Positive Solution for a Class of Degenerate Quasilinear Elliptic Equations in R-N

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

VERY RAPIDLY VARYING BOUNDARIES IN EQUATIONS WITH NONLINEAR BOUNDARY CONDITIONS. THE CASE of A NON UNIFORMLY LIPSCHITZ DEFORMATION

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

Rapidly varying boundaries in equations with nonlinear boundary conditions. The case of a Lipschitz deformation

We analyze the behavior of solutions of nonlinear elliptic equations with nonlinear boundary conditions of type partial derivative u/partial derivative n + g( x, u) = 0 when the boundary of the domain varies very rapidly. We show that the limit boundary condition is given by partial derivative u/partial derivative n+gamma(x) g(x, u) = 0, where gamma(x) is a factor related to the oscillations of the boundary at point x. For the case where we have a Lipschitz deformation of the boundary,. is a bounded function and we show the convergence of the solutions in H-1 and C-alpha norms and the convergence of the eigenvalues and eigenfunctions of the linearization around the solutions. If, moreover, a solution of the limit problem is hyperbolic, then we show that the perturbed equation has one and only one solution nearby.

Substitution-newton-Raphson method for the solution of electric network equations

The power flow problem, in transmission networks, has been well solved, for most cases, using Newton-Raphson method (NR) and its decoupled versions. Generally speaking, the solution of a non-linear system of equations refers to two methods: NR and Successive Substitution. The proposal of this paper is to evaluate the potential of the Substitution-Newton-Raphson Method (SNR), which combines both methods, on the solution of the power flow problem. Simulations were performed using a two-bus test network in order to observe the characteristics of these methods. It was verified that the NR is faster than SNR, in terms of convergence, considering non-stressed scenarios. For those cases where the power flow in the network is closed to the limits (stressed system), the SNR converges faster. This paper presents the power flow formulation of the SNR and describes its potential for its application in special cases such as stressed scenarios. © 2006 IEEE.

The boson-fermion correspondence from linear ODEs

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

Estimativa da área foliar de Brachiaria plantaginea usando dimensões lineares do limbo foliar

Com o objetivo de obter uma equação que, por meio de parâmetros lineares dimensionais das folhas, permita a estimativa da área foliar de Brachiaria plantaginea, estudaram-se relações entre a área foliar real (Sf) e os parâmetros dimensionais do limbo foliar, como o comprimento ao longo da nervura principal (C) e a largura máxima (L), perpendicular à nervura principal. As equações lineares simples, exponenciais e geométricas obtidas podem ser usadas para estimação da área foliar do capim-marmelada. do ponto de vista prático, deve-se optar pela equação linear simples, envolvendo o produto C x L, usando-se a equação de regressão Sf = 0,7338 x (C x L), o que equivale a tomar 73,38% do produto entre o comprimento ao longo da nervura principal e a largura máxima, com um coeficiente de determinação de 0,8754.

Estimativa da área foliar de Typha latifolia usando dimensões lineares do limbo foliar

Com o objetivo de obter uma equação que, através de parâmetros lineares dimensionais das folhas, permita a estimativa da área foliar de Typha latifolia, estudaram-se relações entre a área foliar real (Sf) e parâmetros dimensionais do limbo foliar, como o comprimento ao longo da nervura principal (C) e a largura máxima (L), perpendicular à nervura principal. As equações lineares simples, exponenciais e geométricas obtidas podem ser usadas para estimação da área foliar da taboa. do ponto de vista prático, sugere-se optar pela equação linear simples que envolve o produto C x L, usando-se a equação de regressão Sf = 0,9651 x (C x L), que equivale a tomar 96,51% do produto entre o comprimento ao longo da nervura principal e a largura máxima, com um coeficiente de determinação de 0,9411.

Estimativa da área foliar de Tridax procumbens usando dimensões lineares do limbo foliar

Com o objetivo de obter uma equação que, através de parâmetros lineares dimensionais das folhas, permita a estimativa da área foliar de Tridax procumbens, estudaram-se relações entre a área foliar real (Sf) e os parâmetros dimensionais do limbo foliar, como o comprimento ao longo da nervura principal (C) e a largura máxima (L), perpendicular à nervura principal. As equações lineares simples, exponenciais e geométricas obtidas podem ser usadas para estimação da área foliar da erva-de-touro. do ponto de vista prático, sugere-se optar pela equação linear simples envolvendo o produto C x L, usando-se a equação de regressão Sf = 0,6008 x (C x L), que equivale a tomar 60,08% do produto entre o comprimento ao longo da nervura principal e a largura máxima, com um coeficiente de determinação de 0,8731.

Área foliar de duas trepadeiras infestantes de cana-de-açúcar utilizando dimensões lineares de folhas

Esta pesquisa teve como objetivo obter uma equação, por meio de medidas lineares dimensionais das folhas, que permitisse a estimativa da área foliar de Momordica charantia e Pyrostegia venusta. Entre maio e dezembro de 2007, foram estudadas as correlações entre a área folia real (Sf) e as medidas dimensionais do limbo foliar, como o comprimento ao longo da nervura principal (C) e a largura máxima (L) perpendicular à nervura principal. Todas as equações, exponenciais geométricas ou lineares simples, permitiram boas estimativas da área foliar. do ponto de vista prático, sugere-se optar pela equação linear simples envolvendo o produto C x L, considerando-se o coeficiente linear igual a zero. Desse modo, a estimativa da área foliar de Momordica charantia pode ser feita pela fórmula Sf = 0,4963 x (C x L), e a de Pyrostegia venusta, por Sf = 0,6649 x (C x L).

Crescimento aéreo e radicular de arroz de terras altas em função da adubação fosfatada e bioestimulante

The use of plant regulators that stimulate root growth can increase phosphorus uptake by upland rice. The objective of this study was to evaluate shoot and root growth of upland rice fertilized with different phosphorus doses with and without biostimulant. The experiment was carried out in greenhouse in the Faculdade de Ciencias Agronomicas-UNESP, in Botucatu-SP. The treatments consisted of six phosphorus doses applied in sowing (0, 12,5, 25, 50, 100 and 200 mg dm(-3)), with and without Stimulate (R) applied in the seeds (cv. Primavera). The plants were grown for 78 days and then cut at soil level to evaluate leaf area and leaves and collar dry matter. Root samples that were harvested on the same day had their root diameter and dry matter evaluated. The experimental design was the completely randomized, with three replications, arranged as a factorial 2x6. Variance analysis and regression were used to data evaluation. Linear and quadratic equations were adjusted at a probability level of 5%, using those with higher determination coefficient (R(2)). The increase on the phosphorus dose contributed to the lower matter production and leaf area of the plants when the biostimulant was applied. For shoot phosphorus accumulation and root evaluations, the same behavior was observed. It was concluded that the use of Stimulate (R) in seeds, for fitomass production or root system evaluation, was only efficient in low phosphorus doses.

An efficient Hopfield network to solve economic dispatch problems with transmission system representation

Economic dispatch (ED) problems have recently been solved by artificial neural network approaches. Systems based on artificial neural networks have high computational rates due to the use of a massive number of simple processing elements and the high degree of connectivity between these elements. The ability of neural networks to realize some complex non-linear function makes them attractive for system optimization. All ED models solved by neural approaches described in the literature fail to represent the transmission system. Therefore, such procedures may calculate dispatch policies, which do not take into account important active power constraints. Another drawback pointed out in the literature is that some of the neural approaches fail to converge efficiently toward feasible equilibrium points. A modified Hopfield approach designed to solve ED problems with transmission system representation is presented in this paper. The transmission system is represented through linear load flow equations and constraints on active power flows. The internal parameters of such modified Hopfield networks are computed using the valid-subspace technique. These parameters guarantee the network convergence to feasible equilibrium points, which represent the solution for the ED problem. Simulation results and a sensitivity analysis involving IEEE 14-bus test system are presented to illustrate efficiency of the proposed approach. (C) 2004 Elsevier Ltd. All rights reserved.

Resolvendo problemas de fluxo de potência ótimo DC através de uma rede de hopfield modificada

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

Interfacial concentrations of chloride and bromide in zwitterionic micelles with opposite dipoles: Experimental determination by chemical trapping and a theoretical description

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

Optimal and sub-optimal control in Dengue epidemics

This work concerns the application of the optimal control theory to Dengue epidemics. The dynamics of this insect-borne disease is modelled as a set of non-linear ordinary differential equations including the effect of educational campaigns organized to motivate the population to break the reproduction cycle of the mosquitoes by avoiding the accumulation of still water in open-air recipients. The cost functional is such that it reflects a compromise between actual financial spending (in insecticides and educational campaigns) and the population health (which can be objectively measured in terms of, for instance, treatment costs and loss of productivity). The optimal control problem is solved numerically using a multiple shooting method. However, the optimal control policy is difficult to implement by the health authorities because it is not practical to adjust the investment rate continuously in time. Therefore, a suboptimal control policy is computed assuming, as the admissible set, only those controls which are piecewise constant. The performance achieved by the optimal control and the sub-optimal control policies are compared with the cases of control using only insecticides when Breteau Index is greater or equal to 5 and the case of no-control. The results show that the sub-optimal policy yields a substantial reduction in the cost, in terms of the proposed functional, and is only slightly inferior to the optimal control policy. Copyright (C) 2001 John Wiley & Sons, Ltd.

Boundary oscillations and nonlinear boundary conditions

We study how oscillations in the boundary of a domain affect the behavior of solutions of elliptic equations with nonlinear boundary conditions of the type partial derivative u/partial derivative n + g(x, u) = 0. We show that there exists a function gamma defined on the boundary, that depends on an the oscillations at the boundary, such that, if gamma is a bounded function, then, for all nonlinearities g, the limiting boundary condition is given by partial derivative u/partial derivative n + gamma(x)g(x, u) = 0 (Theorem 2.1, Case 1). Moreover, if g is dissipative and gamma infinity then we obtain a Dirichlet an boundary condition (Theorem 2.1, Case 2).