Nonlinear diffraction patterns can be obtained by focusing a laser beam through a thin slice of the material. Here, we investigated experimentally the formation of the far field nonlinear diffraction patterns of cw laser beam at 532 nm passing through a quartz cuvette containing multi-wall carbon nanotubes (MWCNT's) suspended in acetone and in DI water at concentrations of 0.030.wt.%, 0.045 wt.%, 0.060 wt.%, and 0.075 wt.%. Our results show that increasing the concentration of both types of suspensions (MWCNTs in acetone and MWCNTs DI water) led to increase in the number of pattern rings which indicates an increase in their nonlinear refractive indices. Moreover, MWCNTs DI water suspension at a concentration of 0.075 wt. % was more effic

This research study Blur groups (Fuzzy Sets) which is the perception of the most modern in the application in various practical and theoretical areas and in various fields of life, was addressed to the fuzzy random variable whose value is not real, but the numbers Millbh because it expresses the mysterious phenomena or uncertain with measurements are not assertive. Fuzzy data were presented for binocular test and analysis of variance method of random Fuzzy variables , where this method depends on a number of assumptions, which is a problem that prevents the use of this method in the case of non-realized.

The aim of this paper is to introduce and study the notion type of fibrewise topological spaces, namely fibrewise fuzzy j-topological spaces, Also, we introduce the concepts of fibrewise j-closed fuzzy topological spaces, fibrewise j-open fuzzy topological spaces, fibrewise locally sliceable fuzzy j-topological spaces and fibrewise locally sectionable fuzzy j-topological spaces. Furthermore, we state and prove several Theorems concerning these concepts, where j = {δ, θ, α, p, s, b, β}.

 In this work the design and application of a fuzzy logic controller to DC-servomotor is investigated. The proposed strategy is intended to improve the performance of the original control system by use of a fuzzy logic controller (FLC) as the motor load changes. Computer simulation demonstrates that FLC is effective in position control of a DC-servomotor comparing with conventional one.

In this paper, we deal with games of fuzzy payoffs problem while there is uncertainty in data. We use the trapezoidal membership function to transform the data into fuzzy numbers and utilize the three different ranking function algorithms. Then we compare between these three ranking algorithms by using trapezoidal fuzzy numbers for the decision maker to get the best gains

A computational investigation has been carried out on the design and properties of the electrostatic mirror. In this research, we suggest a mathematical expression to represent the axial potential of an electrostatic mirror. The electron beam path under zero magnification condition had been investigated as mirror trajectory with the aid of fourth – order – Runge – Kutta method. The spherical and chromatic aberration coefficients of mirror has computed and normalized in terms of the focal length. The choice of the mirror depends on the operational requirements, i.e. each optical element in optical system has suffer from the chromatic aberration, for this case, it is use to operate the mirror in optical system at various values

In this paper, an Integral Backstepping Controller (IBC) is designed and optimized for full control, of rotational and translational dynamics, of an unmanned Quadcopter (QC). Before designing the controller, a mathematical model for the QC is developed in a form appropriate for the IBC design. Due to the underactuated property of the QC, it is possible to control the QC Cartesian positions (X, Y, and Z) and the yaw angle through ordering the desired values for them. As for the pitch and roll angles, they are generated by the position controllers. Backstepping Controller (BC) is a practical nonlinear control scheme based on Lyapunov design approach, which can, therefore, guarantee the convergence of the position tracking