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The article presents a study on the comparison of kinetics of chromium carbide formation on carburized and uncarburized AISI 1020 steel substrates. It cites the analysis on AISI samples and the use of thermo-reactive diffusion process. It notes that the kinetics of chromium carbide coating by salt bath immersion showed a parabolic relationship between carbide layer thickness and treatment line. It also states that the activation energy of the substrates was 87.9 and 225.6 kJ/mol, respectively.

Abstract. In this paper, a Haar wavelet-based method for optimal control of the second-order linear systems with respect to a quadratic cost function for any length of time is proposed. A Haar wavelet integral operational matrix and properties of the Kronecker product are used in finding the approximate solutions of optimal trajectories and optimal control by solving only two algebraic equations instead of solving the Riccati differential equation. Numerical results of a typical example are presented to illustrate the advantage of the approach. [ABSTRACT FROM AUTHOR]