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

In the present work theoretical relations are derived for the efficiency evaluation for the generation of the third and the fourth harmonics u$ing crystal cascading configuration. These relations can be applied to a wide class of nonlinear optical materials. Calculations are made for beta barium borate (BBO) crystal with ruby laser /.=694.3 nm . The case study involves producing the third harmonics at X. =231.4 nm of the fundamental beam. The formula of efficiency involves many parameters, which can be changed to enhance the efficiency. The results showed that the behavior of the efficiency is not linear with the crystal length. It is found that the efficiency increases when the input power increases. 'I'he walk-off length is calculated for

In this study, the adsorption of Zn (NO3)2 is carried out by using surfaces of malvaparviflora. The validity of the adsorption is evaluated by using atomic absorption Spectrophotometry through determination the amount of adsorbed Zn (NO3)2. Various parameters such as PH, adsorbent weight and contact time are studied in terms of their effect on the reaction progress. Furthermore, Lagergren’s equation is used to determine adsorption kinetics. It is observed that high removal of Zn (NO3)2 is obtained at PH=2. High removal of Zn (NO3)2 is at the time equivalent of 60 min and reaches equilibrium,where 0.25gm is the best weight of adsorbant . For kinetics the reaction onto malvaparviflora follows pseudo first order Lagergren’s equation.

Abstract

The study presents a mathematical model with a disaggregating approach to the problem of production planning of a fida Company; which belongs to the ministry of Industry. The study considers disaggregating the entire production into 3 productive families of (hydraulic cylinders, Aldblatt (dampers), connections hydraulics with each holds similar characteristics in terms of the installation cost, production time and stock cost. The Consequences are an ultimate use of the available production capacity as well as meeting the requirements of these families at a minimal cost using linear programming. Moreover, the study considers developing a Master production schedule that drives detailed material and production requi

ABSTRACT Background: According to Branemark’s protocol, the waiting period between tooth extraction and implant placement is 6–8 months; this is the late placement technique. Achieving and maintaining implant stability are prerequisites for a dental implant to be successful. Resonance Frequency Analysis (RFA) is a noninvasive diagnostic method that measures implant stability. The aim of this study was to investigate the influence of treatment protocol and implant dimensions on primary implant stability utilizing RFA. Materials and methods: This study included 63 Iraqi patients (37 male, 26 female; ranging 22-66 years). According to treatment protocol, the sample was divided into 2 groups; A (delayed) & B (immediate). Dental im