This paper is concerned with introducing and studying the first new approximation operators using mixed degree system and second new approximation operators using mixed degree system which are the core concept in this paper. In addition, the approximations of graphs using the operators first lower and first upper are accurate then the approximations obtained by using the operators second lower and second upper sincefirst accuracy less then second accuracy. For this reason, we study in detail the properties of second lower and second upper in this paper. Furthermore, we summarize the results for the properties of approximation operators second lower and second upper when the graph G is arbitrary, serial 1, serial 2, reflexive, symmetric, tra

Throughout this paper we study the properties of the composition operator
C
p1  o
p2  o…o
pn  induced by the composition of finite numbers of special
automorphisms of U,
pi  (z)  i
i
p z
1 p z


Such that pi  U, i  1, 2, …, n, and discuss the relation between the product of
finite numbers of automorphic composition operators on Hardy space H2 and some
classes of operators.

this research concern with material function subject by using it in Baghdad education in formational places , because it considered as one of the most important spaces which needs a material presentation for the interior consistings that shares with prepairing the right mode for thos who use these spaces, regarding to that this research includes four chapters: Chapter one: concern with the research problem represented by the following question: can we use the material to place the hole spaces of information place ? So the aim of the research seems very obvious in functioning the material these places, and to take a close view on the importance of the research the theory , implementation and objective limits also concerning the terminolog

In this paper, a new type of supra closed sets is introduced which we called supra β*-closed sets in a supra topological space. A new set of separation axioms is defined, and its many properties are examined. The relationships between supra β*-Ti –spaces (i = 0, 1, 2)   are studied and shown with instances. Additionally, new varieties of supra β*-continuous maps have been taken into consideration based on the supra β*-open sets theory. 

In this paper, certain types of regularity of topological spaces have been highlighted, which fall within the study of generalizations of separation axioms. One of the important axioms of separation is what is called regularity, and the spaces that have this property are not few, and the most important of these spaces are Euclidean spaces. Therefore, limiting this important concept to topology is within a narrow framework, which necessitates the use of generalized open sets to obtain more good characteristics and preserve the properties achieved in general topology. Perhaps the reader will realize through the research that our generalization preserved most of the characteristics, the most important of which is the hereditary property. Two t

Artificial fish swarm algorithm (AFSA) is one of the critical swarm intelligent algorithms. In this
paper, the authors decide to enhance AFSA via diversity operators (AFSA-DO). The diversity operators will
be producing more diverse solutions for AFSA to obtain reasonable resolutions. AFSA-DO has been used to
solve flexible job shop scheduling problems (FJSSP). However, the FJSSP is a significant problem in the
domain of optimization and operation research. Several research papers dealt with methods of solving this
issue, including forms of intelligence of the swarms. In this paper, a set of FJSSP target samples are tested
employing the improved algorithm to confirm its effectiveness and evaluate its ex

Liquisolid compact is the most promising technique for increasing dissolution rate and bioavailability of poorly soluble drugs.Clopidogrel bisulfate is an oral antiplatelets used for treatment and prophylaxis of cardiovacular and peripheral vascular diseases related to platelets aggreagation.Clopidogrel has low solubility at high pH media of intestine and low bioavailability of a bout 50% after oral doses.The purpose of this work was to enhance dissolution pattern of clopidogrel through its formulation into liquisolid tablets.A mathematical model was used to calculate the optimum quantities of tween 80 , carrier (Avicel PH 102) and coating material (Aerosil 200) needed to prepare acceptably flowing and compactible powder mixtures.The liq