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.

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.

Evidence for Reductive Genome Evolution and Lateral Acquisition of Virulence Functions in Two Corynebacterium pseudotuberculosis Strains

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Involvement of median raphe nucleus 5-HT1A receptors in the regulation of generalized anxiety-related defensive behaviours in rats

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

Colombeau's theory and shock wave solutions for systems of PDEs

In this article we study the existence of shock wave solutions for systems of partial differential equations of hydrodynamics with viscosity in one space dimension in the context of Colombeau's theory of generalized functions. This study uses the equality in the strict sense and the association of generalized functions (that is the weak equality). The shock wave solutions are given in terms of generalized functions that have the classical Heaviside step function as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function that have to satisfy part of the equations in the strict sense and part of the equations in the sense of association.

Paracoccidioidomycosis in a Dog: Case Report of Generalized Lymphadenomegaly

Paracoccidioidomycosis (PCM) is a severe systemic mycosis, endemic in Latin America and highly prevalent in Brazil, where it ranks eighth as a mortality cause among infectious and parasitic diseases in humans. The disease in animals has been little explored. It is observed that armadillos can harbor the fungus at high frequencies, although the active disease has not been well documented in this wild mammal. Dogs are susceptible to experimental infection, and the naturally acquired PCM-disease was reported only recently in a dog from Brazil. The present work reports the second case of naturally acquired PCM in a 6-year-old female dog that presented emaciation, lymphadenomegaly, and hepatosplenomegaly. Biochemical and pulmonary radiographic evaluation did not reveal any abnormalities. PCM was diagnosed by clinical findings, culturing, immunohistochemistry, and histopathology of popliteal lymph node. The fungus was recovered from popliteal lymph node, and the molecular analysis showed respective sequencing similarities of 99 and 100% for 803 nucleotides of the Gp43 gene and 592 nucleotides from the ITS-5.8S region of Paracoccidioides brasiliensis. Immunohistochemistry revealed severe lymphadenitis and presented numerous yeasts, which reacted against the gp43 antibody. Histopathology revealed a severe granulomatous lymphadenitis associated with numerous single or multiple budding yeasts. After diagnosis, the dog was successfully treated with itraconazol for 2 years. Veterinarians should be aware of the importance of considering PCM for differential diagnosis, especially in dogs from PCM-endemic areas, whose monophagocytic system involvement is evident.

A combination of clinical and microbiological management of generalized aggressive periodontitis in primary teeth. A case report

International Journal of Paediatric Dentistry 2012; 22: 310316 Background. Generalized aggressive periodontitis (GAP) in primary teeth is a rare periodontal disease that occurs during or soon after eruption of the primary teeth. An association with systemic diseases is a possibility. Case Report. A 4-year-old Brazilian girl presented with GAP involving the entire primary dentition. The patient and her parents and sister were subjected to microbiological testing to identify the microorganisms involved in the disease. The patient underwent tooth extraction to eradicate the disease and received a prosthesis for the restoration of masticatory function. After the permanent teeth erupted, fixed orthodontic appliances were place to restore dental arch form and occlusion. Conclusions. The results show the importance of an early diagnosis of GAP and of a multidisciplinary approach involving laboratory and clinical management to treat the disease and to restore masticatory function, providing a better quality of life for patients.

Zeros of Jacobi functions of second kind

The number of zeros in (- 1, 1) of the Jacobi function of second kind Q(n)((alpha, beta)) (x), alpha, beta > - 1, i.e. The second solution of the differential equation(1 - x(2))y (x) + (beta - alpha - (alpha + beta + 2)x)y' (x) + n(n + alpha + beta + 1)y(x) = 0,is determined for every n is an element of N and for all values of the parameters alpha > - 1 and beta > - 1. It turns out that this number depends essentially on alpha and beta as well as on the specific normalization of the function Q(n)((alpha, beta)) (x). Interlacing properties of the zeros are also obtained. As a consequence of the main result, we determine the number of zeros of Laguerre's and Hermite's functions of second kind. (c) 2005 Elsevier B.V. All rights reserved.