Geometrias não-eucludianas como anomalias: implicações para o ensino de geometria e medidas

This present research the aim to show to the reader the Geometry non-Euclidean while anomaly indicating the pedagogical implications and then propose a sequence of activities, divided into three blocks which show the relationship of Euclidean geometry with non-Euclidean, taking the Euclidean with respect to analysis of the anomaly in non-Euclidean. PPGECNM is tied to the line of research of History, Philosophy and Sociology of Science in the Teaching of Natural Sciences and Mathematics. Treat so on Euclid of Alexandria, his most famous work The Elements and moreover, emphasize the Fifth Postulate of Euclid, particularly the difficulties (which lasted several centuries) that mathematicians have to understand him. Until the eighteenth century, three mathematicians: Lobachevsky (1793 - 1856), Bolyai (1775 - 1856) and Gauss (1777-1855) was convinced that this axiom was correct and that there was another geometry (anomalous) as consistent as the Euclid, but that did not adapt into their parameters. It is attributed to the emergence of these three non-Euclidean geometry. For the course methodology we started with some bibliographical definitions about anomalies, after we ve featured so that our definition are better understood by the readers and then only deal geometries non-Euclidean (Hyperbolic Geometry, Spherical Geometry and Taxicab Geometry) confronting them with the Euclidean to analyze the anomalies existing in non-Euclidean geometries and observe its importance to the teaching. After this characterization follows the empirical part of the proposal which consisted the application of three blocks of activities in search of pedagogical implications of anomaly. The first on parallel lines, the second on study of triangles and the third on the shortest distance between two points. These blocks offer a work with basic elements of geometry from a historical and investigative study of geometries non-Euclidean while anomaly so the concept is understood along with it s properties without necessarily be linked to the image of the geometric elements and thus expanding or adapting to other references. For example, the block applied on the second day of activities that provides extend the result of the sum of the internal angles of any triangle, to realize that is not always 180° (only when Euclid is a reference that this conclusion can be drawn)

Resonances and subharmonic bifurcations of large amplitude periodic orbits of planar polynomial vector fields

In this work are studied periodic perturbations, depending on two parameters, of planar polynomial vector fields having an annulus of large amplitude periodic orbits, which accumulate on a symmetric infinite heteroclinic cycle. Such periodic orbits and the heteroclinic trajectory can be seen only by the global consideration of the polynomial vector fields on the whole plane, and not by their restriction to any compact set. The global study involving infinity is performed via the Poincare Compactification. It is shown that, for certain types of periodic perturbations, one can seek, in a neighborhood of the origin in the parameter plane, curves C-(m) of subharmonic bifurcations, for which the periodically perturbed system has subharmonics of order m, for any integer m.

Reversibility properties of semigroup actions on homogeneous spaces

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Generic Bifurcations of Planar Filippov Systems via Geometric Singular Perturbations

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

On fuzzy ideals and fuzzy filters of fuzzy lattices

In the literature there are several proposals of fuzzi cation of lattices and ideals concepts. Chon in (Korean J. Math 17 (2009), No. 4, 361-374), using the notion of fuzzy order relation de ned by Zadeh, introduced a new notion of fuzzy lattice and studied the level sets of fuzzy lattices, but did not de ne a notion of fuzzy ideals for this type of fuzzy lattice. In this thesis, using the fuzzy lattices de ned by Chon, we de ne fuzzy homomorphism between fuzzy lattices, the operations of product, collapsed sum, lifting, opposite, interval and intuitionistic on bounded fuzzy lattices. They are conceived as extensions of their analogous operations on the classical theory by using this de nition of fuzzy lattices and introduce new results from these operators. In addition, we de ne ideals and lters of fuzzy lattices and concepts in the same way as in their characterization in terms of level and support sets. One of the results found here is the connection among ideals, supports and level sets. The reader will also nd the de nition of some kinds of ideals and lters as well as some results with respect to the intersection among their families. Moreover, we introduce a new notion of fuzzy ideals and fuzzy lters for fuzzy lattices de ned by Chon. We de ne types of fuzzy ideals and fuzzy lters that generalize usual types of ideals and lters of lattices, such as principal ideals, proper ideals, prime ideals and maximal ideals. The main idea is verifying that analogous properties in the classical theory on lattices are maintained in this new theory of fuzzy ideals. We also de ne, a fuzzy homomorphism h from fuzzy lattices L and M and prove some results involving fuzzy homomorphism and fuzzy ideals as if h is a fuzzy monomorphism and the fuzzy image of a fuzzy set ~h(I) is a fuzzy ideal, then I is a fuzzy ideal. Similarly, we prove for proper, prime and maximal fuzzy ideals. Finally, we prove that h is a fuzzy homomorphism from fuzzy lattices L into M if the inverse image of all principal fuzzy ideals of M is a fuzzy ideal of L. Lastly, we introduce the notion of -ideals and - lters of fuzzy lattices and characterize it by using its support and its level set. Moreover, we prove some similar properties in the classical theory of - ideals and - lters, such as, the class of -ideals and - lters are closed under intersection. We also de ne fuzzy -ideals of fuzzy lattices, some properties analogous to the classical theory are also proved and characterize a fuzzy -ideal on operation of product between bounded fuzzy lattices L and M and prove some results.

Treatment with Azadirachta indica in diabetic pregnant rats: Negative effects on maternal outcome

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The role of salt abuse on risk for hypercalciuria

Background: Elevated sodium excretion in urine resulting from excessive sodium intake can lead to hypercalciuria and contribute to the formation of urinary stones. The aim of this study was to evaluate salt intake in patients with urinary lithiasis and idiopathic hypercalciuria (IH).Methods: Between August 2007 and June 2008, 105 lithiasic patients were distributed into 2 groups: Group 1 (n = 55): patients with IH (urinary calcium excretion > 250 mg in women and 300 mg in men with normal serum calcium); Group 2 (n = 50): normocalciuric patients (NC). Inclusion criteria were: age over 18 years, normal renal function (creatinine clearance >= 60 ml/min), absent proteinuria and negative urinary culture. Pregnant women, patients with intestinal pathologies, chronic diarrhea or using corticoids were excluded. The protocol of metabolic investigation was based on non-consecutive collection of two 24-hour samples for dosages of: calcium, sodium, uric acid, citrate, oxalate, magnesium and urinary volume. Food intake was evaluated by the three-day dietary record quantitative method, and the Body Mass Index (BMI) was calculated and classified according to the World Health Organization (WHO). Sodium intake was evaluated based on 24-hour urinary sodium excretion.Results: The distribution in both groups as regards mean age (42.11 +/- 10.61 vs. 46.14 +/- 11.52), weight (77.14 +/- 16.03 vs. 75.99 +/- 15.80), height (1.64 +/- 0.10 vs. 1.64 +/- plusorminus 0.08) and BMI (28.78 +/- 5.81 vs. 28.07 +/- 5.27) was homogeneous. Urinary excretion of calcium (433.33 +/- 141.92 vs. 188.93 +/- 53.09), sodium (280.08 +/- 100.94 vs. 200.44.93 +/- 65.81), uric acid (880.63 +/- 281.50 vs. 646.74 +/- 182.76) and magnesium (88.78 +/- 37.53 vs. 64.34 +/- 31.84) was significantly higher in the IH group (p < 0.05). There was no statistical difference in calcium intake between the groups, and there was significantly higher salt intake in patients with IH than in NC.Conclusions: This study showed that salt intake was higher in patients with IH as compared to NC.

Genotoxic and mutagenic effects of fipronil on mice

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Ultra-structure and histochemistry of digestive cells of Podisus nigrispinus (Hemiptera: Pentatomidae) fed with prey reared on bt-cotton

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

STABLE PIECEWISE POLYNOMIAL VECTOR FIELDS

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On the algebraic K theory of the massive D8 and M9-branes

In this paper we review some basic relations of algebraic K theory and we formulate them in the language of D-branes. Then we study the relation between the D8-branes wrapped on an orientable, compact manifold W in a massive Type IIA, supergravity background and the M9-branes wrapped on a compact manifold Z in a massive d = 11 supergravity background from the K-theoretic point of view. By interpreting the D8-brane charges as elements of K-0(C(W)) and the (inequivalent classes of) spaces of gauge fields on the M9-branes as the elements of K-0(C(Z) x ((k) over bar*) G) where G is a one-dimensional compact group, a connection between charges and gauge fields is argued to exists. This connection could be realized as a composition map between the corresponding algebraic K theory groups.

Dissipative hydrodynamics coupled to chiral fields

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

New proposal of classification of seeds based on forms of phytochrome instead of photoblastism

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Periodic orbits for a class of reversible quadratic vector field on R-3

For a class of reversible quadratic vector fields on R-3 we study the periodic orbits that bifurcate from a heteroclinic loop having two singular points at infinity connected by an invariant straight line in the finite part and another straight line at infinity in the local chart U-2. More specifically, we prove that for all n is an element of N, there exists epsilon(n) > 0 such that the reversible quadratic polynomial differential systemx = a(0) + a(1y) + a(3y)(2) + a(4Y)(2) + epsilon(a(2x)(2) + a(3xz)),y = b(1z) + b(3yz) + epsilon b(2xy),z = c(1y) +c(4az)(2) + epsilon c(2xz)in R-3, with a(0) < 0, b(1)c(1) < 0, a(2) < 0, b(2) < a(2), a(4) > 0, c(2) < a(2) and b(3) is not an element of (c(4), 4c(4)), for epsilon is an element of (0, epsilon(n)) has at least n periodic orbits near the heteroclinic loop. (c) 2007 Elsevier B.V. All rights reserved.

Non-isothermal kinetic of oxidation of tungsten carbide

Tungsten carbide, WC, has shown dissimilar thermal behavior when it is heated on changeable heating rate and flow of oxidant atmosphere. The oxidation of WC to WO3 tends to be in a single and slow kinetic step on slow heating rate and/or low flux of air. Kinetic parameters, on non-isothermal condition, could be evaluated to the oxidation of WC to heating rate below 15 degrees C min(-1) or low flow of air (10 mL min(-1)). The reaction is governed by nucleation and growth at 5 to 10 degrees C min(-1) then the tendency is to be autocatalytic, JMA and SB, respectively.