On optimality conditions for optimal control problem in coefficients for Δp-Laplacian

In this paper we study an optimal control problem for a nonlinear monotone Dirichlet problem where the control is taken as L^infinity(Omega) coefficient of Delta_p-Laplacian. Given a cost function, the objective is to derive first-order optimality conditions and provide their substantiation. We propose some ideas and new results concerning the differentiability properties of the Lagrange functional associated with the considered control problem. The obtained adjoint boundary value problem is not coercive and, hence, it may admit infinitely many solutions. That is why we concentrate not only on deriving the adjoint system, but also, following the well-known Hardy-Poincaré Inequality, on a formulation of sufficient conditions which would guarantee the uniqueness of the adjoint state to the optimal pair

Approximation of an Optimal Control Problem in the Coefficient for Variational Inequality with Anisotropic p-Laplacian

We study an optimal control problem for a variational inequality with the so-called anisotropic $p$-Laplacian in the principle part of this inequality. The coefficients of the anisotropic $p$-Laplacian, the matrix $A(x)$, we take as a control. The optimal control problem is to minimize the discrepancy between a given distribution $y_d\in L^2(\Omega)$ and the solutions $y\in K\subset W^{1,p}_0(\Omega)$ of the corresponding variational inequality. We show that the original problem is well-posed and derive existence of optimal pairs. Since the anisotropic $p$-Laplacian inherits the degeneracy with respect to unboundedness of the term $|(A(x)\nabla y,\nabla y)_{\mathbb{R}^N}|^{\frac{p-2}{2}}$, we introduce a two-parameter model for the relaxation of the original problem. Further we discuss the asymptotic behavior of relaxed solutions and show that some optimal pairs to the original problem can be attained by the solutions of two-parametric approximated optimal control problems

On an Optimal -Control Problem in Coefficients for Linear Elliptic Variational Inequality

We consider optimal control problems for linear degenerate elliptic variational inequalities with homogeneous Dirichlet boundary conditions. We take the matrix-valued coefficients in the main part of the elliptic operator as controls in . Since the eigenvalues of such matrices may vanish and be unbounded in , it leads to the "noncoercivity trouble." Using the concept of convergence in variable spaces and following the direct method in the calculus of variations, we establish the solvability of the optimal control problem in the class of the so-called -admissible solutions

On optimality conditions for optimal control problem in coefficients for Δp-Laplacian

In this paper we study an optimal control problem for a nonlinear monotone Dirichlet problem where the control is taken as -coefficient of -Laplacian. Given a cost function, the objective is to derive first-order optimality conditions and provide their substantiation. We propose some ideas and new results concerning the differentiability properties of the Lagrange functional associated with the considered control problem. The obtained adjoint boundary value problem is not coercive and, hence, it may admit infinitely many solutions. That is why we concentrate not only on deriving the adjoint system, but also, following the well-known Hardy-Poincare Inequality, on a formulation of sufficient conditions which would guarantee the uniqueness of the adjoint state to the optimal pair. MSC:35J70, 49J20, 49J45, 93C73

On Optimization of a Highly Re-Entrant Production System

We discuss the optimal control problem stated as the minimization in the $L^2$-sense of the mismatch between the actual out-flux and a demand forecast for a hyperbolic conservation law that models a highly re-entrant production system. The output of the factory is described as a function of the work in progress and the position of the switch dispatch point (SDP) where we separate the beginning of the factory employing a push policy from the end of the factory, which uses a quasi-pull policy. The main question we discuss in this paper is about the optimal choice of the input in-flux, push and quasi-pull constituents, and the position of SDP

Test results of a 60 volt bipolar nickel-hydrogen battery

In July, l986, a high-voltage nickel-hydrogen battery was assembled at the NASA Lewis Research Center. This battery incorporated bipolar construction techniques to build a 50-cell stack with approximately 1.0 A-hr capacity (C) and an open-circuit voltage of 65 V. The battery was characterized at both low and high current rates prior to pulsed and nonpulsed discharges. Pulse discharges at 5 and 10 C were performed before placing the battery on over 1400, 40% depth-of-discharge, low-earth-orbit cycles. The successful demonstration of a high-voltage bipolar battery in one containment vessel has advanced the technology to where nickel-hydrogen high-voltage systems can be constructed of several modules instead of hundreds of individual cells

Component variations and their effects on bipolar nickel-hydrogen cell performance

A 50 cell bipolar nickel-hydrogen battery was assembled to demonstrate the feasibility of constructing a high voltage stack of cells. Various component combinations were tested in this battery. The battery had approximately 1 ampere-hour of capacity and was constructed from components with an active area of 2" X 2". The components were parametrically varied to give a comparison of nickel electrodes, hydrogen electrodes, separators, fill procedures and electrolyte reservoir plate thicknesses. Groups of five cells were constructed using the same components; ten combinations were tested in all. The battery was thoroughly characterized at various change and discharge rates as well as with various pulse patterns and rates. Over a period of 1400 40% DOD LEO cycles some of the groups began to exhibit performance differences. In general, only separator variations had a significant effect on cell performance. It also appears that shunt currents may have been operating within the stack, resulting in electrolyte transfer from one cell to another, thus contributing to cell performance variations

Brainstem Reflexes in Idiopathic Cervical Dystonia: Does Medullary Dysfunction Play a Role?

Background: Neurophysiological markers in dystonia have so far not been sistematically applied in clinical practice due to limited reproducibility of results and low correlations with clinical findings. Exceptions might be represented by the blink reflex (BR), including its recovery cycle (BRRC) and the trigemino-cervical reflex (TCR) which, compared to other neurophysiological methods, have shown more consistent alterations in cervical dystonia (CD). However, a comparison between the two techniques, and their possible correlation with disease symptoms, have not been thoroughly investigated. Objectives: To assess the role of BR, BRCC and TCR in the pathophysiology of idiopathic cervical dystonia. Methods: Fourteen patients and 14 age-matched healthy controls (HC) were recruited. Neurophysiological outcome measures included latency of R1 and R2 components of the BR, R2 amplitude, BRRC, latency and amplitude of P19/N31 complex of TCR. Clinical and demographic features of patients were also collected, including age at disease onset, disease duration, presence of tremor, sensory trick and pain. The Toronto Western Spasmodic Torticollis Rating Scale was used to characterize dystonia. Results: Compared to HC, CD patients showed increased latency of the BR R2 and decreased suppression of the BRRC. They also showed increased latency of the P19 and decreased amplitude of P19/N31 complex of TCR. The latency of P19 component of TCR was positively correlated with disease duration. Conclusions: We propose that the increased latency of R2 and P19 observed here might be reflective of brainstem dysfunction, mediated either by local interneuronal excitability changes or by subtle structural damage

Sum of exit times in series of metastable states in probabilistic cellular automata

Reversible Probabilistic Cellular Automata are a special class of automata whose stationary behavior is described by Gibbs--like measures. For those models the dynamics can be trapped for a very long time in states which are very different from the ones typical of stationarity. This phenomenon can be recasted in the framework of metastability theory which is typical of Statistical Mechanics. In this paper we consider a model presenting two not degenerate in energy metastable states which form a series, in the sense that, when the dynamics is started at one of them, before reaching stationarity, the system must necessarily visit the second one. We discuss a rule for combining the exit times from each of the metastable states

The inclusion of fresh forage in the lactating buffalo diet affects fatty acid and sensory profile of mozzarella cheese

The aim of this study was to determine the effect of inclusion of fresh forage in diet for lactating buffalo on properties of mozzarella cheese under intensive farming conditions. Thirty-two buffalo cows were equally allotted into 2 groups fed diets with (fresh group, FRS) or without (control group, CTL) fresh sorghum. The study consisted of 2 trials. In the first one, animals from group FRS were fed a diet containing 10 kg of fresh sorghum (10-FRS diet) that was doubled to 20 kg (20-FRS diet) in the second trial. All diets were isonitrogenous and isoenergetic, and fresh forage accounted for 13.4 and 26.5 of dietary dry matter, respectively, for the 10-FRS and 20-FRS diet. In each trial, milk from the 2 groups was used to produce 3 batches/diet of Mozzarella di Bufala Campana Protected Designation of Origin cheese. Milk yield and composition were not influenced by dietary treatment. The use of 10-FRS diet did not affect any properties of mozzarella. As the inclusion rate of fresh sorghum doubled to 20 kg, an increment of unsaturated fatty acid percentages and a lowering of short-chain and saturated fatty acids were observed. Moreover, the sensory characteristics of mozzarella were modified, although no effects were observed on consumer acceptance. We conclude that the use of green fodder can represent a low-cost feeding strategy to improve the healthiness of buffalo mozzarella under intensive farming conditions with no detrimental effect on consumer blind acceptance