The purpose of this paper is to introduce and study the concepts of fuzzy generalized open sets, fuzzy generalized closed sets, generalized continuous fuzzy proper functions and prove results about these concepts.

     A graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense related. The objects correspond to mathematical abstractions called vertices (also called nodes or points) and each of the related pairs of vertices is called an edge (also called link or line). A directed graph is a graph in which edges have orientation. A simple graph is a graph that does not have more than one edge between any two vertices and no edge starts and ends at the same vertex.  For a simple undirected graph G with order n, and let  denotes its complement. Let δ(G), ∆(G) denotes the minimum degree and maximum degree of G respectively. The complement degree polynomial of G is the polynomial CD[G,x]= , where C

In this work,  the study of corona domination in graphs is carried over which was initially proposed by G. Mahadevan et al. Let be a simple graph. A dominating set S of a graph is said to be a corona-dominating set if every vertex in is either a pendant vertex or a support vertex. The minimum cardinality among all corona-dominating sets is called the corona-domination number and is denoted by (i.e) . In this work, the exact value of the corona domination number for some specific types of graphs are given. Also, some results on the corona domination number for some classes of graphs are obtained and the method used in this paper is a well-known number theory concept with some modification this method can also be applied to obt

In this work, measurements of activity concentration of naturally occurring radioactive materials (NORM) isotopes and their related hazard indices for several materials such as crude oil, sludge and water in Ahdeb oil fields in Waste governorate using high pure germanium coaxial detection technique. The average values for crude oil samples were174.72Bq/l, 43.46Bq/l, 355.07Bq/l, 264.21Bq/l, 122.52nGy/h, 0.7138, 1.1861, 0.601 mSv/y, 0.1503mSv/y and 1.8361 for Ra-226, Ac-228, K-40, Ra eq, D, H-external and H-internal respectively. According to the results; the ratio between ²³⁸U to ²³²Th was 4, which represents the natural ratio in the crust earth; therefore, one can be strongly suggested that the geo-stricture of the

The research aimed to evaluate the financial performance of the Public Company for the manufacture of medicines and medical supplies / Samarra - Iraq to know the strengths and weaknesses that affect its performance, as well as to compare its performance in the years between (2017-2019), which are characterized by security stability with its performance in previous years (2014 -2016) which is characterized by security instability, to assess the extent of its ability to achieve growth in performance, by answering the main question, what is the evaluation of the performance of the Public Company for the manufacture of medicines and medical supplies / Samarra - Iraq in the light of financial indicators?

Number theorists believe that primes play a central role in Number theory and that solving problems related to primes could lead to the resolution of many other unsolved conjectures, including the prime k-tuples conjecture. This paper aims to demonstrate the existence of this conjecture for admissible k-tuples in a positive proportion. The authors achieved this by refining the methods of “Goldston, Pintz and Yildirim” and “James Maynard” for studying bounded gaps between primes and prime k-tuples. These refinements enabled to overcome the previous limitations and restrictions and to show that for a positive proportion of admissible k-tuples, there is the existence of the prime k-tuples conjecture holding for each “k”. The sig

The study attempts to assess water quality in Abu-Zirig Marsh which used epiphytic Diatom community for assessing water quality. Many of Diatom indices {Trophic diatom index (TDI), Diatom index (DI), Generic diatom index (GDI) have been used to give qualitative information about the status of the freshwater ecosystem(good, moderate, high pollution). In this study, the epiphytic diatoms on both host aquatic plants Phragmites australis and Typha domengensis were collected from Abu-Zirig Marsh within Thi-Qar Province at three sites in Autumn, 2018 and winter, 2019. Epiphytic diatoms were Identified by the preparation of permanent slides method, some species of epiphytic diatom showed dominance such as Cyclotella menegh

The present study aims to establish an empirical correlation between biochemical oxygen demand (BOD5) and chemical oxygen demand (COD) of the sewage flowing in Al-Diwaniyah wastewater treatment plant. The strength of the wastewater entering the plant varied from medium to high. High concentrations of BOD5 and COD in the effluent were obtained due to the poor performance of the plant. This was observed from the BOD5 /COD ratios that did not confirm with the typical ratios for the treated sewage. Regression equations for BOD5 and COD removal percentages were suggested which can be used to evaluate rapid effluent assessment after the treatment processes or optimal process control to improve the performance of wastewater treatment plants.

The aim of this paper is to introduce and study the notion type of fibrewise topological spaces, namely fibrewise fuzzy j-topological spaces, Also, we introduce the concepts of fibrewise j-closed fuzzy topological spaces, fibrewise j-open fuzzy topological spaces, fibrewise locally sliceable fuzzy j-topological spaces and fibrewise locally sectionable fuzzy j-topological spaces. Furthermore, we state and prove several Theorems concerning these concepts, where j = {δ, θ, α, p, s, b, β}.