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Many reports and patents address tracking-type systems to complete and optimized the acquisition of solar energy. However, fixed-type systems contribute the most of the market to the solar photovoltaic system (SPVS) for the existing buildings. Based on this fact, it is important to discuss and understand the feasible setup parameters to achieve the optimum radiation-collection-efficiency of a fixed-type system. The purpose of the present report is to provide the methodology and to investigate the optimum angles of the system facilities through minimum mathematics. The calculations show that for the demonstrated locations, the maximum efficiency for the whole year of a fixed-type system can reach more than 61% efficiency, compared to a total tracking system at the same location and time intervals. Based on these calculations, the appropriate optical system can be designed to improve system performance for the majority buildings requirements in any location.

Stresses distribution between the interfaces of the materials is critical for structures like thin film layers, organic/inorganic light emitting diode layers and various kinds of modern optical-electronics components with stacking materials properties. The classical Aleck's model ( 1949 ) can be considered as a very simple and a practical method to analyze these kinds of structures. In order to deal with it, the integration scheme is used to solve the displacement equations with zero displacements on the clamped edge including the clamped corner. The condition of zero traction is imposed at all of the grid points on the free surface except for the clamped corner of layers. The results show a stress singularity at the clamped corner. This agrees with an existing finite element solution performed on a very fine grid. By contrast, the known Kantorovich solution for Aleck problem from Blech and Kantor (1984) did not predict such stress singularity. As remarked by Blech and Kantor, the Kantorovich solution posed difficulties in convergence in the immediate vicinity of the clamped corner, thus is questionable to apply the results for the layer structures through this model.

Under the existence of system uncertainties, external disturbances, and input nonlinearity, complete synchronization and anti-synchronization between two chaotic gyros are achieved by introducing a novel adaptive terminal sliding mode (ATSM) controller. In the literature, by taking account of input nonlinearity, the magnitudes of bounded nonlinear dynamics of synchronous error system were required in the designed sliding mode controller. In this study, the proposed ATSM controller associated with time-varying feedback gains can tackle nonlinear dynamics according to the novel adaptive rules. These feedback gains are not necessary to be determined in advance but updated by the adaptive rules without known the magnitudes of bounded nonlinear dynamics, system uncertainties, and external disturbances. Sufficient conditions to guarantee stable synchronization are given in the sense of the Lyapunov stability theorem, and the numerical simulations are performed to verify the effectiveness of presented schemes.