This paper contains an equivalent statements of a pre-  space, where  are considered subsets of with the product topology. An equivalence relation between the preclosed set  and a pre-  space, and a relation between a pre-  space and the preclosed set  with some conditions on a function  are found. In addition, we have proved that the graph  of  is preclosed in if  is a pre-  space, where the equivalence relation  on  is open.

     On the other hand, we introduce the definition of a pre-stable ( pre-stable) set by depending on the concept of a pre-neighborhood, where we get that every stable set is pre-stable. Moreover, we obtain that

Graphic design art depends on changeable cognitive systems which their relation and items relying on the accumulation of humane knowledge and thong and the humane look to the venality and his explanation to the relation between him and the venality , then the graphic design art becomes an important item of this accumulation knowledge besides , it is on kind of knowledge kinds . The technological advancement in communication lauds to increasing in communication media and design methods , where the computer and its application in graphic design promotes the design process because of it's capalebities which lead to in creasing in production process , minimizing the cost and time and achieving creative and aesthetic aspect because of it's fe

Proxy-based sliding mode control PSMC is an improved version of PID control that combines the features of PID and sliding mode control SMC with continuously dynamic behaviour. However, the stability of the control architecture maybe not well addressed. Consequently, this work is focused on modification of the original version of the proxy-based sliding mode control PSMC by adding an adaptive approximation compensator AAC term for vibration control of an Euler-Bernoulli beam. The role of the AAC term is to compensate for unmodelled dynamics and make the stability proof more easily. The stability of the proposed control algorithm is systematically proved using Lyapunov theory. Multi-modal equation of motion is derived using the Galerkin metho

The research aimed to achieve many objectives represented in two variables, which are the impacted factors and the aggregate planning alternatives of workforce in Educational Al- yarmouk Hospital , This research started from a problem focused on finding solutions to the demand’s  fluctuation  or the energy limitation while the study importance is emerged from diagnosis the suitable strategy and adopt the suitable alternatives due to their importance in meeting the demand for the health service submitted by the hospital .This study  based on choosing assumptions of connection relationship and the impact among the mentioned variables in the(surgery and internal diseases) departments. The research is dependent on ch

The research aims at the identity of the accounting information and its characteristics, and then to study the possibility of using accounting information in rationalizing the decisions of capital expenditure. The study relied upon the descriptive analytical approach it is suitable to the nature of this study, the hypotheses of the study were tested by using a number of statistical methods by relying on statistical package program (SPSS), and the research concluded that the companies listed in Khartoum Stock Exchange using accounting information in the comparison between investment alternatives available and estimating the number of years required to recover of the investment cost, the challenges that cause weakness in using the

In this research, we find the Bayesian formulas and the estimation of Bayesian expectation for product system of Atlas Company.  The units of the system have been examined by helping the technical staff at the company and by providing a real data the company which manufacturer the system.  This real data include the failed units for each drawn sample, which represents the total number of the manufacturer units by the company system.  We calculate the range for each estimator by using the Maximum Likelihood estimator.  We obtain that the expectation-Bayesian estimation is better than the Bayesian estimator of the different partially samples which were drawn from the product system after  it checked by the

This paper aims to improve the voltage profile using the Static Synchronous Compensator (STATCOM) in the power system in the Kurdistan Region for all weak buses. Power System Simulation studied it for Engineers (PSS\E) software version 33.0 to apply the Newton-Raphson (NR) method. All bus voltages were recorded and compared with the Kurdistan region grid index (0.95≤V ≤1.05), simulating the power system and finding the optimal size and suitable location of Static Synchronous Compensator (STATCOM)for bus voltage improvement at the weakest buses. It shows that Soran and New Koya substations are the best placement for adding STATCOM with the sizes 20 MVAR and 40 MVAR. After adding STATCOM with the sizes [20MVAR and 40MV

The combination of high protein content and a soft seed coat makes the wheat-rye hybrid Triticale (Triticosecale) vulnerable to attack by rice weevils. Drying triticale grain to moisture contents safe for storage can prevent infestation by rice weevils, but if grain is being stored for seed, high drying temperatures can affect seed germination. Grain can be effectively dried at low temperatures, but low-temperature drying is difficult in hot, humid regions such as the Gulf Coast. This study nvestigated the effects of drying temperatures from 35°C to 45°C on triticale seed germination and found no statistical differences between the germination rates of the seed at any of the drying temperatures and the germination rates of controls. Final