Resonances and subharmonic bifurcations of large amplitude periodic orbits of planar polynomial vector fields

In this work are studied periodic perturbations, depending on two parameters, of planar polynomial vector fields having an annulus of large amplitude periodic orbits, which accumulate on a symmetric infinite heteroclinic cycle. Such periodic orbits and the heteroclinic trajectory can be seen only by the global consideration of the polynomial vector fields on the whole plane, and not by their restriction to any compact set. The global study involving infinity is performed via the Poincare Compactification. It is shown that, for certain types of periodic perturbations, one can seek, in a neighborhood of the origin in the parameter plane, curves C-(m) of subharmonic bifurcations, for which the periodically perturbed system has subharmonics of order m, for any integer m.

Periodic perturbations of quadratic planar polynomial vector fields

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Large amplitude oscillations for a class of symmetric polynomial differential systems in R³

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Chronic fluoxetine treatment alters cardiovascular functions in unanesthetized rats

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

Comparative study between RBF and radial-PPS neural networks

The study of function approximation is motivated by the human limitation and inability to register and manipulate with exact precision the behavior variations of the physical nature of a phenomenon. These variations are referred to as signals or signal functions. Many real world problem can be formulated as function approximation problems and from the viewpoint of artificial neural networks these can be seen as the problem of searching for a mapping that establishes a relationship from an input space to an output space through a process of network learning. Several paradigms of artificial neural networks (ANN) exist. Here we will be investigated a comparative of the ANN study of RBF with radial Polynomial Power of Sigmoids (PPS) in function approximation problems. Radial PPS are functions generated by linear combination of powers of sigmoids functions. The main objective of this paper is to show the advantages of the use of the radial PPS functions in relationship traditional RBF, through adaptive training and ridge regression techniques.

Bloch-Kohn and Wannier-Kohn functions in one dimension

Bloch and Wannier functions of the Kohn type for a quite general one-dimensional Hamiltonian with inversion symmetry are studied. Important clarifications on null minigaps and the symmetry of those functions are given, with emphasis on the Kronig-Penney model. The lack of a general selection rule on the miniband index for optical transitions between edge states in semiconductor superlattices is discussed. A direct method for the calculation of Wannier-Kohn functions is presented.

Wannier functions of isolated bands in one-dimensional crystals

We present a simple procedure to obtain the maximally localized Wannier function of isolated bands in one-dimensional crystals with or without inversion symmetry. First, we discuss the generality of dealing with real Wannier functions. Next, we use a transfer-matrix technique to obtain nonoptimal Bloch functions which are analytic in the wave number. This produces two classes of real Wannier functions. Then, the minimization of the variance of the Wannier functions is performed, by using the antiderivative of the Berry connection. In the case of centrosymmetric crystals, this procedure leads to the Wannier-Kohn functions. The asymptotic behavior of the Wannier functions is also analyzed. The maximally localized Wannier functions show the expected exponential and power-law decays. Instead, nonoptimal Wannier functions may show reduced exponential and anisotropic power-law decays. The theory is illustrated with numerical calculations of Wannier functions for conduction electrons in semiconductor superlattices.

Wannier functions of a one-dimensional photonic crystal with inversion symmetry

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

An approach to generalized holomorphic functions

A study of the generalized holomorphic functions, HG(Omega), having in mind its strict elements, i.e. those which are in HG(Omega) - H(Omega), as well as the possibility of the existence of hybrid elements, i.e. elements which have, in a part of a domain Omega subset of C-n, the strict behaviour and, in another part of the same domain, the classical behaviour, is carried out in this work. The study of hybrid elements is important in the approach of a concept of generalized domain of holomorphy.

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.

A influência da criopreservação nas células mesenquimais indiferenciadas do ligamento periodontal de humanos análise comparativa in vitro

Cryopreservation is a process where cells or biological tissues are preserved by freezing at very low temperatures and aims to cease reversibly, in a controlled manner, all the biological functions of living tissues, i.e., maintain cell preservation so that it can recover with high degree of viability and functional integrity. This study aimed to evaluate the influence of cryopreservation on the mesenchymal stem cells originating from the periodontal ligament of human third molars by in vitro experiments. Six healthy teeth were removed and the periodontal cells grown in culture medium containing α-MEM supplemented with antibiotics and 15% FBS in a humidified atmosphere with 5% CO2 at 37° C. Cells isolated from each sample were divided into two groups: Group I - immediate cell culture (not fresh cryopreserved cells) and Group II - cell cryopreservation, during a period of 30 days. Analyses of rates of cell adhesion and proliferation in different groups were performed by counting the cells adhered to the wells, in intervals of 24, 48 and 72 hours after the start of cultivation. The number of cells in each well was obtained by counting viable cells with the use of hemocytometer and the method of exclusion of cells stained by trypan blue. The difference between groups for each of the times was analyzed by Wilcoxon test. Regarding the temporal evolution for each group, analysis was done by Friedman's test to verify the existence of differences between times and, when it existed, the Wilcoxon penalty was applied. The results showed no statistically significant difference between the two groups analyzed in this study. Therefore, we conclude that the cryopreservation process, after a period of 30 days, did not influence the cell type studied, and there was no difference in growth capacity in vitro between the groups

Fermion localization on a split brane

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Parameter-dependent Lyapunov functions for state-derivative feedback control in polytopic linear systems

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

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.

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.