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 assessment of the environmental impact of the cement industry using the Leopold Matrix is ​​to determine the negative and positive impacts on the environment resulting from this industry, and what are the long-term and short-term effects, direct and indirect, and the amount of these effects and potential risks, and that this evaluation process is done through a number of methods, including Matrix method, including (Leopold).

The importance of the research because the cement occupies is of great importance in the world, especially in our country, Iraq, in the sector of construction and modernity, and the toxic emissions and solid waste produced by the production of this material. <

Many strains of lactic bacteria produce antimicrobial peptides of bacteriocins that are antibiotics used against pathogenic strains. The present work aimed to use a banana peels medium in the fermentation process to replace the commercial MRS medium for decreasing the cost of bacteriocins LAB production. Based on the result, banana peel was a cost-effective and viable alternative carbon source for the production and development of bacteriocin-producing Lactobacilli. The growth of lactobacilli in commercial MRS medium and Banana Peel medium showed no differences, therefore banana peel waste can be used to produce Lactobacilli bacteriocins. Lactobacillus strains grew exceptionally well at 37 C and pH 6.0.

Urban land uses of all kinds are the constituent elements of the urban spatial structure. Because of the influence of economic and social factors, cities in general are characterized by the dynamic state of their elements over time. Urban functions occur in a certain way with different spatial patterns. Hence, urban planners and the relevant urban management teams should understand the future spatial pattern of these changes by resorting to quantitative models in spatial planning. This is to ensure that future predictions are made with a high level of accuracy so that appropriate strategies can be used to address the problems arising from such changes. The Markov chain method is one of the quantitative models used in spatial planning to ana

Soil stabilization with stone powder is a good solution for the construction of subgrade for road way and railway lines, especially under the platforms and mostly in transition zones between embankments and rigid structures, where the mechanical properties of supporting soils are very influential. Stone powder often has a unique composition which justifies the need for research to study the feasibility of using this stone powder type for ground improvement applications. This paper presents results from a comprehensive laboratory study carried out to investigate the feasibility of using stone powder for improvement of engineering properties of clays.

The stone powder contains bassanite (CaSO₄. ½ H

In the present work, pattern recognition is carried out by the contrast and relative variance of clouds. The K-mean clustering process is then applied to classify the cloud type; also, texture analysis being adopted to extract the textural features and using them in cloud classification process. The test image used in the classification process is the Meteosat-7 image for the D3 region.The K-mean method is adopted as an unsupervised classification. This method depends on the initial chosen seeds of cluster. Since, the initial seeds are chosen randomly, the user supply a set of means, or cluster centers in the n-dimensional space.The K-mean cluster has been applied on two bands (IR2 band) and (water vapour band).The textural analysis is used

Transport is a problem and one of the most important mathematical methods that help in making the right decision for the transfer of goods from sources of supply to demand centers and the lowest possible costs, In this research, the mathematical model of the three-dimensional transport problem in which the transport of goods is not homogeneous was constructed. The simplex programming method was used to solve the problem of transporting the three food products (rice, oil, paste) from warehouses to the student areas in Baghdad, This model proved its efficiency in reducing the total transport costs of the three products. After the model was solved in (Winqsb) program, the results showed that the total cost of transportation is (269,

  Survival analysis is the analysis of data that are in the form of times from the origin of time until the occurrence of the end event, and in medical research, the origin of time is the date of registration of the individual or the patient in a study such as clinical trials to compare two types of medicine or more if the endpoint It is the death of the patient or the disappearance of the individual. The data resulting from this process is called survival times. But if the end is not death, the resulting data is called time data until the event. That is, survival analysis is one of the statistical steps and procedures for analyzing data when the adopted variable is time to event and time. It could be d

This paper is concerned with introducing and studying the M-space by using the mixed degree systems which are the core concept in this paper. The necessary and sufficient condition for the equivalence of two reflexive M-spaces is super imposed. In addition, the m-derived graphs, m-open graphs, m-closed graphs, m-interior operators, m-closure operators and M-subspace are introduced. From an M-space, a unique supratopological space is introduced. Furthermore, the m-continuous (m-open and m-closed) functions are defined and the fundamental theorem of the m-continuity is provided. Finally, the m-homeomorphism is defined and some of its properties are investigated.