order to reflect on the proposals of these issues in the courses, which will be undergoing reformulation. The opinions of students in one of these courses regarding the meaning of the term ""foundations"", as well as the data obtained from the survey and the remarks regarding legislation, may lead to considerations about the possibilities for a better qualification of the initial education of Mathematics teachers.

Do labor aos mitos: uma nova linha no mapa das pesquisas em Etnomatemática

In this paper we highlight the existence of a new line of research within the Ethnomathematics Program. In its origin, research in this area has sought to contribute to understanding regarding the diversity of mathematical thought through a careful look at work activities. In recent years, however, we have paid increasing attention to the affirmations of anthropologists that myths can be used to understand the most basic questions of human thought as well as specific questions regarding the society that produced them. Based on this idea, the myths of different peoples are perceived as informative with respect to their Ethnomathematics. Thus, together with work activities, myths constitute a source of support on which we draw to develop this line of research.

A formação de professores e suas relações com cultura e sociedade: a educação escolar indígena no centro das atenções

This paper reflects the current situation surrounding indigenous teacher education by means of the construction of a dialogue among three educators, two of them non-indigenous educators involved with indigenous school education and one indigenous educator committed to the education of his people. Teacher education, situated in a socio-cultural way, is the center of attention in this paper. ""Listening"" as a way of talking with the ""other"" is one of the theoretical focuses of this exercise between teacher educators and teachers, which uses dialogue as a means to increase awareness. In the dialogic process mentione, it was possible to realize how rich a dynamic between educators from different cultural contexts can be. The desire of the indigenous educator and his/her people to contribute their ideas to the construction of the indigenous school became evident. This shows the great challenge for non-indigenous educators seeking to contribute to the organization of the school education of distinct indigenous nations.

A Análise Matemática no Ensino Universitário Brasileiro: a contribuição de Omar Catunda

The goal of this paper is to show the diffusion, reception, and utilization of Omar Catunda's book Course of Mathematical Analysis for mathematics and engineering teaching in Brazilian universities, e. g., University of Sao Paulo and the University of Bahia from 1950 to 1976. We used interviews of some ex-alumni or users of his book. We also present some signs of the influence of his book and of Catunda himself at University of Rio Grande do Sul. We argue that Catunda and his book were important agents of process of modernizing the teaching of calculus and analysis, through his classes as well as his book.

High-Density Lipoprotein Inhibits the Uptake of Modified Low-Density Lipoprotein and the Expression of CD36 and Fc gamma RI

Aim: Modified low-density lipoprotein (mLDL), mainly upon oxidative and enzymatic modification, is the major atherogenic lipoprotein. Conversely, high-density lipoprotein (HDL) is considered anti-atherogenic because of its ability to remove cholesterol. The aim of this work was to analyze both the influence of HDL on the uptake of mLDL and the expression of CD36 and Fc gamma I receptors on monocytic cell lines during cell differentiation. Methods: Uptake of fluorescein isothiocyanate (FITC)-conjugated LDL and FITC-conjugated mLDL, i.e., copper-oxidized LDL (oxLDL) or trypsin enzyme modified LDL (enzLDL), was analyzed, as well as the expression of CD36 and Fc gamma RI in THP-1 and U937 cells, using flow cytometry. Results: HDL inhibited the uptake of mLDL, which varied in degree depending on the cell line or type of mLDL. Further, HDL rapidly decreased CD36 and Fc gamma RI involved in the uptake of mLDL. Conclusions: We demonstrate that modified LDL promotes specific LDL receptor-independent uptake by monocytic cell lines, and that the uptake of LDL and enzLDL is less than that of oxLDL. In this process, HDL diminishes the uptake of LDL or mLDL, which may involve the down-regulation of receptors (CD36 and Fc gamma I). This regulatory process represents another way by which HDL can be anti-atherogenic and it depends on the type of modification of LDL and the stage of differentiation of monocytes to macrophages.

Laser Phototherapy as Topical Prophylaxis Against Radiation-Induced Xerostomia

The common consequences of radiotherapy (RT) to the head and neck are oral mucositis, xerostomia, and severe pain. The aim of this study was to verify how laser phototherapy (LPT) used for oral mucositis could influence xerostomia symptoms and hyposalivation of patients undergiong RT. Patients were divided into two groups: 12 individuals receiving three laser irradiations per week (G1) and 10 patients receiving one laser irradiation per week (G2). A diode laser (660 nm, 6 J/cm(2), 0.24 J, 40mW) was used until completely healing of the lesions or the end of the RT. At the first and last laser sessions, whole resting and stimulated saliva were collected, and questionnaires were administered. According to Wilcoxon and Student statistical test, xerostomia for G1 was lower than for G2 (p<0.05), and salivary flow rate was no different before and after RT, except for stimulated collection of G2, which was lower (p<0.05). Our results suggest that LPT can be beneficial as an auxiliary therapy for hypofunction of salivary glands.

Ionic and Histological Studies of Salivary Glands in Rats with Diabetes and Their Glycemic State After Laser Irradiation

Objectives: To evaluate the effect of laser irradiation (LI) on the glycemic state and the histological and ionic parameters of the parotid and submandibular glands in rats with diabetes. Methods: One hundred twenty female rats were divided into eight groups. Diabetes was induced by administration of streptozotocin and confirmed later according to results of glycemia testing. Twenty-nine days after the induction, the parotid and submandibular glands of the rats were irradiated with 5, 10, and 20 J/cm(2) using a laser diode (660nm/100mW) (without diabetes: C5, C10, and C20; with diabetes: D5, D10, and D20, respectively). On the following day, the rats were euthanized, and blood glucose determined. Histological and ionic analyses were performed. Results: Rats with diabetes without irradiation (D0) showed lipid droples accumulation in the parotid gland, but accumulation decreased after 5, 10, and 20 J/cm(2) of laser irradiation. A decrease in fasting glycemia level from 358.97 +/- 56.70 to 278.33 +/- 87.98mg/dL for D5 and from 409.50 +/- 124.41 to 231.80 +/- 120.18 mg/dL for D20 (p < 0.05) was also observed. Conclusion: LI should be explored as an auxiliary therapy for control of complications of diabetes because it can alter the carbohydrate and lipid metabolism of rats with diabetes.

Improvement in Quality of Life of An Oncological Patient by Laser Phototherapy

Objective and Background Data: Common side effects of radiotherapy (RT) to the head and neck include oral mucositis, xerostomia, and severe pain. The aim of this study is to report improvement in the quality of life of an oncological patient by laser phototherapy (LPT). Clinical Case and Laser Phototherapy Protocol: The patient, a 15-year-old girl diagnosed with mucoepidermoid carcinoma, underwent surgical excision of a tumor of the left palatomaxilla. After that, she was subjected to 35 sessions of RT (2 Gy/d). Clinical examination revealed the spread of severe ulcerations to the jugal mucosa, gums, lips, hard palate, and tongue (WHO mucositis score 3). She had difficulty in moving her tongue and she was unable to eat any solid food. Oral hygiene orientation and LPT were performed throughout all RT sessions. A continuous diode laser, 660 nm, 40 mW, 6 J/cm(2), 0.24 J per point in contact mode, with spot size of 0.04 cm(2) was used in the entire oral cavity. A high-power diode laser at 1 W, 10 sec per cm of mucositis, approximately 10 J/cm(2), was used in defocused mode only on ulcerative lesions. After the first laser irradiation session, decreases in pain and xerostomia were reported; however, a more significant improvement was seen after five sessions. At that point although the mucositis score was still 2, the patient reported that she was free of pain, and consequently a palatine plate could be made to rehabilitate the entire surgical area. Seventeen laser irradiation sessions were necessary to eliminate all oral mucositis lesions. Conclusion: Normal oral function and consequent improvements in the quality of life of this oncologic patient were observed with LPT.

O Intuitivo e o Lógico no Conhecimento Matemático: análise de uma proposta pedagógica em relação a abordagens filosóficas atuais e ao contexto educacional da matemática

In this paper, we consider Meneghetti & Bicudo's proposal (2003) regarding the constitution of mathematical knowledge and analyze it with respect to the following two focuses: in relation to conceptions of mathematical knowledge following the fundamentalist crisis in mathematics; and in the educational context of mathematics. The investigation of the first focus is done analyzing new claims in mathematical philosophy. The investigation of the second focus is done firstly via a theoretical reflection followed by an examination of the implementation of the proposal in the process of development of didactic materials for teaching and learning Mathematics. Finally, we present the main results of the application of one of those materials.

A Draft of the Human Septin Interactome

Background: Septins belong to the GTPase superclass of proteins and have been functionally implicated in cytokinesis and the maintenance of cellular morphology. They are found in all eukaryotes, except in plants. In mammals, 14 septins have been described that can be divided into four groups. It has been shown that mammalian septins can engage in homo- and heterooligomeric assemblies, in the form of filaments, which have as a basic unit a hetero-trimeric core. In addition, it has been speculated that the septin filaments may serve as scaffolds for the recruitment of additional proteins. Methodology/Principal Findings: Here, we performed yeast two-hybrid screens with human septins 1-10, which include representatives of all four septin groups. Among the interactors detected, we found predominantly other septins, confirming the tendency of septins to engage in the formation of homo- and heteropolymeric filaments. Conclusions/Significance: If we take as reference the reported arrangement of the septins 2, 6 and 7 within the heterofilament, (7-6-2-2-6-7), we note that the majority of the observed interactions respect the ""group rule"", i.e. members of the same group (e. g. 6, 8, 10 and 11) can replace each other in the specific position along the heterofilament. Septins of the SEPT6 group preferentially interacted with septins of the SEPT2 group (p<0.001), SEPT3 group (p<0.001) and SEPT7 group (p<0.001). SEPT2 type septins preferentially interacted with septins of the SEPT6 group (p<0.001) aside from being the only septin group which interacted with members of its own group. Finally, septins of the SEPT3 group interacted preferentially with septins of the SEPT7 group (p<0.001). Furthermore, we found non-septin interactors which can be functionally attributed to a variety of different cellular activities, including: ubiquitin/sumoylation cycles, microtubular transport and motor activities, cell division and the cell cycle, cell motility, protein phosphorylation/signaling, endocytosis, and apoptosis.

NMR quadrupolar system described as Bose-Einstein-condensate-like system

This paper presents a description of nuclear magnetic resonance (NMR) of quadrupolar systems using the Holstein-Primakoff (HP) formalism and its analogy with a Bose-Einstein condensate (BEC) system. Two nuclear spin systems constituted of quadrupolar nuclei I=3/2 ((23)Na) and I=7/2 ((133)Cs) in lyotropic liquid crystals were used for experimental demonstrations. Specifically, we derived the conditions necessary for accomplishing the analogy, executed the proper experiments, and compared with quantum mechanical prediction for a Bose system. The NMR description in the HP representation could be applied in the future as a workbench for BEC-like systems, where the statistical properties may be obtained using the intermediate statistic, first established by Gentile. The description can be applied for any quadrupolar systems, including new developed solid-state NMR GaAS nanodevices.

The MX2 macromolecular crystallography beamline: a wiggler X-ray source at the LNLS

The Brazilian Synchrotron Light Laboratory [Laboratorio Nacional de Luz Sincrotron (LNLS), Campinas, SP, Brazil] is the first commissioned synchrotron light source in the southern hemisphere. The first wiggler macromolecular crystallography beamline (MX2) at the LNLS has been recently constructed and brought into operation. Here the technical design, experimental set-up, parameters of the beamline and the first experimental results obtained at MX2 are described. The beamline operates on a 2.0 T hybrid 30-pole wiggler, and its optical layout includes collimating mirror, Si( 111) double-crystal monochromator and toroidal bendable mirror. The measured flux density at the sample position at 8.7 eV reaches 4.8 x 10(11) photons s(-1) mm(-2) (100 mA)(-1). The beamline is equipped with a MarResearch Desktop Beamline Goniostat (MarDTB) and 3 x 3 MarMosaic225 CCD detector, and is controlled by a customized version of the Blu-Ice software. A description of the first X-ray diffraction data sets collected at the MX2 LNLS beamline and used for macromolecular crystal structure solution is also provided.

DAVID HOMEOMORPHISMS VIA CARLESON BOXES

We construct a family of examples of increasing homeomorphisms of the real line whose local quasi-symmetric distortion blows up almost everywhere, which nevertheless can be realized as the boundary values of David homeomorphisms of the upper half-plane. The construction of such David extensions uses Carleson boxes.

An alternative to the Pythagorean rule? Reevaluating Problem 1 of cuneiform tablet BM 34 568

The first problem of the Seleucid mathematical cuneiform tablet BM 34 568 calculates the diagonal of a rectangle from its sides without resorting to the Pythagorean rule. For this reason, it has been a source of discussion among specialists ever since its first publication. but so far no consensus in relation to its mathematical meaning has been attained. This paper presents two new interpretations of the scribe`s procedure. based on the assumption that he was able to reduce the problem to a standard Mesopotamian question about reciprocal numbers. These new interpretations are then linked to interpretations of the Old Babylonian tablet Plimpton 322 and to the presence of Pythagorean triples in the contexts of Old Babylonian and Hellenistic mathematics. (C) 2007 Elsevier Inc. All rights reserved.

Residual stresses in titanium nitride thin films obtained with step variation of substrate bias voltage during deposition

In this work, a series of depositions of titanium nitride (TiN) films on M2 and D2 steel substrates were conducted in a Triode Magnetron Sputtering chamber. The temperature; gas flow and pressure were kept constant during each run. The substrate bias was either decreased or increased in a sequence of steps. Residual stress measurements were later conducted through the grazing X-ray diffraction method. Different incident angles were used in order to change the penetration depth and to obtain values of residual stress at different film depths. A model described by Dolle was adapted as an attempt to calculate the values of residual stress at each incident angle as a function of the value from each individual layer. Stress results indicated that the decrease in bias voltage during the deposition has produced compressive residual stress gradients through the film thickness. On the other hand, much less pronounced gradients were found in one of the films deposited with increasing bias voltage. (C) 2010 Elsevier B.V. All rights reserved.