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 concept of semi-essential semimodule has been studied by many researchers.

     In this paper, we will develop these results by setting appropriate conditions, and defining new properties, relating to our concept, for example (fully prime semimodule, fully essential semimodule and semi-complement subsemimodule) such that: if for each subsemimodule of -semimodule  is prime, then  is fully prime. If every semi-essential subsemimodule of -semimodule  is essential then  is fully essential. Finally, a prime subsemimodule  of  is called semi-relative intersection complement (briefly, semi-complement) of subsemimodule  in , if , and whenever  with  is a prime subsemimodule in , , then .  Furthermore, some res

The present study was aimed to find out the role of humoral immunity in the pathogenesis of psoriasis. Complements C3, C4 and immunoglobulin IgE .The study included 55 Iraqi patients with psoriasis 30 (15 females ,15 males) were untreated with any drugs. The other patient group consisted of 25 (9 female and 16 male) treated with a biological treatment (infliximab) ,and 30 (13 males ,12 females) healthy control group. Blood sample were withdrawn (5) ml of venous blood for both patients and members of the control ,to conduct the Immunological tests to determine the quantitative for each of total IgE by using (ELISA) and C3,C4 by Single Radial Immunodiffuse (SIRD). The results showed significant increase in the level of probability (P <0.0

This study was conducted in Diyala province for renal failure patients during the periods August 2015 - April 2016. Hundred renal failure patients were enrolled in the study after diagnosis by the consultant physician at Ibn-Sina Center for Dialysis in Baquba Teaching Hospital according to criteria adopted by the World Health Organization for diagnosis of renal failure disease. The number of males in patient’s sample was 61 (61%) and females was 39 (39%) with an age range of 10 – 88 year (44.7 ± 22.1 year). In addition, the study included 50 apparently healthy individuals and considered as a group control, in which the number of males and females was similar (25 individual), with an age range of 18 – 88 year (51.7 ± 17.3 year). The

The Specific activity of extracellular superoxide dismutase (EC-SOD) was measured in healthy persons and in patients with benign and malignant brain tumors. The results show decrease of the EC-SOD specific activity in sera of patients with benign and malignant brain tumors in comparison to that of control group.This study concentrated on studying the changes that occur in sera EC-SOD activity of patients with benign and malignant brain tumors, in comparison to that of normal individuals. The result also revealed that this isoenzyme is present in many different molecular weights forms (as judged by polyacrylamide gel electrophoresis), some of these with no enzymatic activity. Conversion among these forms occurs in the malignant sera

This work is concerned with the vibration attenuation of a smart beam interacting with fluid using proportional-derivative PD control and adaptive approximation compensator AAC. The role of the AAC is to improve the PD performance by compensating for unmodelled dynamics using the concept of function approximation technique FAT. The key idea is to represent the unknown parameters using the weighting coefficient and basis function matrices/vectors. The weighting coefficient vector is updated using Lyapunov theory. This controller is applied to a flexible beam provided with surface bonded piezo-patches while the vibrating beam system is submerged in a fluid. Two main effects are considered: 1) axial stretching of the vibrating beam that leads