Análise do efeito da discretização do modelo de velocidades nas migrações Kirchhoff e Kirchhoff-Gaussian- Beam 2D pré-empilhamento em profundidade

O Feixe Gaussiano (FG) é uma solução assintótica da equação da elastodinâmica na vizinhança paraxial de um raio central, a qual se aproxima melhor do campo de ondas do que a aproximação de ordem zero da Teoria do Raio. A regularidade do FG na descrição do campo de ondas, assim como a sua elevada precisão em algumas regiões singulares do meio de propagação, proporciona uma forte alternativa no imageamento sísmicos. Nesta dissertação, apresenta-se um novo procedimento de migração sísmica pré-empilhamento em profundidade com amplitudes verdadeiras, que combina a flexibilidade da migração tipo Kirchhoff e a robustez da migração baseada na utilização de Feixes Gaussianos para a representação do campo de ondas. O algoritmo de migração proposto é constituído por dois processos de empilhamento: o primeiro é o empilhamento de feixes (“beam stack”) aplicado a subconjuntos de dados sísmicos multiplicados por uma função peso definida de modo que o operador de empilhamento tenha a mesma forma da integral de superposição de Feixes Gaussianos; o segundo empilhamento corresponde à migração Kirchhoff tendo como entrada os dados resultantes do primeiro empilhamento. Pelo exposto justifica-se a denominação migração Kirchhoff-Gaussian-Beam (KGB).Afim de comparar os métodos Kirchhoff e KGB com respeito à sensibilidade em relação ao comprimento da discretização, aplicamos no conjunto de dados conhecido como Marmousi 2-D quatro grids de velocidade, ou seja, 60m, 80m 100m e 150m. Como resultado, temos que ambos os métodos apresentam uma imagem muito melhor para o menor intervalo de discretização da malha de velocidade. O espectro de amplitude das seções migradas nos fornece o conteúdo de frequência espacial das seções das imagens obtidas.

Zero sets of bivariate Hermite polynomials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Synthesis, characterization and thermal behavior of heterobimetallic carbonyl compounds of the type [W(CO)(4)(bipy)(CuX)] (X=Cl, N-3, ClO4 and BF4)

Four new heterobimetallic metal carbonyls were synthesized by the reaction of [W(CO)4(bipy)] (1) with copper(I) compounds leading to species with the general formula [W(CO)4(bipy)(CuX)] (X = Cl, N3, ClO4, BF4) (2-5). The metal carbonyl compounds were characterized by elemental analysis, infrared and UV -visible electronic spectroscopy and thermogravimetric analysis. The IR data for 2-5 show carbonyl stretching band patterns similar to compound 1 ; ie they exhibit the same number of bands. The UV - vis results show a dissociation reaction generating the starting compound 1 and CuX as consequence of a weak interaction between 1 and CuX. Thermal decomposition mechanisms as well as the thermal stability are influenced by the CuX fragments. The thermal stability decreases in the order [W(CO)4(bipy)] > [W(CO)4(bipy)(CuCl)] > [W(CO)4(bipy) (CuBF4)]. The X-ray results show the formation of WO3, CuWO4, Cu2O and CuO as final decomposition products.

The tangential variation of a localized flux-type eigenvalue problem

In this work the differentiability of the principal eigenvalue lambda = lambda(1)(Gamma) to the localized Steklov problem -Delta u + qu = 0 in Omega, partial derivative u/partial derivative nu = lambda chi(Gamma)(x)u on partial derivative Omega, where Gamma subset of partial derivative Omega is a smooth subdomain of partial derivative Omega and chi(Gamma) is its characteristic function relative to partial derivative Omega, is shown. As a key point, the flux subdomain Gamma is regarded here as the variable with respect to which such differentiation is performed. An explicit formula for the derivative of lambda(1) (Gamma) with respect to Gamma is obtained. The lack of regularity up to the boundary of the first derivative of the principal eigenfunctions is a further intrinsic feature of the problem. Therefore, the whole analysis must be done in the weak sense of H(1)(Omega). The study is of interest in mathematical models in morphogenesis. (C) 2011 Elsevier Inc. All rights reserved.

Generalized Differential Quadrature Finite Element Method applied to Advanced Structural Mechanics

Over the years the Differential Quadrature (DQ) method has distinguished because of its high accuracy, straightforward implementation and general ap- plication to a variety of problems. There has been an increase in this topic by several researchers who experienced significant development in the last years. DQ is essentially a generalization of the popular Gaussian Quadrature (GQ) used for numerical integration functions. GQ approximates a finite in- tegral as a weighted sum of integrand values at selected points in a problem domain whereas DQ approximate the derivatives of a smooth function at a point as a weighted sum of function values at selected nodes. A direct appli- cation of this elegant methodology is to solve ordinary and partial differential equations. Furthermore in recent years the DQ formulation has been gener- alized in the weighting coefficients computations to let the approach to be more flexible and accurate. As a result it has been indicated as Generalized Differential Quadrature (GDQ) method. However the applicability of GDQ in its original form is still limited. It has been proven to fail for problems with strong material discontinuities as well as problems involving singularities and irregularities. On the other hand the very well-known Finite Element (FE) method could overcome these issues because it subdivides the computational domain into a certain number of elements in which the solution is calculated. Recently, some researchers have been studying a numerical technique which could use the advantages of the GDQ method and the advantages of FE method. This methodology has got different names among each research group, it will be indicated here as Generalized Differential Quadrature Finite Element Method (GDQFEM).

Estimating the number of motor units using random sums with independently thinned terms

The problem of estimating the numbers of motor units N in a muscle is embedded in a general stochastic model using the notion of thinning from point process theory. In the paper a new moment type estimator for the numbers of motor units in a muscle is denned, which is derived using random sums with independently thinned terms. Asymptotic normality of the estimator is shown and its practical value is demonstrated with bootstrap and approximative confidence intervals for a data set from a 31-year-old healthy right-handed, female volunteer. Moreover simulation results are presented and Monte-Carlo based quantiles, means, and variances are calculated for N in{300,600,1000}.

Boron-Bearing Kornerupine from Fiskenaesset, West Greenland: A Reexamination of Specimens from the Type Locality

In 1884, Lorenzen proposed the formula MgAI2SiO6 for his new mineral kornerupine from Fiskenæsset and did not suspect it to contain boron. Lacroix and de Gramont (1919) reported boron in Fiskenæsset kornerupine, while Herd (1973) found none. New analyses (ion microprobe mass analyser and spectrophotometric) of kornerupine in three specimens from the type locality, including the specimens analysed by Lorenzen and Herd, indicate the presence of boron in all three, in amounts ranging from 0.50 to 1.44 wt.% B203, e.g. (Li0.04 Na0.01 Ca0.01) (Mg3.49 Mn0.01 Fe0.17 Ti0.01 Al5.64)Σ9.30 (Si3.67 Al1.02 B0.31)Σ5 O21 (OH0.99 F0.01) for Lorenzen's specimen. Textures and chemical compositions suggest that kornerupine crystallized in equilibrium in the following assemblages, all with anorthite (An 92-95) and phlogopite (XFe = atomic Fe/(Fe + Mg) = 0.028-0.035): (1) kornerupine (0.045)-gedrite (0.067); (2) kornerupine (0.038-0.050)-sapphirine (0.032-0.035); and (3) kornerupine (0.050)-hornblende. Fluorine contents of kornerupine range from 0.01 to 0.06%, of phlogopite, from 0.09 to 0.10%. In the first assemblage, sapphirine (0.040) and corundum are enclosed in radiating bundles of kornerupine; additionally sapphirine, corundum, and/or gedrite occur with chlorite and pinite (cordierite?) as breakdown products of kornerupine. Kornerupine may have formed by reactions such as: gedrite + sapphirine + corundum + B203 (in solution) + H20 = kornerupine + anorthite + Na-phlogopite under conditions of the granulite facies. Boron for kornerupine formation was most likely remobilized by hydrous fluids from metasedimentary rocks occurring along the upper contact of the Fiskenæsset gabbro-anorthosite complex with amphibolite.

Effects of colostrum versus formula feeding on hepatic glucocorticoid and α1- and β2-adrenergic receptors in neonatal calves and their effect on glucose and lipid metabolism

Neonatal energy metabolism in calves has to adapt to extrauterine life and depends on colostrum feeding. The adrenergic and glucocorticoid systems are involved in postnatal maturation of pathways related to energy metabolism and calves show elevated plasma concentrations of cortisol and catecholamines during perinatal life. We tested the hypothesis that hepatic glucocorticoid receptors (GR) and α₁- and β₂-adrenergic receptors (AR) in neonatal calves are involved in adaptation of postnatal energy metabolism and that respective binding capacities depend on colostrum feeding. Calves were fed colostrum (CF; n=7) or a milk-based formula (FF; n=7) with similar nutrient content up to d 4 of life. Blood samples were taken daily before feeding and 2h after feeding on d 4 of life to measure metabolites and hormones related to energy metabolism in blood plasma. Liver tissue was obtained 2 h after feeding on d 4 to measure hepatic fat content and binding capacity of AR and GR. Maximal binding capacity and binding affinity were calculated by saturation binding assays using [(3)H]-prazosin and [(3)H]-CGP-12177 for determination of α₁- and β₂-AR and [(3)H]-dexamethasone for determination of GR in liver. Additional liver samples were taken to measure mRNA abundance of AR and GR, and of key enzymes related to hepatic glucose and lipid metabolism. Plasma concentrations of albumin, triacylglycerides, insulin-like growth factor I, leptin, and thyroid hormones changed until d 4 and all these variables except leptin and thyroid hormones responded to feed intake on d 4. Diet effects were determined for albumin, insulin-like growth factor I, leptin, and thyroid hormones. Binding capacity for GR was greater and for α₁-AR tended to be greater in CF than in FF calves. Binding affinities were in the same range for each receptor type. Gene expression of α₁-AR (ADRA1) tended to be lower in CF than FF calves. Binding capacity of GR was related to parameters of glucose and lipid metabolism, whereas β₂-AR binding capacity was negatively associated with glucose metabolism. In conclusion, our results indicate a dependence of GR and α₁-AR on milk feeding immediately after birth and point to an involvement of hepatic GR and AR in postnatal adaptation of glucose and lipid metabolism in calves.

Metabolic and hormonal response to intermittent high-intensity and continuous moderate intensity exercise in individuals with type 1 diabetes: a randomised crossover study.

AIMS/HYPOTHESIS To investigate exercise-related fuel metabolism in intermittent high-intensity (IHE) and continuous moderate intensity (CONT) exercise in individuals with type 1 diabetes mellitus. METHODS In a prospective randomised open-label cross-over trial twelve male individuals with well-controlled type 1 diabetes underwent a 90 min iso-energetic cycling session at 50% maximal oxygen consumption ([Formula: see text]), with (IHE) or without (CONT) interspersed 10 s sprints every 10 min without insulin adaptation. Euglycaemia was maintained using oral (13)C-labelled glucose. (13)C Magnetic resonance spectroscopy (MRS) served to quantify hepatocellular and intramyocellular glycogen. Measurements of glucose kinetics (stable isotopes), hormones and metabolites complemented the investigation. RESULTS Glucose and insulin levels were comparable between interventions. Exogenous glucose requirements during the last 30 min of exercise were significantly lower in IHE (p = 0.02). Hepatic glucose output did not differ significantly between interventions, but glucose disposal was significantly lower in IHE (p < 0.05). There was no significant difference in glycogen consumption. Growth hormone, catecholamine and lactate levels were significantly higher in IHE (p < 0.05). CONCLUSIONS/INTERPRETATION IHE in individuals with type 1 diabetes without insulin adaptation reduced exogenous glucose requirements compared with CONT. The difference was not related to increased hepatic glucose output, nor to enhanced muscle glycogen utilisation, but to decreased glucose uptake. The lower glucose disposal in IHE implies a shift towards consumption of alternative substrates. These findings indicate a high flexibility of exercise-related fuel metabolism in type 1 diabetes, and point towards a novel and potentially beneficial role of IHE in these individuals. TRIAL REGISTRATION ClinicalTrials.gov NCT02068638 FUNDING: Swiss National Science Foundation (grant number 320030_149321/) and R&A Scherbarth Foundation (Switzerland).

Analytic Kramer kernels, Lagrange-type interpolation series and de Branges spaces

The classical Kramer sampling theorem provides a method for obtaining orthogonal sampling formulas. In particular, when the involved kernel is analytic in the sampling parameter it can be stated in an abstract setting of reproducing kernel Hilbert spaces of entire functions which includes as a particular case the classical Shannon sampling theory. This abstract setting allows us to obtain a sort of converse result and to characterize when the sampling formula associated with an analytic Kramer kernel can be expressed as a Lagrange-type interpolation series. On the other hand, the de Branges spaces of entire functions satisfy orthogonal sampling formulas which can be written as Lagrange-type interpolation series. In this work some links between all these ideas are established.

Remarks on methods for the computation of boundary-element integrals by co-ordinate transformation

It is well known that the evaluation of the influence matrices in the boundary-element method requires the computation of singular integrals. Quadrature formulae exist which are especially tailored to the specific nature of the singularity, i.e. log(*- x0)9 Ijx- JC0), etc. Clearly the nodes and weights of these formulae vary with the location Xo of the singular point. A drawback of this approach is that a given problem usually includes different types of singularities, and therefore a general-purpose code would have to include many alternative formulae to cater for all possible cases. Recently, several authors1"3 have suggested a type independent alternative technique based on the combination of standard Gaussian rules with non-linear co-ordinate transformations. The transformation approach is particularly appealing in connection with the p.adaptive version, where the location of the collocation points varies at each step of the refinement process. The purpose of this paper is to analyse the technique in eference 3. We show that this technique is asymptotically correct as the number of Gauss points increases. However, the method possesses a 'hidden' source of error that is analysed and can easily be removed.

Sampling associated with resolvent-type kernels and lagrange-type interpolation series

In this paper a new class of Kramer kernels is introduced, motivated by the resolvent of a symmetric operator with compact resolvent. The article gives a necessary and sufficient condition to ensure that the associ- ated sampling formula can be expressed as a Lagrange-type interpolation series. Finally, an illustrative example, taken from the Hamburger moment problem theory, is included.

New infinite families of exact sums of squares formulas, Jacobi elliptic functions, and Ramanujan’s tau function

In this paper, we give two infinite families of explicit exact formulas that generalize Jacobi’s (1829) 4 and 8 squares identities to 4n2 or 4n(n + 1) squares, respectively, without using cusp forms. Our 24 squares identity leads to a different formula for Ramanujan’s tau function τ(n), when n is odd. These results arise in the setting of Jacobi elliptic functions, Jacobi continued fractions, Hankel or Turánian determinants, Fourier series, Lambert series, inclusion/exclusion, Laplace expansion formula for determinants, and Schur functions. We have also obtained many additional infinite families of identities in this same setting that are analogous to the η-function identities in appendix I of Macdonald’s work [Macdonald, I. G. (1972) Invent. Math. 15, 91–143]. A special case of our methods yields a proof of the two conjectured [Kac, V. G. and Wakimoto, M. (1994) in Progress in Mathematics, eds. Brylinski, J.-L., Brylinski, R., Guillemin, V. & Kac, V. (Birkhäuser Boston, Boston, MA), Vol. 123, pp. 415–456] identities involving representing a positive integer by sums of 4n2 or 4n(n + 1) triangular numbers, respectively. Our 16 and 24 squares identities were originally obtained via multiple basic hypergeometric series, Gustafson’s Cℓ nonterminating 6φ5 summation theorem, and Andrews’ basic hypergeometric series proof of Jacobi’s 4 and 8 squares identities. We have (elsewhere) applied symmetry and Schur function techniques to this original approach to prove the existence of similar infinite families of sums of squares identities for n2 or n(n + 1) squares, respectively. Our sums of more than 8 squares identities are not the same as the formulas of Mathews (1895), Glaisher (1907), Ramanujan (1916), Mordell (1917, 1919), Hardy (1918, 1920), Kac and Wakimoto, and many others.

The Critical Strips of the Sums 1 + 2z + ... + nz

We give a partition of the critical strip, associated with each partial sum 1 + 2z + ... + nz of the Riemann zeta function for Re z < −1, formed by infinitely many rectangles for which a formula allows us to count the number of its zeros inside each of them with an error, at most, of two zeros. A generalization of this formula is also given to a large class of almost-periodic functions with bounded spectrum.

On some solutions of a functional equation related to the partial sums of the Riemann zeta function

In this paper, we prove that infinite-dimensional vector spaces of α-dense curves are generated by means of the functional equations f(x)+f(2x)+⋯+f(nx)=0, with n≥2, which are related to the partial sums of the Riemann zeta function. These curves α-densify a large class of compact sets of the plane for arbitrary small α, extending the known result that this holds for the cases n=2,3. Finally, we prove the existence of a family of solutions of such functional equation which has the property of quadrature in the compact that densifies, that is, the product of the length of the curve by the nth power of the density approaches the Jordan content of the compact set which the curve densifies.