In this paper, the packing problem for complete (  4)-arcs in  is partially solved. The minimum and the maximum sizes of complete (  4)-arcs in  are obtained. The idea that has been used to do this classification is based on using the algorithm introduced in Section 3 in this paper. Also, this paper establishes the connection between the projective geometry in terms of a complete ( , 4)-arc in  and the algebraic characteristics of a plane quartic curve over the field  represented by the number of its rational points and inflexion points. In addition, some sizes of complete (  6)-arcs in the projective plane of order thirteen are established, namely for  = 53, 54, 55, 56.

In this work, we prove by employing mapping Cone that the sequence and the subsequence of the characteristic-zero are exact and subcomplex respectively in the case of partition (6,6,4) .

 Let  be a connected graph with vertices set  and edges set . The ordinary distance between any two vertices of  is a mapping  from  into a nonnegative integer number such that  is the length of a shortest  path. The maximum distance between two subsets  and  of   is the maximum distance between any two vertices  and  such that  belong to  and  belong to . In this paper, we take a special case of maximum distance when  consists of one vertex and  consists of  vertices, . This distance is defined by: where  is the order of  a graph .

     In this paper, we defined  – polynomials based on

The current research aims to measure the job satisfaction of educational counselors in the general directorate of education of the second Rusafa in the ministry of education of Iraq. Moreover, it aims to identify the significant differences in job satisfaction according to the gender (Male-Female), the length of service (less than 15 years more than 15 years), and the relationship between these two variables. To achieve the objectives of the research, the researcher developed a scale to measure job satisfaction. This tool was applied to sample of (100) educational counselors selected randomly. The results showed that educational counselors have job satisfaction, in which males are more satisfied in their job than females. The results als

In the current work, the mixing ratios ( 𝛿 ) of gamma transitions were calculated from energy levels in the isotopes neodymium 60𝑁𝑎 142−150 populated in the 60Nd 142− 150 (n, n ˊγ) 60Nd 142− 150 using the 𝑎2 ratio method. We used the experimental coefficient (𝑎2 ) for two γ-transitions from the initial state itself, the statistical tensor 𝜌2(𝐽𝑖), associated with factor 𝑎2 , would be the same for the two transitions. The results obtained are in good agreement or within the experimental error with -those previously published. And existing contradictions resulting from inaccuracies in the empirical results of previous work. The current results confirm that the , 𝑎2 − method is used to calculate th

The present work involved designing and synthesizing of a series of new. compounds which their molecules are composed from two biologically active components namely sulfamethoxazole or β-lactam containing drugs and cyclic imides. The target new compounds were synthesized by two steps in the first one a series of six bis (N-drug phthalamic acid_4-yl) ketone (1-6) were prepared from the reaction of sulfamethoxazole or β-lactam containing drugs with benzophenone 3, 3′, 4, 4′ -tetracarboxylic dianhydride.

In the second step, compounds (1-6) were introduced in dehydration reaction via fusion process producing the target compounds bis (N-drug phthalimidyl-4-yl) ketone (7-12). The antibacterial and antifungal high

In this article, the notions  are introduced by using soft ideal and soft semi-open sets, which are - - - -closed sets " -closed" where many of the properties of these sets are clarified. Some games by using soft- -semi, soft separation axioms: like ( ₀   ( ₀  Using many figures and proposition to study the relationships among these kinds of games with some examples are explained.

In The Name of Allah Most Gracious Most Merciful

The characteristics of the doers of good are mentioned in the Holy Book of God, and love for them in five places, and whoever God loves, honors him and gives him victory. As for the love of the righteous, it has to do with loyalty, covenant, and integrity. Committing sins 0 Then after that he mentioned God those who fight in His cause and those who rely on Him and return to Him and turning away from everything else.

     Let R be a commutative ring with unity and an R-submodule N is called semimaximal if and only if

 the sufficient conditions of F-submodules to be semimaximal .Also the concepts of (simple , semisimple) F- submodules and quotient F- modules are  introduced and given some  properties .