The use of Cosine transform to analyze the model-noise pattern alteration with different vibration model applied on multimode fiber optics are studied. It's results compared with the Fourier transform to perform the same analysis using total frequency difference and the computation time, which almost coincide for the both transforms. A discussion for the results and recommendation are introduced.

Most of the known cases of strong gravitational lensing involve multiple imaging of an active galactic nucleus. The properties of lensed active galactic nuclei make them promising systems for astrophysical applications of gravitational lensing. So we present a simple model for strong lensing in the gravitational lensed systems to calculate the age of four lensed galaxies, in the present work we take the freedman models with (k curvature index =0) Euclidian case, and the result show a good agreement with the other models.

The new sustainable development goals set by the UN include a goal of making cities inclusive, safe, sustainable, and resilient. Cities are growing at huge rates, and conditions of deteriorating QOL̛s are increasing in the form of poor access to services, and slums are remarkable, especially in the cities of the Middle East; hence, the research problem can arise from a lack of knowledge regarding the in determination of a way to assess the resilience of cities to develop mechanisms that will improve the quality of urban life. In this study, a tool called CRF has been applied for the assessment of the city's resilience principles of health and quality of life, economics and social, infrastructure and environmental systems, and the principle

Estimation of the tail index parameter of a one - parameter Pareto model has wide important by the researchers because it has awide application in the econometrics science and reliability theorem.

Here we introduce anew estimator of ^"generalized median" type and compare it with the methods of Moments and Maximum likelihood by using the criteria, mean square error.

 The estimator of generalized median type performing best over all.

In this research the results of applying Artificial Neural Networks with modified activation function to
perform the online and offline identification of four Degrees of Freedom (4-DOF) Selective Compliance
Assembly Robot Arm (SCARA) manipulator robot will be described. The proposed model of
identification strategy consists of a feed-forward neural network with a modified activation function that
operates in parallel with the SCARA robot model. Feed-Forward Neural Networks (FFNN) which have
been trained online and offline have been used, without requiring any previous knowledge about the
system to be identified. The activation function that is used in the hidden layer in FFNN is a modified
version of the wavelet func

   For extraction chloro anion complexes of Cd2+ and Hg2+ used many organic agents as extractant according to liquid ion exchange method such as α-Naphthyl amine (α-NA), 4-Amino benzoic acid (4-ABA), 2-[(4-Carboxy methyl phenyl) azo]-4,5-diphenyl imidazole (4CMePADPI) and Cryptand (C222). This study includes definition hydrochloric acid concentration in aqueous phase and shaking with organic phase necessary for extraction as well as shaking time, organic solvent effect, interferences and alkaline salt effect. Thermodynamic showed the ion exchange reaction was exothermic for α-NA, C222 and endothermic for 4-ABA, 4-CMePADPI for extraction CdCl4=, but for extraction HgCl4= was exothermic with 4-ABA, 4CMePADPI and C222 but