In this article, we aim to define a universal set consisting of the subscripts of the fuzzy differential equation (5) except the two elements  and , subsets of that universal set are defined according to certain conditions. Then, we use the constructed universal set with its subsets for suggesting an analytical method which facilitates solving fuzzy initial value problems of any order by using the strongly generalized H-differentiability. Also, valid sets with graphs for solutions of fuzzy initial value problems of higher orders are found.

    In this paper generalized spline method is used for solving linear system of fractional integro-differential equation approximately. The suggested method reduces the system to system of  linear algebraic equations. Different orders of fractional derivative for test example is given in this paper to show the accuracy and applicability of the presented method.

In this paper, we define some generalizations of topological group namely -topological group, -topological group and -topological group with illustrative examples. Also, we define grill topological group with respect to a grill. Later, we deliberate the quotient on generalizations of topological group in particular -topological group. Moreover, we model a robotic system which relays on the quotient of -topological group.

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

Bentonite is widely used in industrial applications. The present study reports the effect of adding different weights of ZnO to the Iraqi bentonite, on surface area, pore volume and real density. These surface properties were evaluated for pure and modified bentonite. The modification was made by adding different ZnO weights such as; ( 0.5%, 1%, 5%, 10% ). The effect of heat exposing for all modified clay samples at 500 ?C have been also evaluated. The results show that the addition of 0.5% ZnO leads to increase the surface area percentage about 36%, increase pore volume percentage about 5.48% and increase the real density percentage about 27.116%. When the samples exposed to 500 ?C, their surface area and pore volumes have been decreased a

Tendon is important structure of the human body, since it can sustain tensile loading. The primary function of this tissue is to stabilize the joints they attached to it during daily activities. As well as, tendon has viscoelastic properties that can determine their response to loading and restrict the potential of injuries. One of the major points that this paper works with is the study of the biomechanical behaviour of tendon in response to tensile loading to describe their biological behaviour. Also, conclude the mathematical expression that may illustrate the tendon behaviour. All of the experiments were made in Physiology laboratories / Medical College/ Al- Nahrain University on ten rats "Rattus Norvegicus" of [108- 360] gm weight f

The last ten years observed a shift enormous scientific in the method and way that it deals professional with the cost accounting and reflected the result those shift enormous scientific of increase the competitive environmental that accompanied the emergence of a modern manufacturing environmental on surface the long roductive life and emergence advanced information technology that give a central focus of his important on client with growing global markets growth on a large scale.

        The research aim to define the concept of cost awareness, the concept and methods of  strategic cost management and the role of cost awareness for managers of industrial units in strategic of cost managem

          The present art icle discusses the prob lems of understanding and translating the lingu istic and cult ural aspect of a foreign lite rary text. The article considers the trans lation process through the pr ism of cult ural orientation. In the process of transl ation, the nati onal cultural iden tity should be expressed to the max imum extent, through all me ans of expre ssion that include imagery and inton ation. In addi tion to the author's sty le, special atte ntion should al so be pa id to tro pes, phraseological uni ts, colloquial wo rds and dial&n

       The article analyzes the neologisms that arose in the Iraqi dialect after the 2003 US-British invasion and the fall of Saddam Hussein's regime, according to the theory I advocate: "The Basic Outline of Reference," a developed theory of Arab legacy and cognitive theory, which came out in 1987 in America, so we have used the terminology of cognitive grammar. In this theory it is stated that the reference is the interaction between four components: perception, imagination, imaginative comprehension and the linguistic sign or symbolization (the neological word in this article), which are closely related, so that none of them can be lacking, because they constitute a holistic whole that belongs to a deeper level. Let us

Summary The objective of the research is to learn the design of a learning educational learning according to the theory of Ausubel in the acquisition of geographical concepts among the students of the fourth primary in the field of geography and the development of their habits of mind. To achieve this, the researcher relied on the two hypotheses the researcher used the design of equal groups the first experimental group was studied according to the design educational educational learning according to the theory and the other is an officer according to the traditional method. The research community consists of fourth grade pupils in primary school day for girls in the Directorate of Education Baghdad, Al-Rusafa, the third academic year 20