Fourier transform, null variety, and Laplacian's eigenvalues

We consider a quantity κ(Ω)—the distance to the origin from the null variety of the Fourier transform of the characteristic function of Ω. We conjecture, firstly, that κ(Ω) is maximised, among all convex balanced domains of a fixed volume, by a ball, and also that κ(Ω) is bounded above by the square root of the second Dirichlet eigenvalue of Ω. We prove some weaker versions of these conjectures in dimension two, as well as their validity for domains asymptotically close to a disk, and also discuss further links between κ(Ω) and the eigenvalues of the Laplacians.

From symmetry breaking to Poisson Point Process in 2D Voronoi Tessellations: the generic nature of hexagons

We bridge the properties of the regular triangular, square, and hexagonal honeycomb Voronoi tessellations of the plane to the Poisson-Voronoi case, thus analyzing in a common framework symmetry breaking processes and the approach to uniform random distributions of tessellation-generating points. We resort to ensemble simulations of tessellations generated by points whose regular positions are perturbed through a Gaussian noise, whose variance is given by the parameter α2 times the square of the inverse of the average density of points. We analyze the number of sides, the area, and the perimeter of the Voronoi cells. For all valuesα >0, hexagons constitute the most common class of cells, and 2-parameter gamma distributions provide an efficient description of the statistical properties of the analyzed geometrical characteristics. The introduction of noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α = 0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise withα <0.12. For all tessellations and for small values of α, we observe a linear dependence on α of the ensemble mean of the standard deviation of the area and perimeter of the cells. Already for a moderate amount of Gaussian noise (α >0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α >2, results converge to those of Poisson-Voronoi tessellations. The geometrical properties of n-sided cells change with α until the Poisson- Voronoi limit is reached for α > 2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established. This law allows for an easy link to the Lewis law for areas and agrees with exact asymptotic results. Finally, for α >1, the ensemble mean of the cells area and perimeter restricted to the hexagonal cells agree remarkably well with the full ensemble mean; this reinforces the idea that hexagons, beyond their ubiquitous numerical prominence, can be interpreted as typical polygons in 2D Voronoi tessellations.

Symmetry-break in Voronoi tessellations

We analyse in a common framework the properties of the Voronoi tessellations resulting from regular 2D and 3D crystals and those of tessellations generated by Poisson distributions of points, thus joining on symmetry breaking processes and the approach to uniform random distributions of seeds. We perturb crystalline structures in 2D and 3D with a spatial Gaussian noise whose adimensional strength is α and analyse the statistical properties of the cells of the resulting Voronoi tessellations using an ensemble approach. In 2D we consider triangular, square and hexagonal regular lattices, resulting into hexagonal, square and triangular tessellations, respectively. In 3D we consider the simple cubic (SC), body-centred cubic (BCC), and face-centred cubic (FCC) crystals, whose corresponding Voronoi cells are the cube, the truncated octahedron, and the rhombic dodecahedron, respectively. In 2D, for all values α>0, hexagons constitute the most common class of cells. Noise destroys the triangular and square tessellations, which are structurally unstable, as their topological properties are discontinuous in α=0. On the contrary, the honeycomb hexagonal tessellation is topologically stable and, experimentally, all Voronoi cells are hexagonal for small but finite noise with α<0.12. Basically, the same happens in the 3D case, where only the tessellation of the BCC crystal is topologically stable even against noise of small but finite intensity. In both 2D and 3D cases, already for a moderate amount of Gaussian noise (α>0.5), memory of the specific initial unperturbed state is lost, because the statistical properties of the three perturbed regular tessellations are indistinguishable. When α>2, results converge to those of Poisson-Voronoi tessellations. In 2D, while the isoperimetric ratio increases with noise for the perturbed hexagonal tessellation, for the perturbed triangular and square tessellations it is optimised for specific value of noise intensity. The same applies in 3D, where noise degrades the isoperimetric ratio for perturbed FCC and BCC lattices, whereas the opposite holds for perturbed SCC lattices. This allows for formulating a weaker form of the Kelvin conjecture. By analysing jointly the statistical properties of the area and of the volume of the cells, we discover that also the cells shape heavily fluctuates when noise is introduced in the system. In 2D, the geometrical properties of n-sided cells change with α until the Poisson-Voronoi limit is reached for α>2; in this limit the Desch law for perimeters is shown to be not valid and a square root dependence on n is established, which agrees with exact asymptotic results. Anomalous scaling relations are observed between the perimeter and the area in the 2D and between the areas and the volumes of the cells in 3D: except for the hexagonal (2D) and FCC structure (3D), this applies also for infinitesimal noise. In the Poisson-Voronoi limit, the anomalous exponent is about 0.17 in both the 2D and 3D case. A positive anomaly in the scaling indicates that large cells preferentially feature large isoperimetric quotients. As the number of faces is strongly correlated with the sphericity (cells with more faces are bulkier), in 3D it is shown that the anomalous scaling is heavily reduced when we perform power law fits separately on cells with a specific number of faces.

Estimating the volume of tephra deposits: a new simple strategy

Volume determination of tephra deposits is necessary for the assessment of the dynamics and hazards of explosive volcanoes. Several methods have been proposed during the past 40 years that include the analysis of crystal concentration of large pumices, integrations of various thinning relationships, and the inversion of field observations using analytical and computational models. Regardless of their strong dependence on tephra-deposit exposure and distribution of isomass/isopach contours, empirical integrations of deposit thinning trends still represent the most widely adopted strategy due to their practical and fast application. The most recent methods involve the best fitting of thinning data using various exponential seg- ments or a power-law curve on semilog plots of thickness (or mass/area) versus square root of isopach area. The exponential method is mainly sensitive to the number and the choice of straight segments, whereas the power-law method can better reproduce the natural thinning of tephra deposits but is strongly sensitive to the proximal or distal extreme of integration. We analyze a large data set of tephra deposits and propose a new empirical method for the deter- mination of tephra-deposit volumes that is based on the integration of the Weibull function. The new method shows a better agreement with observed data, reconciling the debate on the use of the exponential versus power-law method. In fact, the Weibull best fitting only depends on three free parameters, can well reproduce the gradual thinning of tephra deposits, and does not depend on the choice of arbitrary segments or of arbitrary extremes of integration.

Approximation by harmonic polynomials in star-shaped domains and exponential convergence of Trefftz hp-dGFEM

We study the approximation of harmonic functions by means of harmonic polynomials in two-dimensional, bounded, star-shaped domains. Assuming that the functions possess analytic extensions to a delta-neighbourhood of the domain, we prove exponential convergence of the approximation error with respect to the degree of the approximating harmonic polynomial. All the constants appearing in the bounds are explicit and depend only on the shape-regularity of the domain and on delta. We apply the obtained estimates to show exponential convergence with rate O(exp(−b square root N)), N being the number of degrees of freedom and b>0, of a hp-dGFEM discretisation of the Laplace equation based on piecewise harmonic polynomials. This result is an improvement over the classical rate O(exp(−b cubic root N )), and is due to the use of harmonic polynomial spaces, as opposed to complete polynomial spaces.

Optimal V. O2max-to-mass ratio for predicting 15 km performance among elite male cross-country skiers

The aim of this study was 1) to validate the 0.5 body-mass exponent for maximal oxygen uptake (V. O2max) as the optimal predictor of performance in a 15 km classical-technique skiing competition among elite male cross-country skiers and 2) to evaluate the influence of distance covered on the body-mass exponent for V. O2max among elite male skiers. Twenty-four elite male skiers (age: 21.4±3.3 years [mean ± standard deviation]) completed an incremental treadmill roller-skiing test to determine their V. O2max. Performance data were collected from a 15 km classicaltechnique cross-country skiing competition performed on a 5 km course. Power-function modeling (ie, an allometric scaling approach) was used to establish the optimal body-mass exponent for V . O2max to predict the skiing performance. The optimal power-function models were found to be race speed = 8.83⋅(V . O2max m-0.53) 0.66 and lap speed = 5.89⋅(V . O2max m-(0.49+0.018lap)) 0.43e0.010age, which explained 69% and 81% of the variance in skiing speed, respectively. All the variables contributed to the models. Based on the validation results, it may be recommended that V. O2max divided by the square root of body mass (mL⋅min−1 ⋅kg−0.5) should be used when elite male skiers’ performance capability in 15 km classical-technique races is evaluated. Moreover, the body-mass exponent for V . O2max was demonstrated to be influenced by the distance covered, indicating that heavier skiers have a more pronounced positive pacing profile (ie, race speed gradually decreasing throughout the race) compared to that of lighter skiers.

Influência do tamanho da semente na emergência das plântulas de longan (Dimocarpos longan Lour)

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Influência da temperatura na germinação de sementes de Annona Montana

Com o objetivo de avaliar a influência da temperatura sobre a porcentagem de germinação e o índice de velocidade de germinação (IVG) de sementes de Annona montana, conhecida como falsa graviola, espécie com potencial para porta-enxerto das variedades comerciais, testaram-se quatro temperaturas (20; 25; 30 e 35ºC). O trabalho foi desenvolvido em laboratório em câmaras de germinação tipo BOD, utilizando-se de sementes de três plantas provenientes do Banco de Germoplasma do Departamento de Produção Vegetal da Faculdade de Ciências Agrárias e Veterinárias - UNESP, Câmpus de Jaboticabal-SP. O delineamento experimental foi o inteiramente casualizado, com quatro repetições, com dez sementes cada. Pelos resultados obtidos, tem-se que tanto para o parâmetro porcentagem de germinação como para o IVG, os maiores valores observados foram para as sementes na temperatura de 30ºC (55% de germinação e IVG = 0,153), seguido da temperatura de 25ºC (25% de germinação e IVG = 0,088). Para as temperaturas de 20ºC e 35ºC, não foi observada ocorrência de germinação. A análise estatística dos dados de porcentagem de germinação foi transformada em arc-sen square root (x/100) e as médias foram comparadas pelo teste de Tukey, a 5% de probabilidade.

Compressão auto-adaptativa de imagens coloridas

Image compress consists in represent by small amount of data, without loss a visual quality. Data compression is important when large images are used, for example satellite image. Full color digital images typically use 24 bits to specify the color of each pixel of the Images with 8 bits for each of the primary components, red, green and blue (RGB). Compress an image with three or more bands (multispectral) is fundamental to reduce the transmission time, process time and record time. Because many applications need images, that compression image data is important: medical image, satellite image, sensor etc. In this work a new compression color images method is proposed. This method is based in measure of information of each band. This technique is called by Self-Adaptive Compression (S.A.C.) and each band of image is compressed with a different threshold, for preserve information with better result. SAC do a large compression in large redundancy bands, that is, lower information and soft compression to bands with bigger amount of information. Two image transforms are used in this technique: Discrete Cosine Transform (DCT) and Principal Component Analysis (PCA). Primary step is convert data to new bands without relationship, with PCA. Later Apply DCT in each band. Data Loss is doing when a threshold discarding any coefficients. This threshold is calculated with two elements: PCA result and a parameter user. Parameters user define a compression tax. The system produce three different thresholds, one to each band of image, that is proportional of amount information. For image reconstruction is realized DCT and PCA inverse. SAC was compared with JPEG (Joint Photographic Experts Group) standard and YIQ compression and better results are obtain, in MSE (Mean Square Root). Tests shown that SAC has better quality in hard compressions. With two advantages: (a) like is adaptive is sensible to image type, that is, presents good results to divers images kinds (synthetic, landscapes, people etc., and, (b) it need only one parameters user, that is, just letter human intervention is required

Adaptive filter feature identification for structural health monitoring in an aeronautical panel

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Increase of temperature of an ideal nondegenerate quantum gas in a suddenly expanding box due to energy quantization

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Hydrolysis rates of TMOS catalyzed by oxalic acid and stimulated by ultrasound

A simple calorimetric method was employed to study the kinetics of the hydrolysis of the solventless TMOS-water mixtures, under ultrasound stimulation, as a function of the concentration of oxalic acid. The reaction rates were obtained, in relative units, from the measured thermal peak of the reaction as a non-separated function of both the sonication time and the instantaneous temperature of the medium. For concentrations of oxalic acid below 0.01 M, polycondensation reaction starts before complete hydrolysis. For concentrations of oxalic acid above 0.01 M, hydrolysis is complete and, in addition, the inverse of the time, as measured from the starting of ultrasound action until the maximum hydrolysis heat release, was found to be a reasonable relative measure of the average hydrolysis rate constant. The average hydrolysis rate constant was found to be proportional to the square root of the molar concentration of the oxalic acid. This result is in agreement with the literature if we assume small dissociation degree for the catalyst in such a solventless alkoxyde-water medium.

ON DISCRETE SYSMMETRIES OF THE MULTI-BOSON KP HIERARCHIES

We show that the multi-boson KP hierarchies possess a class of discrete symmetries linking them to discrete Toda systems. These discrete symmetries are generated by the similarity transformation of the corresponding Lax operator. This establishes a canonical nature of the discrete transformations. The spectral equation, which defines both the lattice system and the corresponding Lax operator, plays a key role in determining pertinent symmetry structure. We also introduce the concept of the square root lattice leading to a family of new pseudo-differential operators with covariance under additional Backlund transformations.

OPTIMIZATION OF EXTRUSION COOKING PROCESS FOR CHICKPEA (CICER-ARIETINUM, L) DEFATTED FLOUR BY RESPONSE-SURFACE METHODOLOGY

Response surface methodology was employed to optimize the production of a snack food from chickpea. The independent variables, process temperature (123-137-degrees-C) and feed moisture (13-27% d.s.b.) were selected at five levels (rotatable five level composite design: - square-root 2, -1, 0, 1, + square-root 2) in the extrusion of defatted chickpea flour. Response variables were expansion ratio, shear strength of the extrudate and sensory preference assessed by an untrained panel. Expansion ratio increased steadily with decrease in feed moisture similar to cereal extrusion. Regions of maxima were observed for sensory preference and shear strength, and these two product attributes were linearly related. The most acceptable chickpea snack was rated higher than a commercial corn snack.

CLASSICAL EQUIVALENCE OF LAMBDA-R-PHI-2 THEORIES

It is shown that the action functional S[g, phi] = integral d4 x square-root -g[R/k(1 + klambdaphi2) + partial derivative(mu)phi partial derivative(mu)phi] describes, in general, one and the same classical theory whatever may be the value of the coupling constant lambda.