54 resultados para Degree of maps


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

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

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

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Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

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In this note we study coincidence of pairs of fiber-preserving maps f, g : E-1 -> E-2 where E-1, E-2 are S-n-bundles over a space B. We will show that for each homotopy class vertical bar f vertical bar of fiber-preserving maps over B, there is only one homotopy class vertical bar g vertical bar such that the pair (f, g), where vertical bar g vertical bar = vertical bar tau circle f vertical bar can be deformed to a coincidence free pair. Here tau : E-2 -> E-2 is a fiber-preserving map which is fixed point free. In the case where the base is S-1 we classify the bundles, the homotopy classes of maps over S-1 and the pairs which can be deformed to coincidence free. At the end we discuss the self-coincidence problem. (C) 2010 Elsevier B.V. All rights reserved.

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The main purpose of this work is to study coincidences of fiber-preserving self-maps over the circle S 1 for spaces which are fiberbundles over S 1 and the fiber is the Klein bottle K. We classify pairs of self-maps over S 1 which can be deformed fiberwise to a coincidence free pair of maps. © 2012 Pushpa Publishing House.

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Introduction: The aim of this study was to assess the influence of curing time and power on the degree of conversion and surface microhardness of 3 orthodontic composites. Methods: One hundred eighty discs, 6 mm in diameter, were divided into 3 groups of 60 samples according to the composite used-Transbond XT (3M Unitek, Monrovia, Calif), Opal Bond MV (Ultradent, South Jordan, Utah), and Transbond Plus Color Change (3M Unitek)-and each group was further divided into 3 subgroups (n = 20). Five samples were used to measure conversion, and 15 were used to measure microhardness. A light-emitting diode curing unit with multiwavelength emission of broad light was used for curing at 3 power levels (530, 760, and 1520 mW) and 3 times (8.5, 6, and 3 seconds), always totaling 4.56 joules. Five specimens from each subgroup were ground and mixed with potassium bromide to produce 8-mm tablets to be compared with 5 others made similarly with the respective noncured composite. These were placed into a spectrometer, and software was used for analysis. A microhardness tester was used to take Knoop hardness (KHN) measurements in 15 discs of each subgroup. The data were analyzed with 2 analysis of variance tests at 2 levels. Results: Differences were found in the conversion degree of the composites cured at different times and powers (P < 0.01). The composites showed similar degrees of conversion when light cured at 8.5 seconds (80.7%) and 6 seconds (79.0%), but not at 3 seconds (75.0%). The conversion degrees of the composites were different, with group 3 (87.2%) higher than group 2 (83.5%), which was higher than group 1 (64.0%). Differences in microhardness were also found (P < 0.01), with lower microhardness at 8.5 seconds (35.2 KHN), but no difference was observed between 6 seconds (41.6 KHN) and 3 seconds (42.8 KHN). Group 3 had the highest surface microhardness (35.9 KHN) compared with group 2 (33.7 KHN) and group 1 (30.0 KHN). Conclusions: Curing time can be reduced up to 6 seconds by increasing the power, with a slight decrease in the degree of conversion at 3 seconds; the decrease has a positive effect on the surface microhardness.

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In this paper we introduce a type of Hypercomplex Fourier Series based on Quaternions, and discuss on a Hypercomplex version of the Square of the Error Theorem. Since their discovery by Hamilton (Sinegre [1]), quaternions have provided beautifully insights either on the structure of different areas of Mathematics or in the connections of Mathematics with other fields. For instance: I) Pauli spin matrices used in Physics can be easily explained through quaternions analysis (Lan [2]); II) Fundamental theorem of Algebra (Eilenberg [3]), which asserts that the polynomial analysis in quaternions maps into itself the four dimensional sphere of all real quaternions, with the point infinity added, and the degree of this map is n. Motivated on earlier works by two of us on Power Series (Pendeza et al. [4]), and in a recent paper on Liouville’s Theorem (Borges and Mar˜o [5]), we obtain an Hypercomplex version of the Fourier Series, which hopefully can be used for the treatment of hypergeometric partial differential equations such as the dumped harmonic oscillation.

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Climatic factors directly influence growth and productivity of plants inside greenhouses, where temperature can be considered one of the major parameter in this context. Thus, the aim of this research was to develop a low cost device for thermal sensing and data acquisition, and use it in data collection and analysis of spatial variability of temperature inside a greenhouse with tropical climate. The developed equipment for thermal measurements showed a high degree of accuracy and fast responses in measurements, proving its efficiency. The data analysis interpretations were made from the elaborations of variograms and of tridimensional maps generated by a geostatistical software. The processed data analysis presented that a greenhouse without thermal control has spatial variations of air temperature, both in the sampled horizontals layers as in the three analyzed vertical columns, presenting variations of up to 3.6 ºC in certain times.