Schwarzschild generalized black hole horizon and the embedding space

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Optimality conditions for infinite horizon control problems with state constraints

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

THERMAL RADIATION FROM A FLUCTUATING EVENT HORIZON

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the value function for nonautonomous optimal control problems with infinite horizon

In this paper we consider nonautonomous optimal control problems of infinite horizon type, whose control actions are given by L-1-functions. We verify that the value function is locally Lipschitz. The equivalence between dynamic programming inequalities and Hamilton-Jacobi-Bellman (HJB) inequalities for proximal sub (super) gradients is proven. Using this result we show that the value function is a Dini solution of the HJB equation. We obtain a verification result for the class of Dini sub-solutions of the HJB equation and also prove a minimax property of the value function with respect to the sets of Dini semi-solutions of the HJB equation. We introduce the concept of viscosity solutions of the HJB equation in infinite horizon and prove the equivalence between this and the concept of Dini solutions. In the Appendix we provide an existence theorem. (c) 2006 Elsevier B.V. All rights reserved.

Joint rolling-horizon scheduling of materials processing and lot-sizing with sequence-dependent setups

A lot sizing and scheduling problem from a foundry is considered in which key materials are produced and then transformed into many products on a single machine. A mixed integer programming (MIP) model is developed, taking into account sequence-dependent setup costs and times, and then adapted for rolling horizon use. A relax-and-fix (RF) solution heuristic is proposed and computationally tested against a high-performance MIP solver. Three variants of local search are also developed to improve the RF method and tested. Finally the solutions are compared with those currently practiced at the foundry.

The LQ control problem for Markovian jumps linear systems with horizon defined by stopping times

This paper deals with a stochastic optimal control problem involving discrete-time jump Markov linear systems. The jumps or changes between the system operation modes evolve according to an underlying Markov chain. In the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (TN), or the occurrence of a crucial failure event (τΔ), after which the system is brought to a halt for maintenance. In addition, an intermediary mixed case for which T represents the minimum between TN and τΔ is also considered. These stopping times coincide with some of the jump times of the Markov state and the information available allows the reconfiguration of the control action at each jump time, in the form of a linear feedback gain. The solution for the linear quadratic problem with complete Markov state observation is presented. The solution is given in terms of recursions of a set of algebraic Riccati equations (ARE) or a coupled set of algebraic Riccati equation (CARE).

Linear quadratic Gaussian control of discrete-time Markov jump linear systems with horizon defined by stopping times

The linear quadratic Gaussian control of discrete-time Markov jump linear systems is addressed in this paper, first for state feedback, and also for dynamic output feedback using state estimation. in the model studied, the problem horizon is defined by a stopping time τ which represents either, the occurrence of a fix number N of failures or repairs (T N), or the occurrence of a crucial failure event (τ δ), after which the system paralyzed. From the constructive method used here a separation principle holds, and the solutions are given in terms of a Kalman filter and a state feedback sequence of controls. The control gains are obtained by recursions from a set of algebraic Riccati equations for the former case or by a coupled set of algebraic Riccati equation for the latter case. Copyright © 2005 IFAC.

Necessary conditions of optimality for state constrained infinite horizon differential inclusions

This article presents and discusses necessary conditions of optimality for infinite horizon dynamic optimization problems with inequality state constraints and set inclusion constraints at both endpoints of the trajectory. The cost functional depends on the state variable at the final time, and the dynamics are given by a differential inclusion. Moreover, the optimization is carried out over asymptotically convergent state trajectories. The novelty of the proposed optimality conditions for this class of problems is that the boundary condition of the adjoint variable is given as a weak directional inclusion at infinity. This improves on the currently available necessary conditions of optimality for infinite horizon problems. © 2011 IEEE.

A maximum principle for constrained infinite horizon dynamic control systems

This article presents and discusses a maximum principle for infinite horizon constrained optimal control problems with a cost functional depending on the state at the final time. The main feature of these optimality conditions is that, under reasonably weak assumptions, the multiplier is shown to satisfy a novel transversality condition at infinite time. It is also shown that these conditions can also be obtained for impulsive control problems whose dynamics are given by measure driven differential equations. © 2011 IFAC.

A priori reformulations for joint rolling-horizon scheduling of materials processing and lot-sizing problem

In many production processes, a key material is prepared and then transformed into different final products. The lot sizing decisions concern not only the production of final products, but also that of material preparation in order to take account of their sequence-dependent setup costs and times. The amount of research in recent years indicates the relevance of this problem in various industrial settings. In this paper, facility location reformulation and strengthening constraints are newly applied to a previous lot-sizing model in order to improve solution quality and computing time. Three alternative metaheuristics are used to fix the setup variables, resulting in much improved performance over previous research, especially regarding the use of the metaheuristics for larger instances. © 2013 Elsevier Ltd. All rights reserved.

Hawking radiation from Elko particles tunnelling across black-strings horizon

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

ESR dating of pleistocene mammal teeth and its implications for the biostratigraphy and geological evolution of the coastal plain, Rio Grande do Sul, southern Brazil

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Estimativa da erodibilidade do solo para fins conservacionistas na microbacia córrego do Tijuco, SP

The soil erodibility factor is represented by the integrated effect of processes that regulate the water infiltration, soil resistance and the transport of soil particles. Therefore, this study had as objective to estimate the soil erodibility in the Corrego do Tijuco watershed, São Paulo State, Brazil, for guiding farmers in decision making for application of techniques for soil conservation. The soil samples were collected in a regular spacing of 500 m, resulting in a total of 310 points in a 0-20.0 m depth in an area of approximately 8,000 ha. For the estimation of soil erodibility (K) was applied a mathematical model which takes into account the soil organic matter content, the sand and silt size fractions, the soil permeability, and the particle mean diameter for each point of soil sampling. Estimated values greater than 0.040 Mg ha h ha(-1) MJ(-1) mm(-1) were considered very high for this factor. In areas with greater degree of erodibility occurs the Argisols order predominance, that shows high susceptibility to the development of interrill erosion due to its remarkable performance in relation to textural gradient, thereby, the interrill erosion rates can be very intensive due to rapid saturation of upper horizon, increasing the erosion process. At the Latosols (Oxisols) areas were also observed high soil erodibility values that under inappropriate conditions of soil occupation, concentrating runoff of rain water, leading to appear deep gullies.

Variabilidade espacial de atributos do solo e de fatores de erosão em diferentes pedoformas

As formas do relevo podem ser indicadores da variação dos atributos do solo, pois essa variabilidade é causada por pequenas alterações do declive que afetam os processos pedogenéticos bem como o transporte e o armazenamento de água no perfil do solo. O trabalho foi desenvolvido em Catanduva (SP), com o objetivo de caracterizar a variabilidade espacial de atributos do solo e fatores de erosão em diferentes pedoformas sob cultivo de cana-de-açúcar. de acordo com o modelo de Troeh classificou-se as formas do relevo em duas pedoformas, côncava e convexa. Com a utilização de um DGPS levantaram-se as cotas altimétricas, estabelecendo-se uma malha, com intervalos regulares de 50 m, com 270 pontos na pedoforma côncava e 353 pontos na pedoforma convexa, perfazendo um total de 623 pontos, coletados na profundidade de 0,0 - 0,2 m em uma área de 200 ha. em cada ponto da malha foram determinados os atributos químicos do solo, granulometria, espessura do solo e fatores de erosão locais, tais como erosividade (R), erodibilidade (K), fator topográfico (LS), uso e manejo (C), práticas conservacionistas (P), potencial natural de erosão (PNE), perda de solo (A) e risco de erosão (RE). Os dados foram avaliados primeiramente por uma análise estatística exploratória, calculando-se a média, mediana, variância, coeficiente de variação, coeficiente de assimetria, coeficiente de curtose e teste de normalidade. Posteriormente, a dependência espacial foi verificada por meio da técnica de geoestatística utilizando-se semivariogramas. As maiores perdas de solo, risco de erosão e potencial natural de erosão e menor espessura do solo ocorreram na pedoforma convexa, indicando forte dependência espacial com a forma do relevo. A pedoforma côncava proporcionou maior variabilidade espacial, demonstrando que a forma do relevo condiciona padrões diferenciados de variabilidade. A magnitude da variabilidade dos atributos do solo é mais influenciada pela forma do relevo que pela erosão. A espessura do horizonte A+E integrado com a forma do relevo é um indicador de processos erosivos para classe de Argissolos.

Efeitos da compactação em algumas propriedades físicas do solo e seu reflexo no desenvolvimento das raízes de plantas de soja

Estudou-se o efeito de vários níveis de compactação na densidade do solo, porosidade total e resistência à penetração, objetivando determinar o nível que impede o desenvolvimento das raízes de plantas de soja. O trabalho foi realizado em casa de vegetação, com amostras deformadas do horizonte superficial de uma terra roxa estruturada e de um latossolo roxo, controlando os níveis de compactação e o teor de água. A influência da compactação no desenvolvimento das raízes foi avaliada um mês após a germinação. Os valores de densidade do solo, para um mesmo nível de compactação, foram maiores para a terra roxa estruturada. O teor de água ótimo para a compactação foi de 21,0% para a terra roxa estruturada e de 29,8 para o latossolo roxo. A compactação artificial do solo acarretou aumento da resistência à penetração e diminuição da porosidade total. A elevação da sua densidade de 0,90 para 1,30 kg/m³ para a terra roxa estruturada, e de 0,90 para 1,23 kg/m³ para o latossolo roxo, promoveu, respectivamente, diminuição de 39 e de 41% na massa seca das raízes. O desenvolvimento das raízes das plantas ficou impedido quando a densidade do solo atingiu valores de 1,30 e 1,23 kg/m³, respectivamente, para a terra roxa estruturada e o latossolo roxo.