The aim of this paper is to introduce the definition of projective 3-space over Galois field GF(q), q = p^m, for some prime number p and some integer m.

        Also the definitions of (k,n)-arcs, complete arcs, n-secants, the index of the point and the projectively equivalent arcs are given.

        Moreover some theorems about these notations are proved.

This paper designed a fault tolerance for soft real time distributed system (FTRTDS). This system is designed to be independently on specific mechanisms and facilities of the underlying real time distributed system. It is designed to be distributed on all the computers in the distributed system and controlled by a central unit.

Besides gathering information about a target program spontaneously, it provides information about the target operating system and the target hardware in order to diagnose the fault before occurring, so it can handle the situation before it comes on. And it provides a distributed system with the reactive capability of reconfiguring and reinitializing after the occurrence of a failure.

It is shown that if a subset of a topological space (χ, τ) is δ-semi.closed, then it is semi.closed. By use this fact, we introduce the concept regularity of a topological space (χ, τ) via δ-semi.open sets. Many properties and results were investigated and studied. In addition we study some maps that preserve the δ-semi.regularity of spaces.

In general, the importance of cluster analysis is that one can evaluate elements by clustering multiple homogeneous data; the main objective of this analysis is to collect the elements of a single, homogeneous group into different divisions, depending on many variables. This method of analysis is used to reduce data, generate hypotheses and test them, as well as predict and match models. The research aims to evaluate the fuzzy cluster analysis, which is a special case of cluster analysis, as well as to compare the two methods—classical and fuzzy cluster analysis. The research topic has been allocated to the government and private hospitals. The sampling for this research was comprised of 288 patients being treated in 10 hospitals. As t

Through this study, the following has been proven, if  is an algebraically paranormal operator acting on separable Hilbert space, then  satisfies the ( ) property and  is also satisfies the ( ) property for all . These results are also achieved for  ( ) property.    In addition, we prove that for a polaroid operator with finite ascent then after the property ( ) holds for  for all.

Through this study, the following has been proven, if  is an algebraically paranormal operator acting on separable Hilbert space, then  satisfies the ( ) property and  is also satisfies the ( ) property for all . These results are also achieved for  ( ) property.

   In addition, we prove that for a polaroid operator with finite ascent then after the property ( ) holds for  for all .

 In this work, the preparation of some new oxazolidine and thiazolidine derivatives has been conducted. This was done over two steps; the first step included the synthesis of Schiff bases A1-A5 in 72-88% yields by the condensation of isonicotinic acid hydrazide and aldehydes. The second step includes the cyclization of derivatives A1-A5 with glycolic acid and thioglycolic acid to obtain the desired products, oxazolidine derivatives B1-B5 (44-60% yields) and thiazolidine derivatives C1-C5 (41-61% yields), respectively. The structure of the prepared compounds was characterized using FT-IR, 1H NMR, and 13C NMR spectroscopy. Some of the produced compounds were tested for antioxidant properties.  

The fuzzy assignment models (FAMs) have been explored by various literature to access classical values, which are more precise in our real-life accomplishment. The novelty of this paper contributed positively to a unique application of pentagonal fuzzy numbers for the evaluation of FAMs. The new method namely Pascal's triangle graded mean (PT-GM) has presented a new algorithm in accessing the critical path to solve the assignment problems (AP) based on the fuzzy objective function of minimising total cost. The results obtained have been compared to the existing methods such as, the centroid formula (CF) and centroid formula integration (CFI). It has been demonstrated that operational efficiency of this conducted method is exquisitely develo

In this paper, the series solution is applied to solve third order fuzzy differential equations with a fuzzy initial value. The proposed method applies Taylor expansion in solving the system and the approximate solution of the problem which is calculated in the form of a rapid convergent series; some definitions and theorems are reviewed as a basis in solving fuzzy differential equations. An example is applied to illustrate the proposed technical accuracy. Also, a comparison between the obtained results is made, in addition to the application of the crisp solution, when the-level equals one.