An algorithm for automatic checking of exercises in a dynamic geometry system: iGeom

One of the key issues in e-learning environments is the possibility of creating and evaluating exercises. However, the lack of tools supporting the authoring and automatic checking of exercises for specifics topics (e.g., geometry) drastically reduces advantages in the use of e-learning environments on a larger scale, as usually happens in Brazil. This paper describes an algorithm, and a tool based on it, designed for the authoring and automatic checking of geometry exercises. The algorithm dynamically compares the distances between the geometric objects of the student`s solution and the template`s solution, provided by the author of the exercise. Each solution is a geometric construction which is considered a function receiving geometric objects (input) and returning other geometric objects (output). Thus, for a given problem, if we know one function (construction) that solves the problem, we can compare it to any other function to check whether they are equivalent or not. Two functions are equivalent if, and only if, they have the same output when the same input is applied. If the student`s solution is equivalent to the template`s solution, then we consider the student`s solution as a correct solution. Our software utility provides both authoring and checking tools to work directly on the Internet, together with learning management systems. These tools are implemented using the dynamic geometry software, iGeom, which has been used in a geometry course since 2004 and has a successful track record in the classroom. Empowered with these new features, iGeom simplifies teachers` tasks, solves non-trivial problems in student solutions and helps to increase student motivation by providing feedback in real time. (c) 2008 Elsevier Ltd. All rights reserved.

Decay of geometry for Fibonacci critical covering maps of the circle

We study the growth of Df `` (f(c)) when f is a Fibonacci critical covering map of the circle with negative Schwarzian derivative, degree d >= 2 and critical point c of order l > 1. As an application we prove that f exhibits exponential decay of geometry if and only if l <= 2, and in this case it has an absolutely continuous invariant probability measure, although not satisfying the so-called Collet-Eckmann condition. (C) 2009 Elsevier Masson SAS. All rights reserved.

Periodic geodesics and geometry of compact Lorentzian manifolds with a Killing vector field

We study the geometry and the periodic geodesics of a compact Lorentzian manifold that has a Killing vector field which is timelike somewhere. Using a compactness argument for subgroups of the isometry group, we prove the existence of one timelike non self-intersecting periodic geodesic. If the Killing vector field is nowhere vanishing, then there are at least two distinct periodic geodesics; as a special case, compact stationary manifolds have at least two periodic timelike geodesics. We also discuss some properties of the topology of such manifolds. In particular, we show that a compact manifold M admits a Lorentzian metric with a nowhere vanishing Killing vector field which is timelike somewhere if and only if M admits a smooth circle action without fixed points.

COMPARISON RESULTS FOR CONJUGATE AND FOCAL POINTS IN SEMI-RIEMANNIAN GEOMETRY VIA MASLOV INDEX

We prove an estimate on the difference of Maslov indices relative to the choice of two distinct reference Lagrangians of a continuous path in the Lagrangian Grassmannian of a symplectic space. We discuss some applications to the study of conjugate and focal points along a geodesic in a semi-Riemannian manifold.

Understanding the Effect of Adsorption Geometry over Substrate Selectivity in the Surface-Enhanced Raman Scattering Spectra of Simazine and Atrazine

This paper studies the selectivity of Well-defined Au and Ag nanostructures as substrates for the SERS, (surface-enhanced Raman scattering) detection of simazine (6-chloro-N,N`-diethyl-1,3,5-triazine-2,4-diamine) and atrazine (6-chloro-N-ethyl-N`-isopropyl-1,3,5-triazine-2,4-diamine). Our data showed that simazine and atrazine displayed similar SERS spectra when the Au was employed as substrate. Conversely, distinct SERS signatures were obtained upon the utilization of Ag substrates. Density functional theory (DFT) calculations and vibrational assignments suggested that, while simazine and atrazine adsorbed on Au via the N3 position of the triazine ring, simazine adsorbed on Ag via N3 and atrazine via N5. The results presented herein demonstrated that the adsorption geometry of analyte molecules can play a central role over substrate selectivity in SERS, which is particularly important in applications involving ultrasensitive analysis of mixtures containing structurally similar molecules.

Soil texture spatial variability of different parent material in pereira barreto, São Paulo state

The variation of soil textural characteristics is a function of the relief and parent materials. The objective of this work was to study soil texture spatial variability from different parent material in Pereira Barreto, SP. An area of 530.67 hectares was mapped through the use of Global Positioning System receivers and obtaining of Digital Elevation Models. A set of 201 soil samples was collected from every seven hectares, at three depths: 0 - 0.25 m; 0.25 - 0.50 m; and 0.80 - 1.00 m. The amounts of sand, silt and clay were obtained by the pipette method and analyzed by both descriptive statistics and geostatistics. Soil textures varied as a function of parent materials and topography.

Potassium Leaching as Affected by Soil Texture and Residual Fertilization in Tropical Soils

Potassium (K) leaching is affected by soil texture and available K, among other factors. In this experiment, effects of soil texture and K availability on K distribution were studied in the presence of roots, with no excess water. Soils from two 6-year field experiments on a sandy clay loam and a clay soil fertilized yearly with 0, 60, 120, and 180 kg ha-1 of K2O were accommodated in pots that received 90 kg ha-1 of K2O. Soybean was grown up to its full bloom (R2). Under field conditions, K leaching below the arable layer increased with K rates, but the effect was less noticeable in the clay soil. Potassium leaching in a sandy clay loam soil was related to soil K contents from prior fertilizations. With no excess water, in the presence of soybean roots, K distribution in the profile was significant in the lighter textured soil but was not apparent on the heavier textured soil.

Correction of soil acidity in the subsurface of an oxisol with sandy loam texture under no-tillage

No Rio Grande do Sul (RS), muitas áreas sob plantio direto apresentam elevada saturação por Al e baixa saturação por bases na camada de 0,10-0,20 m (subsuperfície), e isso pode diminuir a produção de grãos de culturas anuais. O objetivo do presente trabalho foi avaliar se a ocorrência de alta saturação por Al e baixa saturação por bases em subsuperfície (0,10-0,20 m), no plantio direto, pode representar um ambiente restritivo para a produção de culturas, bem como avaliar os modos de incorporação de calcário na correção da acidez do solo em subsuperfície. Para isso, foi realizado um experimento com os cultivos de soja (2005/ 2006), milho (2006/2007), trigo (2007) e soja (2007/2008), em um Latossolo Vermelho distrófico típico (Empresa Brasileira de Pesquisa Agropecuária (EMBRAPA), 2006) de textura franco arenosa, há quatro anos sob plantio direto, no município de Tupanciretã (RS). Os seis tratamentos foram: sem revolvimento com ou sem calcário; lavração com ou sem calcário; e escarificação com ou sem calcário. Aos 24 meses após a aplicação dos tratamentos e nas camadas de 0-0,05, 0,05-0,10, 0,10-0,15, 0,15-0,20 e 0,20-0,30 m, foram avaliados os valores de pH-H2O, saturação por Al e por bases. Avaliou-se a produtividade de soja (2005/2006), milho (2006/2007), trigo (2007) e soja (2007/2008). A acidez do solo em subsuperfície não alterou a produtividade das culturas quando as propriedades de acidez na camada de 0-0,10 m estavam em níveis em que não se recomenda a aplicação de calcário, segundo a CQFSRS/SC (2004). A incorporação de calcário com aração foi o modo mais eficiente de corrigir a acidez em profundidade.

Fractal analysis of leaf-texture properties as a tool for taxonomic and identification purposes: a case study with species from Neotropical Melastomataceae (Miconieae tribe)

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Fuzzy Logic and Geostatistical Techniques for Spatialization of Soil Texture in Region with Rough Terrains

From the geotechnical standpoint, it is interesting to analyse the soil texture in regions with rough terrain due to its relation with the infiltration and runoff processes and, consequently, the effect on erosion processes. The purpose of this paper is to present a methodology that provides the soil texture spatialization by using Fuzzy logic and Geostatistic. The results were correlated with maps drawn specifically for the study area. The knowledge of the spatialization of soil properties, such as the texture, can be an important tool for land use planning in order to reduce the potential soil losses during rain seasons. (c) 2011 Published by Elsevier Ltd. Selection and peer-review under responsibility of Spatial Statistics 2011

Investigation of Plasma Immersion Ion Implantation Process in Magnetic Mirror Geometry

Plasma immersion ion implantation (PIII) with low external magnetic field has been investigated both numerically and experimentally. The static magnetic field considered is essentially nonuniform and is generated by two magnetic coils installed outside the vacuum chamber. Experiments have been conducted to investigate the effect of two of the most important PIII parameters: target voltage and gas pressure. In that context, it was found that the current density increased when the external parameters were varied. Later, the PIII process was analyzed numerically using the 2.5-D computer code KARAT. The numerical results show that the system of crossed E x B fields enhances the PIII process. The simulation showed an increase of the plasma density around the target under the operating and design conditions considered. Consequently, an increase of the ion current density on the target was observed. All these results are explained through the mechanism of gas ionization by collisions with electrons drifting in crossed E x B fields.

Boundary identification criteria and geometry analysis of Al 7050 stretch zone from elevation profiles

This article describes the development of a method for analysis of the shape of the stretch zone surface based on parallax measurement theory and using digital image processing techniques. Accurate criteria for the definition of the boundaries of the stretch zone are established from profiles of fracture surfaces obtained from crack tip opening displacement tests on Al-7050 alloy samples. The elevation profiles behavior analysis is based on stretch zone width and height parameters. It is concluded that the geometry of the stretch zone profiles under plane strain conditions can be described by a semi-parabolic relationship. (C) Elsevier B.V., 1999. All rights reserved.

Differential geometry of intersection curves in R(4) of three implicit surfaces

We present algorithms for computing the differential geometry properties of intersection Curves of three implicit surfaces in R(4), using the implicit function theorem and generalizing the method of X. Ye and T. Maekawa for 4-dimension. We derive t, n, b(1), b(2) vectors and curvatures (k(1), k(2), k(3)) for transversal intersections of the intersection problem. (C) 2008 Elsevier B.V. All rights reserved.

Corn texture and particle size in broiler diets

The objective of this study was to evaluate the effect of corn texture and the particle size on broiler performance, carcass yield, nutrient digestibility, and digestive organ morphometrics. In Experiment I, 720 male Cobb chicks were distributed in a completely randomized experimental design with a 2 x 3 factorial arrangement, consisting two corn textures (dented and hard) and three corn particle sizes, was applied, with four replicates of 30 birds each. Corn particle size was classified according to geometric mean diameter (GMD) as fine - 0.46 mm; medium - 0.73 mm, and coarse - 0.87 mm. In Experiment II, 120 broiler chicks were used to evaluate corn digestibility during the periods of 16 to 22 days and 35 to 41 days of age, using the method of total excreta collection. In Experiment I, corn particle size influenced body weight, average weight gain, feed intake and feed conversion ratio of 21-day-old birds. Corn texture and particle size did not affect the performance of 42-day-old broilers or carcass traits. In Experiment II, there was no influence of corn texture and particle size on digestive organ weights. Dented corn increased nitrogen excretion in the first trial, and hard corn improved dry matter digestibility in the second metabolic trial. Corn with fine particle size promotes better performance of broilers at 21 days of age. Hard corn results in higher dry matter digestibility and lower nitrogen excretion, and consequently higher production factor in 42-day-old broilers.