5 resultados para Equilateral triangles

em Queensland University of Technology - ePrints Archive


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The molecular structure of the sodium borate mineral ameghinite NaB3O3(OH)4 has been determined by the use of vibrational spectroscopy. The crystal structure consists of isolated [B3O3(OH)4]- units formed by one tetrahedron and two triangles. H bonds and Na atoms link these polyanions to form a 3-dimensional framework. The Raman spectrum is dominated by an intense band at 1027 cm-1, attributed to BO stretching vibrations of both the trigonal and tetrahedral boron. A series of Raman bands at 1213, 1245 and 1281cm-1 are ascribed to BOH in-plane bending modes. The infrared spectra are characterized by strong overlap of broad multiple bands. An intense Raman band found at 620 cm-1 is attributed to the bending modes of trigonal and tetrahedral boron. Multiple Raman bands in the OH stretching region are observed at 3206, 3249 and 3385 cm-1. Raman spectroscopy coupled with infrared spectroscopy has enabled aspects about the molecular structure of the borate mineral ameghinite to be assessed.

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Colemanite CaB3O4(OH)3 H2O is a secondary borate mineral formed from borax and ulexite in evaporate deposits of alkaline lacustrine sediments. The basic structure of colemanite contains endless chains of interlocking BO2(OH) triangles and BO3(OH) tetrahedrons with the calcium, water and extra hydroxide units interspersed between these chains. The Raman spectra of colemanite is characterized by an intense band at 3605 cm-1 assigned to the stretching vibration of OH units and a series of bands at 3182, 3300, 3389 and 3534 cm-1 assigned to water stretching vibrations. Infrared bands are observed in similar positions. The BO stretching vibrations of the trigonal and tetrahedral boron are characterized by Raman bands at 876, 1065 and 1084 cm-1. The OBO bending mode is defined by the Raman band at 611 cm-1. It is important to characterize the very wide range of borate minerals including colemanite because of the very wide range of applications of boron containing minerals.

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A travel article about touring in the Rockies, Alberta. MORAINE Lake, held up by a crown of mountains near the small town of Lake Louise, is opal blue. You'd need a precious stone to cut the surface. And even on a hot morning in August, there are plenty around: diamonds of snow decorate the mountain tops and, in their reflections, slice the lake with white triangles. We are at the start of a track that climbs from the lake to Mt Temple, the tallest mountain in the area and two or three hours' walk away. When the track zigzags back, we glimpse the lake through gaps in the conifer forest...

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A new mesh adaptivity algorithm that combines a posteriori error estimation with bubble-type local mesh generation (BLMG) strategy for elliptic differential equations is proposed. The size function used in the BLMG is defined on each vertex during the adaptive process based on the obtained error estimator. In order to avoid the excessive coarsening and refining in each iterative step, two factor thresholds are introduced in the size function. The advantages of the BLMG-based adaptive finite element method, compared with other known methods, are given as follows: the refining and coarsening are obtained fluently in the same framework; the local a posteriori error estimation is easy to implement through the adjacency list of the BLMG method; at all levels of refinement, the updated triangles remain very well shaped, even if the mesh size at any particular refinement level varies by several orders of magnitude. Several numerical examples with singularities for the elliptic problems, where the explicit error estimators are used, verify the efficiency of the algorithm. The analysis for the parameters introduced in the size function shows that the algorithm has good flexibility.