The importance of topology as a tool in preference theory is what motivates this study in which we characterize topologies generating by digraphs. In this paper, we generalized the notions of rough set concepts using two topological structures generated by out (resp. in)-degree sets of vertices on general digraph. New types of topological rough sets are initiated and studied using new types of topological sets. Some properties of topological rough approximations are studied by many propositions.

For the generality of fuzzy ideals in TM-algebra, a cubic ideal in this algebra has been studied, such as cubic ideals and cubic T-ideals. Some properties of these ideals are investigated. Also, we show that the cubic T-ideal is a cubic ideal, but the converse is not generally valid. In addition, a cubic sub-algebra is defined, and new relations between the level subset and a cubic sub-algebra are discussed. After that, cubic ideals and cubic T-ideals under homomorphism are studied, and the image (pre-image) of cubic T-ideals is discussed. Finally, the Cartesian product of cubic ideals in Cartesian product TM-algebras is given. We proved that the product of two cubic ideals of the Cartesian product of two TM-algebras is also a cubic ideal.

Borrowing in linguistics refers to the process whereby a group of speakers incorporates certain foreign linguistic components into their home language via a process known as linguistic borrowing. The process by which these foreign linguistic elements, known as loanwords, go through phonological, morphological, or semantic changes in order for them to fit the grammar of the recipient language is referred to as loanword adaptation. Loanwords go through these changes in order for them to become compatible with the grammar of the recipient language. One of the most divisive topics in loanword phonology is whether adaptations occur at the phonemic or phonetic levels, and current literature distinguishes three primary viewpoints: nativiza

This research aims at identifying the level of Reflective Judgment for University students in term of gender and stage. To this end, the researcher used Khaleel's scale (2016) for the Reflective Judgment. The scale was administered to the sample of the study which is (200) male and female level first-fourth university students. The results have shown that university students are on the level five of the Reflective Judgment, and the first-stage students have reflective judgment more than fourth-stage students. In the light of these results, the researcher has come with a number of recommendations and suggestions.     

The aim of the research is to study the biology, life cycles, distribution and structure of the reproductive organ of Leucozonella retteri in natural conditions. Zoological and malacological methods are used in the work. The collection of the material was carried out according to A.A. Shileiko method. According to the results of the conducted studies, the differences between Leucozonella retteri and other species in the structure of the reproductive organ were manifested in the following. The lower part of the sperm is straight, the ovary is slightly curved. The paw pad is 8, located in 4x2 positions. The stylophore is large spherical. The vagina is cylindrical, its length is 5-6 times greater than the width. The penis is large and conve

Our active aim in this paper is to prove the following Let Ŕ be a ring having an
idempotent element e(e  0,e 1) . Suppose that R is a subring of Ŕ which
satisfies:
(i) eR  R and Re  R .
(ii) xR  0 implies x  0 .
(iii ) eRx  0 implies x  0( and hence Rx  0 implies x  0) .
(iv) exeR(1 e)  0 implies exe  0 .
If D is a derivable map of R satisfying D(R )  R ;i, j 1,2. ij ij Then D is
additive. This extend Daif's result to the case R need not contain any non-zero
idempotent element.

     Let  be any connected graph with vertices set  and edges set .  For any two distinct vertices  and , the detour distance between  and  which is denoted by  is a longest path between  and  in a graph . The detour polynomial of a connected graph  is denoted by ;  and is defined by . In this paper, the detour polynomial of the theta graph and the uniform theta graph will be computed.

      Let R be a commutative ring with unity. And let E be a unitary R-module. This paper introduces the notion of 2-prime submodules as a generalized concept of 2-prime ideal, where proper submodule H of module F over a ring R is said to be 2-prime if , for r R and x F implies that  or . we prove many properties for this kind of submodules, Let H is a submodule of module F over a ring R then H is a 2-prime submodule if and only if [N ] is a 2-prime submodule of E, where r R. Also, we prove that if F is a non-zero multiplication module, then [K: F] [H: F] for every submodule k of F such that H K. Furthermore, we will study the basic properties of this kind of submodules.

Thep resent study was conducted for monitoring of the evaporative cooling tower in methanol production plant using digital computer' visuql Basic computer program was used for the monitoring of the performance of the cooling tower. The structure program consists of sub programs and forms to show all the related variabltes such as temperature, flow rate, pressure ...etc, that affect the cooling tower operation and give alarms and important function informition regarding these variables.