Some remarks on the operator of Foias and Williams

In this paper we study the Foias-Williams operator

where , and is a Hankel operator with symbol . We exhibit a relationship between the similarity of to a contraction and the rate of decay of , the absolute values of the Fourier coefficients of the symbol .

     

Periodic optimal control for parabolic Volterra-Lotka type equations

This paper considers the optimal harvesting control of a biological species, whose growth is governed by the parabolic diffusive Volterra-Lotka equation. We prove that such equation with L^∞ periodic coefficients has an unique positive periodic solution. We show the existence and uniqueness of an optimal control, and under certain conditions, we characterize the optimal control in terms of a parabolic optimality system. A monotone sequence which converges to the optimal control is constructed.     

Analysis of corrosion scales formed on steel at high temperatures in hydrocarbons containing model naphthenic acids and sulfur compounds

Corrosive naphthenic acids and sulfur compounds in crude oils present a major challenge for refineries from a corrosion perspective. Although it is accepted that some sulfur compounds may form protective FeS scales on the metal surface and deter corrosion, attempting to correlate the characteristics of FeS scale with its protective properties has not been successful. Given the complex chemical compositions of real crudes, model sulfur compound and model naphthenic acids were used to mimic the corrosion by crude fractions in the present study. The iron sulfide scale formed by the model sulfur/acid compounds was challenged by naphthenic acids under high‐velocity conditions to examine its protectiveness against corrosion. Moreover, the scale was analyzed with transmission electron microscope/energy dispersive X‐ray spectroscopy technique, and a layer of iron oxide formed on the 5Cr steel was found when naphthenic acids were present in the solution. The iron oxide layer appeared to be important for maintaining protection against naphthenic acid corrosion, and further analysis revealed that it was composed of magnetite. Copyright © 2015 John Wiley & Sons, Ltd.     

Elasticity from the force network ensemble in granular media

Transmission of forces in static granular materials is studied within the framework of the force network ensemble, by numerically evaluating the mechanical response of hexagonal packings of frictionless grains and rectangular packings of frictional grains. In both cases, close to the point of application of the overload, the response is nonlinear and displays two peaks, while at larger length scales, it is linear and elasticlike. The crossover between these two behaviors occurs at a depth that increases with the magnitude of the overload and decreases with increasing friction.     

Compact Composition Operators and Deddens Algebras

We consider the Deddens algebras associated to compact composition operators on the Hardy space \(H^2\) on the unit disk. When the compact composition operator corresponds to a function \(\varphi \) that satisfies \(\varphi (0)=0\) and \(\varphi '(0)\ne 0\), we show that the lattice of invariant subspaces of this algebra is \(\{0\}\cup \{z^n H^2: n=0,1,2,\ldots \}\). As a consequence, for this class of operators the associated Deddens algebra is weakly dense in the algebra of lower triangular matrices.     

Brachistochrone with limited reaction of constraint in an arbitrary force field

The paper considers brachistochronic motion of a particle along a curve y=y(x) in an arbitrary force field in the vertical plane of Cartesian coordinate system. The curve is treated as a bilateral or unilateral constraint that can be smooth or rough. The projection of the reaction force of the curve onto the normal to the curve is confined to the fixed limits. A control variable u is given as the second derivative of the function y(x) relative to the horizontal coordinate?x of the particle, i.e., u=d ² y/dx ². Applying Pontryagin??s maximum principle and singular optimal control theory, the problem is reduced to numerical solving of the corresponding two-point boundary value problem. The procedure based on the shooting method is used to solve the boundary value problem. Two examples with friction forces of the viscous friction and Coulomb friction type have been solved.     

Optimal damping control and nonlinear parabolic systemes

An optimal control problem for a parabolic equation when the control parameter is the zero order coefficient of the differential operator is considered. An optimality system is derived. Under a certain sign condition, the problem is solved completely, by proving uniqueness and providing a constructive existence proof for the nonlinear parabolic optimality system.     

Catalytic reduction of NO by CO over Pd — doped Perovskite-type catalysts

The perovskite type oxides (nominal formula LaTi_0.5Mg_0.5O₃) with addition of Pd were prepared by annealing the ethanol solution of precursors in nitrogen flow at 1200°C and characterized by X-ray powder diffraction (XRD), X-ray photoelectron spectroscopy (XPS) and temperature programmed desorption of NO (NO-TPD). Their activity was evaluated for NO reduction by CO under stoichiometric and oxidizing conditions and for direct decomposition of NO. Pd substituted samples exhibited high NO reduction activity and selectivity towards N₂. Nearly complete elimination of NO was achieved at 200°C. Two simultaneous reactions, NO reduction by CO and direct decomposition of NO as well as two forms of NO adsorption were observed on the surface of Pd substituted perovskite samples. The distribution of Pd in different catalytically active sites or complexes on at the catalyst surface may be responsible for the proceeding of two reactions: NO reduction with CO and direct NO decomposition.