This work aims to introduce and to study a new kind of divisor graph which is  called idempotent divisor graph, and it is  denoted by . Two non-zero distinct vertices v₁ and v₂ are adjacent if and only if , for some non-unit idempotent element . We establish some fundamental properties of ,  as well as it’s connection with . We also study planarity of this graph.

A series of new maleimide monomers substituted with Schiff base moieties were synthesized via acid-catalyzed condensation of 3-(N-maleimidyl)phenyl hydrazide with aromatic aldehydes and ketones. The newly synthesized monomers were introduced in free radical chain growth homopolymerization producing five new polymaleimides with pendent Schiff base moieties .The new monomers were introduced also in free radical chain growth copolymerization with acrylonitrile producing new five copolymaleimides containing pendent Schiff base moieties. The new homopolymers and copolymers are of great importance since incorporation of bulky Schiff base moieties in their repeating units exhibit them better solubility and processing properties which made them

Suppose that  is a finite group and  is a non-empty subset of  such that  and . Suppose that  is the Cayley graph whose vertices are all elements of  and two vertices  and  are adjacent if and only if . In this paper, we introduce the generalized Cayley graph denoted by  that  is a graph with vertex set consists of all column matrices  which all components are in  and two vertices  and  are adjacent if and only if , where  is a column matrix that each entry is the inverse of similar entry of  and  is  matrix with all entries in  ,  is the transpose of  and . In this paper, we clarify some basic properties of the new graph and assign the structure of  when  is complete graph , complete bipartite graph  and complete

         Let  be any group with identity element (e) . A subgroup intersection graph of  a subset  is the Graph with V ( ) =  - e and two separate peaks c and d contiguous for c and d if and only if      , Where  is a Periodic subset of resulting from  . We find some topological indicators in this paper and Multi-border (Hosoya and Schultz) of   , where    ,  is aprime number.

This paper deals with constructing a model of fuzzy linear programming with application on fuels product of Dura- refinery , which consist of seven products that have direct effect ondaily consumption . After Building the model which consist of objective function represents the selling prices ofthe products and fuzzy productions constraints and fuzzy demand constraints addition to production requirements constraints , we used program of ( WIN QSB )  to find the optimal solution

 We use the idea of Grill, this study generalized a new sort of linked space like –connected –hyperconnected and investigated its features, as well as the relationship between it and previously described notation. It also developed new sorts of functions, such as hyperconnected space, and identifying their relationship, by offering numerous instance and attributes that belong to this set. This set will serve as a starting point for further research into the sets many future possibilities. Also, we use some of the theorems and observations previously studied and relate them to the grill and the Alpha group, and benefit from them in order to obtain new results in this research. We applied the concept of Connected to them and obtained

The goal of the research is to introduce new types of maps called semi totally Bc-continuous map and totally Bc-continuous map furthermore, study its properties. Additionally, we study the relationship of these functions and other known mappings are discussed.

     . Suppose that  is the Cayley graph whose vertices are all elements of  and two vertices  and  are adjacent if and only if . In this paper,we introduce the generalized Cayley graph denoted by  which is a graph with a vertex set consisting of all column matrices  in which all components are in  and two vertices  and  are adjacent if and only if , where  is a column matrix that each entry is the inverse of the similar entry of  and  is  matrix with all entries in  ,  is the transpose of  and  and m . We aim to provide some basic properties of the new graph and determine the structure of  when  is a complete graph  for every , and n, m  .

The study was carried out in plant tissue culture laboratory, University of Baghdad during the period 2017-2019, as factorial experiment in complete randomized design, to study the effect of PEG at (0, 2, 4, 6 and 8%) on physiological and chemical changes in callus of three sunflower (Ishaqi 1, Aqmar and Al-haga) induced by the cultivation of the young stem in vitro under water stress. The content of callus cells of SOD, POD, CAT and APX enzymes as well as content of hydrogen peroxide were determined as indicators to determine the effect of PEG in callus tissue cells cultivated on medium equipped with the PEG concentrations. The results showed that cultivars were differs significantly and Al-hajavariety was superior in increasing SOD to 24.

Our goal in this work is to describe the structure of a class of bimodal self maps on the compact real interval I with zero topological entropy and transitive.