Computing Distance Functions from Generalized Sources on Weighted Polyhedral Surfaces

We present algorithms for computing approximate distance functions and shortest paths from a generalized source (point, segment, polygonal chain or polygonal region) on a weighted non-convex polyhedral surface in which obstacles (represented by polygonal chains or polygons) are allowed. We also describe an algorithm for discretizing, by using graphics hardware capabilities, distance functions. Finally, we present algorithms for computing discrete k-order Voronoi diagrams

Generalized Higher-Order Voronoi Diagrams on Polyhedral Surfaces

We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a possibly non-convex polyhedral surface in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) on a polyhedral surface with obstacles. To obtain the discrete Voronoi diagrams our algorithms, exploiting hardware graphics capabilities, compute shortest path distances defined by the sites

Idoneidad didáctica de un protocolo sociocultural de enseñanza y aprendizaje de las matemáticas

En este estudio se evalúa la adecuación de un protocolo para la enseñanza del concepto de poliedro regular, destinado a alumnos de 14 y 15 años. Este protocolo se ha diseñado desde una perspectiva sociocultural y su evaluación se basa en la aplicación de los criterios de idoneidad didáctica que ofrece el enfoque ontosemiótico. La idoneidad se estudia con la revisión de sus diferentes dimensiones: matemática, cognitiva, interaccional, mediacional, emocional y ecológica. El análisis ha permitido detectar algunos factores que favorecen la validez del protocolo y la adecuación para su empleo en el aula, como el tipo de discurso, el uso de material manipulable o el trabajo cooperativo

Comparison of the bacterial Enhancin-like proteins from Yersinia and Bacillus spp. with a baculovirus Enhancin

Enhancins are a class of metalloproteases found in some baculoviruses that enhance viral infection by degrading the peritrophic, membrane (PM) of the insect midgut. However, sequencing has revealed enhancin-like genes with 24-25% homology to viral enhancins, in the genomes of Yersinia pestis and Bacillus anthracis. AcMNPV does not encode enhancin therefore recombinant AcMNPV budded viruses (BVs) and polyhedra inclusion bodies (PIBs) were generated expressing the bacterial Enhancins. Bacterial Enhancins were found to be cytotoxic when compared to viral enhancin, however, larval bioassays suggested that the bacterial Enhancins did not enhance infection in the same way as viral Enhancin. This suggests that the bacterial Enhancins may have evolved a distinct biochemical function. (c) 2005 Elsevier Inc. All rights reserved.

Topotactic oxidation of TiGaPO-1, a pyridine-templated titanium gallophosphate with a new octahedral-tetrahedral 3-D framework structure containing Ti-III/Ti-IV

The first 3-D open-framework TiGaPO complex, constructed from (TiO6)-O-III, (TiO6)-O-IV, GaO4, and PO4 polyhedra, contains pyridinium cations in a 1-D pore network and can be oxidized in air at 543 K with retention of the original framework structure.

Three-dimensional random Voronoi tessellations: From cubic crystal lattices to Poisson point processes

We perturb the SC, BCC, and FCC crystal structures with a spatial Gaussian noise whose adimensional strength is controlled by the parameter a, and analyze the topological and metrical properties of the resulting Voronoi Tessellations (VT). The topological properties of the VT of the SC and FCC crystals are unstable with respect to the introduction of noise, because the corresponding polyhedra are geometrically degenerate, whereas the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. For weak noise, the mean area of the perturbed BCC and FCC crystals VT increases quadratically with a. In the case of perturbed SCC crystals, there is an optimal amount of noise that minimizes the mean area of the cells. Already for a moderate noise (a>0.5), the properties of the three perturbed VT are indistinguishable, and for intense noise (a>2), results converge to the Poisson-VT limit. Notably, 2-parameter gamma distributions are an excellent model for the empirical of of all considered properties. The VT of the perturbed BCC and FCC structures are local maxima for the isoperimetric quotient, which measures the degre of sphericity of the cells, among space filling VT. In the BCC case, this suggests a weaker form of the recentluy disproved Kelvin conjecture. Due to the fluctuations of the shape of the cells, anomalous scalings with exponents >3/2 is observed between the area and the volumes of the cells, and, except for the FCC case, also for a->0. In the Poisson-VT limit, the exponent is about 1.67. As the number of faces is positively correlated with the sphericity of the cells, the anomalous scaling is heavily reduced when we perform powerlaw fits separately on cells with a specific number of faces.

Benders, metric and cutset inequalities for multicommodity capacitated network design

Solving multicommodity capacitated network design problems is a hard task that requires the use of several strategies like relaxing some constraints and strengthening the model with valid inequalities. In this paper, we compare three sets of inequalities that have been widely used in this context: Benders, metric and cutset inequalities. We show that Benders inequalities associated to extreme rays are metric inequalities. We also show how to strengthen Benders inequalities associated to non-extreme rays to obtain metric inequalities. We show that cutset inequalities are Benders inequalities, but not necessarily metric inequalities. We give a necessary and sufficient condition for a cutset inequality to be a metric inequality. Computational experiments show the effectiveness of strengthening Benders and cutset inequalities to obtain metric inequalities.

Lead and aluminum bonding in Pb-Al metaphosphate glasses

The bonding properties of cations in phosphate glasses determine many short- and medium-range structural features in the glass network, hence influencing bulk properties. In this work, Pb-Al-metaphosphate glasses (1 - x)Pb-(PO(3))(2)center dot xAI(PO(3))(3) with 0 <= - x <= 1 were analyzed to determine the effect of the substitution of Pb by Al on the glass structure in the metaphosphate composition. The glass transition temperature and density were measured as a function of the Al concentration. The vibrational and structural properties were probed by Raman spectroscopy and nuclear magnetic resonance of (31)P, (27)Al, and (207)Pb. Aluminum incorporates homogeneously in the glass creating a stiffer and less packed network. The average coordination number for Al decreases from 5.9 to 5.0 as x increases from 0.1 to 1, indicating more covalent Al-O bonds. The coordination number of Pb in these glasses is greater than 8, showing an increasing ionic behavior for compositions richer in Al. A quantitative analysis of the phosphate speciation shows definite trends in the bonding of AlO(n) groups and phosphate tetrahedra. In glasses with x < 0.48, phosphate groups share preferentially only one nonbridging O corner with an AlO(n) coordination polyhedron. For x > 0.48 more than one nonbridging O can be linked to AlO(n) polyhedra. There is no corner sharing of O between AlO(n) and PbO(n) polyhedra nor between AlO(n) themselves throughout the compositional range. The PbO(n) coordination polyhedra show considerable nonbridging O sharing, with each O participating in the coordination sphere of at least two Pb. The bonding preferences determined for Al are consistent with the behavior observed in Na-Al and Ca-Al metaphosphates, indicating this may be a general behavior for ternary phosphate glasses.

New cutting-planes for the time-and/or precedence-constrained ATSP and directed VRP

In this paper, we introduce five classes of new valid cutting planes for the precedence-constrained (PC) and/or time-window-constrained (TW) Asymmetric Travelling Salesman Problems (ATSPs) and directed Vehicle Routing Problems (VRPs). We show that all five classes of new inequalities are facet-defining for the directed VRP-TW, under reasonable conditions and the assumption that vehicles are identical. Similar proofs can be developed for the VRP-PC. As ATSP-TW and PC-ATSP can be formulated as directed identical-vehicle VRP-TW and PC-VRP, respectively, this provides a link to study the polyhedral combinatorics for the ATSP-TW and PC-ATSP. The first four classes of these new cutting planes are cycle-breaking inequalities that are lifted from the well-known D^-_k and D⁺_k inequalities (see Grötschel and Padberg in Polyhedral theory. The traveling salesman problem: a guided tour of combinatorial optimization, Wiley, New York, 1985). The last class of new cutting planes, the TW ₂ inequalities, are infeasible-path elimination inequalities. Separation of these constraints will also be discussed. We also present prelimanry numerical results to demonstrate the strengh of these new cutting planes.

Avaliação preliminar da viabilidade de produção in vitro de um isolado brasileiro de baculovírus Spodoptera frugiperda MNPV

In vivo production of viral biopesticides is the major source of viral insecticides currently in the marketplace. However, this system presents limitations during production scale-up. For the Spodoptera frugiperda nucleopolyhedrovirus (SfMNPV), the insect used for replication has cannibalistic characteristics, thus production is even more difficult. Insect cells are commonly used for in vitro baculovirus production. Most of these cell lines are derived from Lepidoptera species. The Sf21 cell line is derived from Spodoptera frugiperda caterpillar ovarian tissue, and its clonal isolate Sf9 has been used for biopesticide production due to its ease of growth in suspension cultures. In this work, the in vitro production capabilities of a Brazilian SfMNPV isolate obtained from cornfields was evaluated. Comparison of polyhedra production was carried out using both Sf21 and Sf9 cells, based on volumetric and specific yields. Both cell lines were cultivated in Hyclone medium supplemented with different fetal bovine serum concentrations (2,5 and 5%). The best results were obtained using Sf9 cells supplemented with 5% serum. These results were further confirmed quantitively through kinetic parameter estimation for both cells lines and different serum concentrations. After seven successive passages, this system still presented high specific polyhedra production

A relação de Euler para poliedros

In this paper we analyze the Euler Relation generally using as a means to visualize the fundamental idea presented manipulation of concrete materials, so that there is greater ease of understanding of the content, expanding learning for secondary students and even fundamental. The study is an introduction to the topic and leads the reader to understand that the notorious Euler Relation if inadequately presented, is not sufficient to establish the existence of a polyhedron. For analyzing some examples, the text inserts the idea of doubt, showing cases where it is not fit enough numbers to validate the Euler Relation. The research also highlights a theorem certainly unfamiliar to many students and teachers to research the polyhedra, presenting some very simple inequalities relating the amounts of edges, vertices and faces of any convex polyhedron, which clearly specifies the conditions and sufficient necessary for us to see, without the need of viewing the existence of the solid screen. And so we can see various polyhedra and facilitate understanding of what we are exposed, we will use Geogebra, dynamic application that combines mathematical concepts of algebra and geometry and can be found through the link http://www.geogebra.org

Photo luminescence: A probe for short, medium and long-range self-organization order in ZrTiO4 oxide

Photoluminescent disordered ZrTiO4 powders were obtained by the polymeric precursor soft-chemical method. This oxide system (ordered and disordered) was characterized by photoluminescence, Raman spectroscopy, X-ray diffraction, differential scanning calorimetry and UV vis absorption experiments. The UV absorption tail formation in the disordered oxides was related to the diminution of optical band gap. In the disordered phase, this oxide displayed broad band photoluminescence caused by change in coordination number of titanium and zirconium with oxygen atoms. The gap decreased from 3.09 eV in crystalline oxide to 2.16 eV in disordered oxide. The crystalline oxide presented an orthorhombic alpha-PbO2-type structure in which Zr4+ and Ti4+ were randomly distributed in octahedral coordination polyhedra with oxygen atoms. The amorphous-crystalline transition occurred at almost 700 degrees C, at which point the photoluminescence vanished. The Raman peak at close to 80-200 cm(-1) indicated the presence of locally ordered Ti-O-n and Zr-O-n polyhedra in disordered photoluminescent oxides. (c) 2006 Elsevier B.V. All rights reserved.

Synthesis and structural investigations on TeO2-PbF2-CdF2 glasses and transparent glass-ceramics

New glasses have been prepared in the oxifluoride mixed system TeO2-PbF2-CdF2. Starting from pure TeO2 the addition of the fluorides leads to a decrease in the glasses characteristic temperatures. Also from Raman scattering results a structural evolution was observed where the number of structural units described as [TeO3] trigonal pyramids and [TeO3+1] polyhedra increases at the expense of the [TeO4] trigonal bipyramids supposed to exist in the TeO2, rich samples. Transparent glass ceramics were obtained from the glass with composition 80TeO(2)-10PbF(2)-10CdF(2), (mol%) with the PbTe3O7 crystalline phase being identified by X-ray diffraction and EXAFS measurements performed at the Te K, Cd K and Pb L-III edges. Also from Exafs measurements it is proposed that cadmium ions are preferentially surrounded by oxygen atoms although they were in a fluoride anion environment in the starting material. (C) 2002 Published by Elsevier B.V. Ltd.

Influence of the modifier on the short and long range disorder of stannate perovskites

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Thermal analysis applied in the crystallization study of SrSnO3

SrSnO3 was synthesized by the polymeric precursor method with elimination of carbon in oxygen atmosphere at 250 A degrees C for 24 h. The powder precursors were characterized by TG/DTA and high temperature X-ray diffraction (HTXRD). After calcination at 500, 600 and 700 A degrees C for 2 h, samples were evaluated by X-ray diffraction (XRD), infrared spectroscopy (IR) and Rietveld refinement of the XRD patterns for samples calcined at 900, 1,000 and 1,100 A degrees C. During thermal treatment of the powder precursor ester combustion was followed by carbonate decomposition and perovskite crystallization. No phase transition was observed as usually presented in literature for SrSnO3 that had only a rearrangement of SnO6 polyhedra.