In this paper, we characterize normal composition operators induced by holomorphic self-map , when and .Moreover, we study other related classes of operators, and then we generalize these results to polynomials of degree n.

Necessary and sufficient conditions for the operator equation I AXAX n*, to have a real positive definite solution X are given. Based on these conditions, some properties of the operator A as well as relation between the solutions X andAare given.

In this paper, we will introduce the concept of interval value fuzzy n-fold KU-ideal in KU-algebras, which is a generalization of interval value fuzzy KU-ideal of KU-algebras and we will obtain few properties that is similar to the properties of interval value fuzzy KU-ideal in KU-algebras, see [8]. Also, we construct some algorithms for folding theory applied to KU-ideals in KU-algebras.

The importance of algae as a natural source of various bioactive compounds continues to grow due to their diverse biological activities. One of such compounds is n-hexadecanoic acid, more commonly known as palmitic acid; it is more lipidous than many algal species. It is one of the most common saturated fatty acids in nature. One can find it in algal, animal, and plant oils and is extracted from numerous natural sources. Its chemical and biological attributes enable its widespread use in the pharmaceutical, food, and cosmetic industries. Numerous studies have found that palmitic acid is effective for fungal activities and does have pharmaceutical and environmental promising antioxidant capabilities.

The imbalances and economic problems which it face the countries, it is a result of international economic developments or changes or global crises such as deterioration in trade, sharp changes in oil prices, increasing global indebtedness, sharp changes in foreign exchange rates and other changes, all that, they affect the economic features of any country. and These influences vary from one country to another according to the rigidity of its economy and its potential in maneuvering with economic plans and actions that would reduce the impact or avoidance with minimal damage. Therefore, the countries  that  suffer from accumulated economic problems as a result of mismanagement and poor planning or suffe

The aim of the current research is to know the degree to which middle school teachers and female teachers in the southern border schools use electronic educational alternatives in the field of education from their point of view and its relationship to some variables, and to achieve this goal, a random sample of (200) teachers was selected in southern border schools, and a questionnaire was prepared to collect The data, as well as the descriptive approach was used to achieve this goal. T-test and analysis of variance were used for the statistical treatment. The results concluded that the educational courses provided to male and female teachers are not sufficient. It has also been concluded that the use of electronic educational alternativ