In this work, we present a new techniques to solve the integral equations of the second kind with logarithmic kernel. First, we show the existence and uniqueness of the solution for the given problem in a Hilbert space. Next, we discuss a projection method for solving integral equations with logarithmic kernel of the second kind; the present method based on the shifted Legendre polynomials. We examine the existence of the solution for the approximate equation, and we provide a new error estimate for the numerical solutions. At the end, numerical examples are provided to illustrate the theoretical results.

In any wireless cellular network, power control is one of the most important dynamic radio resource management (RRM) schemes which increases the capacity and performance of the system. In this paper, we present a modified scheme to Distributed Power control that optimize the transmission power of mobile’s and signal-to-interference-plus-noise ratio (SINR) error. This method, based on minimization of performance criterion, achieves the minimum SINR error and power consumption at the next time instant. The Mixed Kalman/H$ınfty$ Filter with covariance intersection has been applied in the proposed scheme to estimate and predict the channel variation and still ensure a good robustness. Finally, the mixed Kalman/H$ınfty$ filter based power control method is compared with Kalman filter and H$ınfty$ filter based power control results show that our method provides robustness against practical impairments, such as measurement uncertainties and fast channel variations.

In this paper, we propose a new n-ZnO/p-Si hetero-junction solar cell design based on both interface engineering and metallic nanoparticles aspects. The merits of using both metallic nanoparticles and grooves morphology in the ZnO/p-Si interface to improve solar cell optical performance are investigated numerically using accurate solutions of Maxwell’s equations. It is found that the proposed structure suggests the possibility to achieve the dual role of improved light-scattering in the Si absorber layer as well as enhancing the absorption in the ZnO thin-film through the Surface Plasmon Resonance effect. Besides, the proposed design exhibits superior optical performance and offers improved total absorbance efficiency (TAE) as compared to the conventional counterpart. Moreover, particle swarm optimization (PSO)-based approach is exploited for the geometrical optimization of the proposed design to achieve higher light trapping capability. It is found that the optimized design yields 50% of relative improvement in the ZnO/p-Si-based solar cell TAE which confirms excellent capability of the proposed design approach for modulating the electric field behavior inside the solar cell structure. The obtained results indicate that the optimized n-ZnO/p-Si hetero-junction solar cell offer the potential for high conversion efficiency at low costs which make it valuable for photovoltaic application.