Let R be a commutative ring with identity 1 and M be a unitary left R-module. A submodule N of an R-module M is said to be pure relative to submodule T of M (Simply T-pure) if for each ideal A of R, N?AM=AN+T?(N?AM). In this paper, the properties of the following concepts were studied: Pure essential submodules relative to submodule T of M (Simply T-pure essential),Pure closed submodules relative to submodule T of M (Simply T-pure closed) and relative pure complement submodule relative to submodule T of M (Simply T-pure complement) and T-purely extending. We prove that; Let M be a T-purely extending module and let N be a T-pure submodule of M. If M has the T-PIP, then N is T-purely extending.

     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

The aim of the research is to measure the length between the variable the efficiency of the tax examiner with its dimensions represented by (scientific questions, practical process (experience), training and development, impartiality and independence, ethics of the profession) and the approved variable discovering the artificial adaptation of profits, and the degree of arrangement of those dimensions its importance and priority, and the research problem has been identified  In a main question that is there any effect of copying the images of the image examiner in discovering the adaptation, the financial statements and reports of the companies (X, Y) and the banks (A, B) were relied on in the interpretation of the results, t

Death is undoubtedly the theme of Don DeLillo’s White Noise. Murray Siskind, a College-on-the-Hill professor who is obsessed with the exploration and reinterpretation of American popular culture, talks about the Tibetan Book of the Dead, and the German mentor of Jack Gladney has been using the Egyptian Book of the Dead, translated into German. The core episode of the story is the Airborne Toxic Event, the associate of Heinrich (Jack’s teenage son), Orestes Mercator, dreams of becoming one of the great figures in the Guinness Book by challenging and confronting death by enclosing himself in a glass pen jam-packed with poisonous snakes, and Heinrich challenges an imprisoned mass murderer in a chess game. The scholarly expertise of Jack c

The primary objective of this paper is to introduce a new concept of fibrewise topological spaces on D is named fibrewise multi- topological spaces on D. Also, we entroduce the concepts of multi-proper, fibrewise multi-compact, fibrewise locally multi-compact spaces, Moreover, we study relationships between fibrewise multi-compact (resp., locally multi-compac) space and some fibrewise multi-separation axioms.

We introduce the notion of interval value fuzzy ideal of TM-algebra as a generalization of a fuzzy ideal of TM-algebra and investigate some basic properties. Interval value fuzzy ideals and T-ideals are defined and several examples are presented. The relation between interval value fuzzy ideal and fuzzy T-ideal is studied. Abstract We introduce the notion of interval value fuzzy ideal of TM-algebra as a generalization of a fuzzy ideal of TM-algebra and investigate some basic properties. Interval value fuzzy ideals and T- ideals are defined and several examples are presented. The relation between interval value fuzzy ideal and fuzzy T-ideal is studied.

Objective: The study aims to determine the effect of Toxoplasma gondii infection on the
genetic sequence of breast cancer patients in the Medical City Hospital – Tumor Unit /
Iraq-Baghdad.
Methodology: A study was carried out in the City of Medicine / Oncology Unit / Baghdad,
during the period 1st June 2016 to 15
th March 2017. Forty samples of tissue and serum
were collected from patients who complaining from Breast cancer and infected with
Toxoplasmosis. Forty sera samples were taken from patients complaining from parasitic
infection only; without breast cancer as control group. Data is analyzed by using of
descriptive and inferential data analysis methods.
Results: The results show that there is an effe

The idea of ech fuzzy soft bi-closure space ( bicsp) is a new one, and its basic features are defined and studied in [1]. In this paper, separation axioms, namely pairwise, , pairwise semi-(respectively, pairwise pseudo and pairwise Uryshon) - fs bicsp's are introduced and studied in both ech fuzzy soft bi-closure space and their induced fuzzy soft bitopological spaces. It is shown that hereditary property is satisfied for , with respect to ech fuzzy soft bi-closure space but for other mentioned types of separations axioms, hereditary property satisfies for closed subspaces of ech fuzzy soft bi-closure space.

A total of (90) blood samples were collected from male patients infected with Toxoplasmosis who recovered from COVID- 19 and attended Kamal Alsamiraai Hospital from 15 January to 15 September 2021. We measured anti-Toxoplasma antibodies (IgG and IgM) detected by ELISA, whereas Anti-COVID-19 antibodies (IgG and IgM) were estimated using Elisa and Afilias. The semen characteristics were also studied among fertile, healthy individuals (control group) and sub-fertile patients. Results showed that the mean sperm count was high among the control group (40.5±1.3x 106/ml) compared with that of the sub-fertile patients (10.3±1.75 and 8.8±1.9 x 106/ml for oligozoospermia, and oligoasthenozoospermia respectively), and it was the highest (44.7±1.4