Composition for a class of generalized functions in Colombeau's theory

In Colombeau's theory, given an open subset Ω of ℝn, there is a differential algebra G(Ω) of generalized functions which contains in a natural way the space D′(Ω) of distributions as a vector subspace. There is also a simpler version of the algebra G,(Ω). Although this subalgebra does not contain, in canonical way, the space D′(Ω) is enough for most applications. This work is developed in the simplified generalized functions framework. In several applications it is necessary to compute higher intrinsic derivatives of generalized functions, and since these derivatives are multilinear maps, it is necessary to define the space of generalized functions in Banach spaces. In this article we introduce the composite function for a special class of generalized mappings (defined in open subsets of Banach spaces with values in Banach spaces) and we compute the higher intrinsic derivative of this composite function.

Composition and invertibility for a class of generalized functions in the Colombeau's theory

In this work we define the composite function for a special class of generalized mappings and we study the invertibility for a certain class of generalized functions with real values.

Schur-SzegA composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Schur-Szegö composition of entire functions

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Heaviside generalized functions and shock waves for a Burger kind equation

The purpose of the work is to study the existence and nonexistence of shock wave solutions for the Burger equations. The study is developed in the context of Colombeau's theory of generalized functions (GFs). This study uses the equality in the strict sense and the weak equality of GFs. The shock wave solutions are given in terms of GFs that have the Heaviside function, in x and ( x, t) variables, as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function, in R-n and R-n x R, in the distributional limit sense.

Analytical optimization of spread and change of exponential decay of generalized Wannier functions in one dimension

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On extension theorems for holomorphic generalized functions

We present two extension theorems for holomorphic generalized functions. The first one is a version of the classic Hartogs extension theorem. In this, we start from a holomorphic generalized function on an open neighbourhood of the bounded open boundary, extending it, holomorphically, to a full open. In the second theorem a generalized version of a classic result is obtained, done independently, in 1943, by Bochner and Severi. For this theorem, we start from a function that is holomorphic generalized and has a holomorphic representative on the bounded domain boundary, we extend it holomorphically the function, for the whole domain.

Laguerre moments and generalized functions

Here we explore the link between the moments of the Laguerre polynomials or Laguerre moments and the generalized functions (as the Dirac delta-function and its derivatives), presenting several interesting relations. A useful application is related to a procedure for calculating mean values in quantum optics that makes use of the so-called quasi-probabilities. One of them, the P-distribution, can be represented by a sum over Laguerre moments when the electromagnetic field is in a photon-number state. Consequently, the P-distribution can be expressed in terms of Dirac delta-function and derivatives. More specifically, we found a direct relation between P-distributions and the Laguerre factorial moments.

Path integral quantization of generalized quantum electrodynamics

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Integration of polyharmonic functions

The results in this paper are motivated by two analogies. First, m-harmonic functions in R(n) are extensions of the univariate algebraic polynomials of odd degree 2m-1. Second, Gauss' and Pizzetti's mean value formulae are natural multivariate analogues of the rectangular and Taylor's quadrature formulae, respectively. This point of view suggests that some theorems concerning quadrature rules could be generalized to results about integration of polyharmonic functions. This is done for the Tchakaloff-Obrechkoff quadrature formula and for the Gaussian quadrature with two nodes.

On partial derivative-Neumann's problem in generalized functions framework

In this paper, we show that the equation delta u/delta (z) over bar + Gu = f, where the elements involved are in generalized functions context, has a local solution in the generalized functions context.

Poly(Lactide-co-Glycolide) Nanocapsules Containing Benzocaine: Influence of the Composition of the Oily Nucleus on Physico-Chemical Properties and Anesthetic Activity

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Antimicrobial resistance and species composition of Enterococcus spp. isolated from waters and sands of marine recreational beaches in Southeastern Brazil

Density, species composition and antimicrobial resistance in bacteria of the Enterococcus genus were evaluated in seawater and sands from 2 marine recreational beaches with different levels of pollution. The 2 beaches showed predominance of Enterococcus faecalis and Enterococcus faecium, in the water and the sand. Dry sand presented higher densities of Enterococcus sp. and higher frequency of resistant strains than wet sand and seawater. The beach with a higher degree of pollution presented higher percentages of resistant strains (66.7% and 61.5%, in sand and in water, respectively) and resistance to a larger number of antimicrobials compared with the less polluted beach, Ilha Porchat (35.7% and 31.25% of resistant strains in sand and water, respectively). in water samples, the highest frequencies of resistance were obtained against streptomycin (38.5%) and erythromycin (25%), whilst in sand, the highest frequencies were observed in relation to erythromycin and tetracycline (38.1% and 14.3%, respectively). These results show that water and sands from beaches with high indexes of faecal contamination of human origin may be potential sources of contamination by pathogens and contribute to the dissemination of bacterial resistance. (C) 2007 Elsevier Ltd. All rights reserved.

Size-related shifts in dietary composition of Centropomus parallelus (Perciformes: Centropomidae) in an estuarine ecosystem of the southeastern coast of Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Growth, lipogenesis and body composition of piracanjuba (Brycon orbignyanus) fingerlings fed different dietary protein and lipid concentrations

Piracanjuba (Brycon orbignyanus) is a Brazilian migratory fast-growing omnivore, very appreciated as a sport fish, which is threatened to extinction in Southern Brazil due to stock over exploitation and dam building. Therefore, efforts have been made to raise this fish in captivity for reintroduction and aquaculture purposes. In the present study, the effects of different dietary protein and lipid concentrations on piracanjuba fingerlings growth performance, feed utilization, body composition, hepatosomatic index (HSI) and activity of the lipogenic enzymes fatty acid synthetase (FAS), glucose-6-phosphate dehydrogenase (G6PD) and malic enzyme (ME) were investigated using a 2 x 3 factorial experiment. Six casein-gelatin based diets were prepared combining two protein (30% and 32%) and three lipid concentrations (5.5%, 8.8% and 12.1%). Eleven fish, average weight 11.30 +/- 0.1 g, were held in each of 18 100-1 aquaria, supplied with recirculating freshwater. Each diet was randomly assigned to triplicate groups of fish and fed to apparent satiation, twice a day for 100 d. Piracanjuba fingerlings' daily weight gain (0.36-0.40 g), specific growth rate (1.43-1.51%), feed utilization and HSI were not influenced by dietary protein or lipid concentration. However, body composition was directly affected by dietary treatment. An increase in body fat and dry matter was observed as dietary lipid increased, for both dietary protein concentrations tested. The activity of FAS was depressed by increasing dietary fat levels but the G6PD activity did not differ among dietary treatments, although ME activity showed some regulation by dietary protein. These results indicate that an increase from 5.5% to 12.1% in the dietary lipid, at a dietary protein concentration of 30% or 32%, promotes body fat accumulation in piracanjuba fingerlings with no improvement in growth, suggesting that the lipid requirement for this species should be 5% or less, when raised for commercial purposes. However, the additional energy reserve from body fat accumulation could be desirable for piracanjuba fingerlings produced for stock enhancement. (C) 2003 Editions scientifiques et medicales Elsevier SAS and Ifremer/IRD/Inra/Cemagref. All rights reserved.