Calculando distância em geometria espacial usando material manipulável como recurso didático

This work presents a proposal for introducing the teaching of Geometry Space study attempts to demonstrate that the use of manipulatives as a teaching resource can be an alternative learning facilitator for fixing the primitive concepts of geometry, the postulates and theorems, position relationships between points, lines and planes and calculating distances. The development makes use of a sequence of activities aimed at ensuring that students can build a more systematic learning and these are divided into four steps

Characterization of granite matrix porosity and pore-space geometry by in situ and laboratory methods

Most available studies of interconnected matrix porosity of crystalline rocks are based on laboratory investigations; that is, work on samples that have undergone stress relaxation and were affected by drilling and sample preparation. The extrapolation of the results to in situ conditions is therefore associated with considerable uncertainty, and this was the motivation to conduct the ‘in situ Connected Porosity’ experiment at the Grimsel Test Site (Central Swiss Alps). An acrylic resin doped with fluorescent agents was used to impregnate the microporous granitic matrix in situ around an injection borehole, and samples were obtained by overcoring. The 3-D structure of the porespace, represented by microcracks, was studied by U-stage fluorescence microscopy. Petrophysical methods, including the determination of porosity, permeability and P -wave velocity, were also applied. Investigations were conducted both on samples that were impregnated in situ and on non-impregnated samples, so that natural features could be distinguished from artefacts. The investigated deformed granites display complex microcrack populations representing a polyphase deformation at varying conditions. The crack population is dominated by open cleavage cracks in mica and grain boundary cracks. The porosity of non-impregnated samples lies slightly above 1 per cent, which is 2–2.5 times higher than the in situ porosity obtained for impregnated samples. Measurements of seismic velocities (Vp ) on spherical rock samples as a function of confining pressure, spatial direction and water saturation for both non-impregnated and impregnated samples provide further constraints on the distinction between natural and induced crack types. The main conclusions are that (1) an interconnected network of microcracks exists in the whole granitic matrix, irrespective of the distance to ductile and brittle shear zones, and (2) conventional laboratory methods overestimate the matrix porosity. Calculations of contaminant transport through fractured media often rely on matrix diffusion as a retardation mechanism.

Effect of denture fabrication and wear on closest speaking space and interocclusal distance during deglutition

Statement of problem. The accuracy of assessing maxillomandibular relationships for trial bases and dentures using phonetic and swallowing methods has not been compared to that observed with definitive prostheses. Thus, there is no evidence to prove whether measurements obtained through such methods remain the same after adaptation to dentures.Purpose. This study investigated changes in the closest speaking space, interocclusal rest space, and interocclusal distance during deglutition in edentulous patients during and after complete denture treatment.Material and methods. Eighteen edentulous subjects participated in this study and measurements were performed after 7 Intervals of time: (1) with occlusion rims and record bases following creation of the maxillomandibular relationship record, (2) with trial dentures, (3) at Insertion of definitive complete dentures, (4) 1 week, (5) 2 weeks, (6) 1 month, and (7) 3 months after insertion. Recordings of interocclusal distances were made with a mandibular kinesiograph. Closest speaking space was measured during the pronunciation of the word 'seis'. The distance between postural rest position and centric occlusion, or interocclusal rest space, was measured using a kinesiograph. Interocclusal distance during deglutition was tested by recording the closest mandibular position recorded during swallowing of 20 mL of water. Data were analyzed using repeated-measure ANOVA, followed by the Student-Newman-Keuls test (alpha=.05).Results. A significant (P <.01)reduction in the mean closest speaking space was found when it was evaluated using occlusion rims and record bases (4.6 mm) compared with other stages (3.0 to 3.4 mm). No significant differences were found in mean interocclusal rest space and interocclusal distance during deglutition among the time periods evaluated.Conclusions. The presence of occlusion rims can influence mandibular position during pronunciation of the /s/ sound. The arrangement of artificial teeth changes the closest speaking space. However, rest position and deglutition were not affected, either during denture fabrication or short-term use.

Gravitational energy of Kerr and Kerr anti-de Sitter space-times in the teleparallel geometry

In the context of the hamiltonian formulation of the teleparallel equivalent of general relativity we compute the gravitational energy of Kerr and Kerr Anti-de Sitter (Kerr-AdS) space-times. The present calculation is carried out by means of an expression for the energy of the gravitational field that naturally arises from the integral form of the constraint equations of the formalism. In each case, the energy is exactly computed for finite and arbitrary spacelike two-spheres, without any restriction on the metric parameters. In particular, we evaluate the energy at the outer event horizon of the black holes. © SISSA/ISAS 2003.

Convergence analysis and validation of low cost distance metrics for computational cost reduction of the Iterative Closest Point algorithm

The Iterative Closest Point algorithm (ICP) is commonly used in engineering applications to solve the rigid registration problem of partially overlapped point sets which are pre-aligned with a coarse estimate of their relative positions. This iterative algorithm is applied in many areas such as the medicine for volumetric reconstruction of tomography data, in robotics to reconstruct surfaces or scenes using range sensor information, in industrial systems for quality control of manufactured objects or even in biology to study the structure and folding of proteins. One of the algorithm’s main problems is its high computational complexity (quadratic in the number of points with the non-optimized original variant) in a context where high density point sets, acquired by high resolution scanners, are processed. Many variants have been proposed in the literature whose goal is the performance improvement either by reducing the number of points or the required iterations or even enhancing the complexity of the most expensive phase: the closest neighbor search. In spite of decreasing its complexity, some of the variants tend to have a negative impact on the final registration precision or the convergence domain thus limiting the possible application scenarios. The goal of this work is the improvement of the algorithm’s computational cost so that a wider range of computationally demanding problems from among the ones described before can be addressed. For that purpose, an experimental and mathematical convergence analysis and validation of point-to-point distance metrics has been performed taking into account those distances with lower computational cost than the Euclidean one, which is used as the de facto standard for the algorithm’s implementations in the literature. In that analysis, the functioning of the algorithm in diverse topological spaces, characterized by different metrics, has been studied to check the convergence, efficacy and cost of the method in order to determine the one which offers the best results. Given that the distance calculation represents a significant part of the whole set of computations performed by the algorithm, it is expected that any reduction of that operation affects significantly and positively the overall performance of the method. As a result, a performance improvement has been achieved by the application of those reduced cost metrics whose quality in terms of convergence and error has been analyzed and validated experimentally as comparable with respect to the Euclidean distance using a heterogeneous set of objects, scenarios and initial situations.

Scalable algorithms for height field illumination

Global illumination algorithms are at the center of realistic image synthesis and account for non-trivial light transport and occlusion within scenes, such as indirect illumination, ambient occlusion, and environment lighting. Their computationally most difficult part is determining light source visibility at each visible scene point. Height fields, on the other hand, constitute an important special case of geometry and are mainly used to describe certain types of objects such as terrains and to map detailed geometry onto object surfaces. The geometry of an entire scene can also be approximated by treating the distance values of its camera projection as a screen-space height field. In order to shadow height fields from environment lights a horizon map is usually used to occlude incident light. We reduce the per-receiver time complexity of generating the horizon map on N N height fields from O(N) of the previous work to O(1) by using an algorithm that incrementally traverses the height field and reuses the information already gathered along the path of traversal. We also propose an accurate method to integrate the incident light within the limits given by the horizon map. Indirect illumination in height fields requires information about which other points are visible to each height field point. We present an algorithm to determine this intervisibility in a time complexity that matches the space complexity of the produced visibility information, which is in contrast to previous methods which scale in the height field size. As a result the amount of computation is reduced by two orders of magnitude in common use cases. Screen-space ambient obscurance methods approximate ambient obscurance from the depth bu er geometry and have been widely adopted by contemporary real-time applications. They work by sampling the screen-space geometry around each receiver point but have been previously limited to near- field effects because sampling a large radius quickly exceeds the render time budget. We present an algorithm that reduces the quadratic per-pixel complexity of previous methods to a linear complexity by line sweeping over the depth bu er and maintaining an internal representation of the processed geometry from which occluders can be efficiently queried. Another algorithm is presented to determine ambient obscurance from the entire depth bu er at each screen pixel. The algorithm scans the depth bu er in a quick pre-pass and locates important features in it, which are then used to evaluate the ambient obscurance integral accurately. We also propose an evaluation of the integral such that results within a few percent of the ray traced screen-space reference are obtained at real-time render times.

Study of the (D)over-barN Interaction in a QCD Coulomb Gauge Quark Model

We study the (D) over barN interaction at low energies with a quark model inspired in the QCD Hamiltonian in Coulomb gauge. The model Hamiltonian incorporates a confining Coulomb potential extracted from a self-consistent quasiparticle method for the gluon degrees of freedom, and transverse-gluon hyperfine interaction consistent with a finite gluon propagator in the infrared. Initially a constituent-quark mass function is obtained by solving a gap equation and baryon and meson bound-states are obtained in Fock space using a variational calculation. Next, having obtained the constituent-quark masses and the hadron waves functions, an effective meson-nucleon interaction is derived from a quark-interchange mechanism. This leads to a short range meson-baryon interaction and to describe long-distance physics vector- and scalar-meson exchanges described by effective Lagrangians are incorporated. The derived effective (D) over barN potential is used in a Lippmann-Schwinger equation to obtain phase shifts. The results are compared with a recent similar calculation using the nonrelativistic quark model.

Husserl on Geometry and Spatial Representation

Husserl left many unpublished drafts explaining (or trying to) his views on spatial representation and geometry, such as, particularly, those collected in the second part of Studien zur Arithmetik und Geometrie (Hua XXI), but no completely articulate work on the subject. In this paper, I put forward an interpretation of what those views might have been. Husserl, I claim, distinguished among different conceptions of space, the space of perception (constituted from sensorial data by intentionally motivated psychic functions), that of physical geometry (or idealized perceptual space), the space of the mathematical science of physical nature (in which science, not only raw perception has a word) and the abstract spaces of mathematics (free creations of the mathematical mind), each of them with its peculiar geometrical structure. Perceptual space is proto-Euclidean and the space of physical geometry Euclidean, but mathematical physics, Husserl allowed, may find it convenient to represent physical space with a non-Euclidean structure. Mathematical spaces, on their turn, can be endowed, he thinks, with any geometry mathematicians may find interesting. Many other related questions are addressed here, in particular those concerning the a priori or a posteriori character of the many geometric features of perceptual space (bearing in mind that there are at least two different notions of a priori in Husserl, which we may call the conceptual and the transcendental a priori). I conclude with an overview of Weyl's ideas on the matter, since his philosophical conceptions are often traceable back to his former master, Husserl.

Quebra da simetria de sabor na interação de mésons charmosos com o núcleon

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Binding of antioxidant flavone isovitexin to human serum albumin investigated by experimental and computational assays

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Diagnóstico de conflitos em áreas de preservação permanente na bacia do Rio Capivara - Botucatu (SP)

The permanent preservation areas (PPA) established by Brazilian law are there to protect the natural environment. With the expansion of space occupied by man and development of economic activities in these areas were engaged in conflicts characterized PPA, where the use is other than the natural vegetation. According to these paradigms work aims to raise these conflict areas in the River Basin Capivara, Botucatu (SP) with the help of GIS Ilwis 3.4, topographic maps of IBGE and satellite images CBERS 2B. The map was generated from PPA in the GIS by distance calculation in relation to drainage, springs and break line on Cuesta de Botucatu. The classes of land use and natural vegetation were determined by interpretation of satellite images and field visits to check their veracity. With the cutting of the map of land use and natural vegetation in relation to PPA unit it was determined that the total 44,63% PPA is in conflict occupied by pasture, forest plantation, orange, annual crops, farms and irrigated rice project in lowland. This diagnostic characterizes the degradation of the environment and highlights the need to harmonize the economic and urban development with the preservation of the environment to ensure sustainability of the region.

Packing a trunk : a physically based approach with full motional freedom

Geometric packing problems may be formulated mathematically as constrained optimization problems. But finding a good solution is a challenging task. The more complicated the geometry of the container or the objects to be packed, the more complex the non-penetration constraints become. In this work we propose the use of a physics engine that simulates a system of colliding rigid bodies. It is a tool to resolve interpenetration conflicts and to optimize configurations locally. We develop an efficient and easy-to-implement physics engine that is specialized for collision detection and contact handling. In succession of the development of this engine a number of novel algorithms for distance calculation and intersection volume were designed and imple- mented, which are presented in this work. They are highly specialized to pro- vide fast responses for cuboids and triangles as input geometry whereas the concepts they are based on can easily be extended to other convex shapes. Especially noteworthy in this context is our ε-distance algorithm - a novel application that is not only very robust and fast but also compact in its im- plementation. Several state-of-the-art third party implementations are being presented and we show that our implementations beat them in runtime and robustness. The packing algorithm that lies on top of the physics engine is a Monte Carlo based approach implemented for packing cuboids into a container described by a triangle soup. We give an implementation for the SAE J1100 variant of the trunk packing problem. We compare this implementation to several established approaches and we show that it gives better results in faster time than these existing implementations.

Sight distance for traffic safety analysis using GIS

Sight distance is of major importance for road safety either when designing new roads or analysing the alignment of existing roads. It is essential that available sight distance in roads is long enough for emergency stops or overtaking manoeuvres. Also, it is vital for engineers/researchers that the tools used for that analysis are both powerful and intuitive. Based on ArcGIS, the application to be presented not only performs an exhaustive sight distance calculation, but allows an accurate analysis of 3D alignment, using all new tools, from a Digital Elevation Model and vehicle trajectory. The software has been successfully utilised to analyse several two-lane rural roads in Spain. In addition, the software produces thematic maps representing sight distance in which supplementary information about crashes, traffic flow, speed or design consistency could be included, allowing traffic safety studies.

Fractal parameters of pore space from CT images of soils under contrasting management practices

Soil structure plays an important role in flow and transport phenomena, and a quantitative characterization of the spatial heterogeneity of the pore space geometry is beneficial for prediction of soil physical properties. Morphological features such as pore-size distribution, pore space volume or pore?solid surface can be altered by different soil management practices. Irregularity of these features and their changes can be described using fractal geometry. In this study, we focus primarily on the characterization of soil pore space as a 3D geometrical shape by fractal analysis and on the ability of fractal dimensions to differentiate between two a priori different soil structures. We analyze X-ray computed tomography (CT) images of soils samples from two nearby areas with contrasting management practices. Within these two different soil systems, samples were collected from three depths. Fractal dimensions of the pore-size distributions were different depending on soil use and averaged values also differed at each depth. Fractal dimensions of the volume and surface of the pore space were lower in the tilled soil than in the natural soil but their standard deviations were higher in the former as compared to the latter. Also, it was observed that soil use was a factor that had a statistically significant effect on fractal parameters. Fractal parameters provide useful complementary information about changes in soil structure due to changes in soil management. Read More: http://www.worldscientific.com/doi/abs/10.1142/S0218348X14400118?queryID=%24%7BresultBean.queryID%7D&

Morphological Functions with Parallel Sets for the Pore Space of X-ray CT Images of Soil Columns

During the last few decades, new imaging techniques like X-ray computed tomography have made available rich and detailed information of the spatial arrangement of soil constituents, usually referred to as soil structure. Mathematical morphology provides a plethora of mathematical techniques to analyze and parameterize the geometry of soil structure. They provide a guide to design the process from image analysis to the generation of synthetic models of soil structure in order to investigate key features of flow and transport phenomena in soil. In this work, we explore the ability of morphological functions built over Minkowski functionals with parallel sets of the pore space to characterize and quantify pore space geometry of columns of intact soil. These morphological functions seem to discriminate the effects on soil pore space geometry of contrasting management practices in a Mediterranean vineyard, and they provide the first step toward identifying the statistical significance of the observed differences.