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 this research, we sought to identify the nature of the relationship between the exchange rate of the Chinese yuan and the value of Chinese exports, through the formulation of a standard model based on the model of common integration, and based on the data of the study and using the test "Angel-Granger" It reflects the relationship between the two research variables, through which the relationship between the RMB exchange rate and the value of Chinese exports was estimated during the period 1978-2017.

Leuconostoc bacteria was isolated from local pickled cabbage (Brassica oleracea capitata) and identified as Leuconostoc mesenteroides by morphology,biochemical and physiological. The local isolated L. mesenteroides bacteria under the optimal conditions of dextran production showed that, the highly production of dextran was 7.7g achieved by using a modified natural media comprised of 100ml whey, 10g refined sugar, 0.5g heated yeast extract, 0.01g CaCl2, 0.001g MgSO4, 0.001g MnCl2 and 0.001g NaCl at pH 6 and 25̊C for 24 hr of fermentation and by using 1ᵡ106 cell/ml as initial inoculums volume. Some applications in food technology (Ice cream, Loaf, Ketchup and Beef preservation) have been performed with processed dextran. The result

The aim of this study was to increasing natural carotenoides production by a locally isolate Rodotorula mucilagenosa M. by determination of the optimal conditions for growth and production of this agents, for encouragest to use it in food application permute artificial pigments which harmfull for consumer health and envieronmental. The optimal condition of carotenoides production from Rhodotorula mucilaginosa M were studied. The results shows the best carbon and nitrogen source were glucose and yeast extract. The carotenoids a mount production was 47430 microgram ̸ litter and 47460 microgram ̸ litter, respectively, and the optimum temperature was 30°C, PH 6, that the carotenoides a mount was 47470 microgram ̸ litter and 47670 microgr

The derivation of 5^th order diagonal implicit type Runge Kutta methods (DITRKM5) for solving 3^rd special order ordinary differential equations (ODEs) is introduced in the present study. The DITRKM5 techniques are the name of the approach. This approach has three equivalent non-zero diagonal elements. To investigate the current study, a variety of tests for five various initial value problems (IVPs) with different step sizes h were implemented. Then, a comparison was made with the methods indicated in the other literature of the implicit RK techniques. The numerical techniques are elucidated as the qualification regarding the efficiency and number of function evaluations compared with another literature of the implic

A simple, rapid and sensitive spectrophotometric method has been proposed for the determination of La (III) using 3-hydroxy -4-(2-hydroxy-phenyl azo) naphthalene -1- sulfonic acid as a chromogenic reagent. This method is based on the formation of a red-pink colored complex, upon the reaction of La(III) with the reagent in an alkaline medium (pH= 9.50), having a maximum absorbance at 459 nm. Beer's law is valid in the concentration range 0.512 µg.ml-1 with a Sandell's sensitivity value of 0.0188 µg.cm-2 and molar absorptivity of 7376.12 L.mol-1.cm-1. The stoichiometric composition of the chelate is 1:3. The effect of the presence of different cations as interferants in the determination of La(III) under the given optimum conditions