The importance of topology as a tool in preference theory is what motivates this study in which we characterize topologies generating by digraphs. In this paper, we generalized the notions of rough set concepts using two topological structures generated by out (resp. in)-degree sets of vertices on general digraph. New types of topological rough sets are initiated and studied using new types of topological sets. Some properties of topological rough approximations are studied by many propositions.

The currency in circulation is a key element of the monetary supply system of the Iraqi economy because itreflects the level of economic activity and the liquidity level in the market. It can be expressed as an important tool when formulating monetary policy. This research aims to analyze and forecast the behavior of the currency in circulation in Iraq using the ARMA-GARCH model for monthly data from 2004 to 2025 to understand the dynamics of monetary liquidity, The sample was divided into two parts: approximately 80% for the training set (2004-2021), and approximately 20% for the testing set (2022-2025). Data were analyzed in Python using many packages. The results showed that the time series was initially non-stationary but became

The orbital motion and longitude for some Jupiter's satellites (Amaletha, Europa, Ganymede and Callisto) were calculated from two different locations Iraq and Syria. A program was designed, the input parameters were the desired year, month, day and the longitude of the location, the output parameters results were applied in form of a file, and this file includes the longitude, orbital motion, and local time of these satellites. A specific date 1-10-2013 was taken, the results of longitude was (20-336) º and orbital motion was (92-331) º for both Iraq and Syria location with observing time (05:24:14-15:18:10) for Iraq and (04:56:33-14:50:30) for Syria. The difference in time between the two locations was constant (00:45:00), these results

In this paper we prove the boundedness of the solutions and their derivatives of the second order ordinary differential equation x ?+f(x) x ?+g(x)=u(t), under certain conditions on f,g and u. Our results are generalization of those given in [1].

This study focuses on studying the effect of reinforced steel in detail, and steel reinforcement (tensile ratio, compression ratio, size, and joint angle shape) on the strength of reinforced concrete (compressive strength) Fc' and searching for the most accurate details of concrete divisions, their behavior, and corner resistance of reinforced concrete joint. The comparison of this paper with previous studies, especially in the studied properties. The conclusions of the chapter are summarized that these effects had a clear effect and a specific effect on the behavior and resistance of the reinforced concrete corner joints under the negative moments and under their influence and the resulting stress conditions. The types of defects that can

The risk assessment for three pipelines belonging to the Basra Oil Company (X1, X2, X3), to develop an appropriate risk mitigation plan for each pipeline to address all high risks. Corrosion risks were assessed using a 5 * 5 matrix. Now, the risk assessment for X1 showed that the POF for internal corrosion is 5, which means that its risk is high due to salinity and the presence of CO, H2S and POF for external corrosion is 1 less than the corrosion, while for Flowline X2 the probability of internal corrosion is 4 and external is 4 because there is no Cathodic protection applied due to CO2, H2S and Flowline X3 have 8 leaks due to internal corrosion so the hazard rating was very high 5 and could be due to salinity, CO2, fluid flow rate

This study is due to insufficient development of the issues of initial training in tennis at youthful (student) age. Objective: development of a methodological and scientific-methodological base of students' tennis with current trends in tennis. Summing up the best practices of modern tennis, we came to the conclusion that the formation of the art of reflection backhands in teaching beginner students of sports specialization to achieve future success. In modern conditions in the development of Russian tennis student opens the possibility of using new technologies and programs. Using these approaches, we have developed a training program and tested students' tennis in the pedagogical experiment, which resulted in its effectiveness.

A theoretical model is developed to determine time evolution of temperature at the surface of an opaque target placed in air for cases characterized by the formation of laser supported absorption waves (LSAW) plasmas. The model takes into account the power temporal variation throughout an incident laser pulse, (i.e. pulse shape, or simply: pulse profile).
Three proposed profiles are employed and results are compared with the square pulse approximation of a constant power.