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Studies of Cr-doped III-V nitrides, dilute magnetic alloys in the zincblende crystal structure, are presented. The objective of the work is to investigate half-metallicity in Al 0.75 Cr 0.25 N, Ga 0.75 Cr 0.25 N, and In 0.75 Cr 0.25 N for their possible application in spin-based electronic devices. The calculated spinpolarized band structures, electronic properties, and magnetic properties of these compounds reveal that Al 0.75 Cr 0.25 N and Ga 0.75 Cr 0.25 N are half-metallic dilute magnetic semiconductors while In 0.75 Cr 0.25 N is metallic in nature. The present theoretical predictions provide evidence that some Cr-doped III-V nitrides can be used in spintronics devices.

In this paper, the convergence analysis of a proposed new conjugate gradient method for unconstrained optimization problems was considered. This method inherits an important property of Polak-Ribiere-Polyak (PRP). Under the exact line search condition, we established the descent condition of the method as well as the global convergence of the method. Numerical results show that our formula is effective by comparing with some existing formulas.

In this paper, we propose a new hybrid conjugate gradient method for unconstrained optimization problems. The proposed method comprises of beta (DY), beta (WHY), beta (RAMI)  and beta (New). The beta (New)  was constructed purposely for this proposed hybrid method.The method possesses sufficient descent property irrespective of the line search. Under Strong Wolfe-Powell line search, we proved that the method is globally convergent. Numerical experimentation shows the effectiveness and robustness of the proposed method when compare with some hybrid as well as some modified conjugate gradient methods.

An iterative algorithm, which is called the integrated optimal control and parameter estimation algorithm, is developed for solving a discrete time nonlinear stochastic control problem. It is based on the integration of the principle of model-reality differences and Kalman filtering theory, where the dynamic integrated system optimization and parameter estimation algorithm are used interactively. In this approach, the weighted least-square output residual is included in the cost function by appropriately monitoring the weighted matrix. An improved linear quadratic Gaussian optimal control model, rather than the original optimal control problem, is solved. Subsequently, the model optimum is updated using the adjusted parameters induced by the differences between the real plant and the model used. These updated solutions converge to the true optimum, despite model-reality differences. For illustration, the optimal control of a nonlinear continuous stirred tank reactor problem is considered and solved by using the method proposed.