In this thesis, we study the topological structure in graph theory and various related results. Chapter one, contains fundamental concept of topology and basic definitions about near open sets and give an account of uncertainty rough sets theories also, we introduce the concepts of graph theory. Chapter two, deals with main concepts concerning topological structures using mixed degree systems in graph theory, which is M-space by using the mixed degree systems. In addition, the m-derived graphs, m-open graphs, m-closed graphs, m-interior operators, m-closure operators and M-subspace are defined and studied. In chapter three we study supra-approximation spaces using mixed degree systems and primary object in this chapter are two topological spaces, namely o-space and i-space. In chapter four we introduce two new approximation operators using mixed degree systems and comparing of them and we find the accuracy of the second new approximation operator is more thin the first new approximation operator. For reason we study in detail the properties of the second new operator. Finally, in chapter five we introduce new generalization of rough set theory using a finite number of graphs by using the second new approximation operators in the preiow chapter. Several characterizations and properties of these concepts are obtained.
The current research dealt with the study of space compatibility and its role in enhancing the functional aspect of the design of the interior spaces of isolation hospitals by finding a system or format that is compatible with the nature of the changes occurring in the structure and function of the space system, as well as contributing to enhancing compatibility between the functional aspect and the interior space. Therefore, the designer must The interior is the study of the functional and spatial aspects as they are the basic aspects for achieving suitability, and through the interaction between the person and the place, the utilitarian performance characteristics are generated that the interior designer is interested in and tries to d
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There is a mutual relationship between the form of a text and its meaning so as separating these two or devaluating the role of one of them leads to the absence of the value therein. Thus, a translation is important as to how it relates the details of a text. That is, the text has special features which go beyond form, and these set out its distinctiveness. Here, we tackle Saleh al-Jafari's Arabic translation of "Rubbayat al-Khayyam" of Naysapour descriptively and analytically by depending on extracts from the original text. This translation is evaluated on the basis of Spanish critic Maria Carmen Valero Garces. Herein, we discuss the effectiveness of this theory in the criticism of literary texts. It has been concluded that al-Jaf
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In this paper the definition of fuzzy normed space is recalled and its basic properties. Then the definition of fuzzy compact operator from fuzzy normed space into another fuzzy normed space is introduced after that the proof of an operator is fuzzy compact if and only if the image of any fuzzy bounded sequence contains a convergent subsequence is given. At this point the basic properties of the vector space FC(V,U)of all fuzzy compact linear operators are investigated such as when U is complete and the sequence ( ) of fuzzy compact operators converges to an operator T then T must be fuzzy compact. Furthermore we see that when T is a fuzzy compact operator and S is a fuzzy bounded operator then the composition TS and ST are fuzzy compact
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An -module is called absolutely self neat if whenever is a map from a maximal left ideal of , with kernel in the filter is generated by the set of annihilator left ideals of elements in into , then is extendable to a map from into . The concept is analogous to the absolute self purity, while it properly generalizes quasi injectivity and absolute neatness and retains some of their properties. Certain types of rings are characterized using this concept. For example, a ring is left max-hereditary if and only if the homomorphic image of any absolutely neat -module is absolutely self neat, and is semisimple if and only if all -modules are absolutely self neat.
This research aims to give a splitting structure of the projective line over the finite field of order twenty-seven that can be found depending on the factors of the line order. Also, the line was partitioned by orbits using the companion matrix. Finally, we showed the number of projectively inequivalent -arcs on the conic through the standard frame of the plane PG(1,27)
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Objective: The aim of the study was to estimate the action atorvastatin(20mg/day) on bone biochemical markers dyslipidemic men. Methodology: This study was conducted between May 2015 and November 2015 in Al-Basrah General hospital in Basra, Iraq, to evaluate important role of atorvastatin (20mg/day)(Lipitor® Pfizer Pharma GmbH.Germany) on bone biochemical markers. Thirty men patients who had been admitted for a variety of medical problems included in the study. All the patients had previously been diagnosed with Dyslipidemia by specialist physician in internal medicine and all patients age below 55 yea
In this paper, we introduce new classes of sets called g *sD -sets , g *sD −α -sets , g *spreD − sets , g *sbD − -sets and g *sD −β -sets . Also, we study some of their properties and relations among them . Moreover, we use these sets to define and study some associative separation axioms .
In this paper we introduced a new class of - called - and study their basic properties in nano topological spaces. We also introduce -closure and -interior and study some of their fundamental properties.
The main focus of this article is to introduce the notion of rough pentapartitioned neutrosophic set and rough pentapartitioned neutrosophic topology by using rough pentapartitioned neutrosophic lower approximation, rough pentapartitioned neutrosophic upper approximation, and rough pentapartitioned neutrosophic boundary region. Then, we provide some basic properties, namely operations on rough pentapartitioned neutrosophic set and rough pentapartitioned neutrosophic topology. By defining rough pentapartitioned neutrosophic set and topology, we formulate some results in the form of theorems, propositions, etc. Further, we give some examples to justify the definitions introduced in this article.
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We study in this paper the composition operator of induced by the function ?(z)=sz+t where , and We characterize the normal composition operator C? on Hardy space H2 and other related classes of operators. In addition to that we study the essential normality of C? and give some other partial results which are new to the best of our knowledge.