In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

In this paper, the general framework for calculating the stability of equilibria, Hopf bifurcation of a delayed prey-predator system with an SI type of disease in the prey population, is investigated. The impact of the incubation period delay on disease transmission utilizing a nonlinear incidence rate was taken into account. For the purpose of explaining the predation process, a modified Holling type II functional response was used. First, the existence, uniform boundedness, and positivity of the solutions of the considered model system, along with the behavior of equilibria and the existence of Hopf bifurcation, are studied. The critical values of the delay parameter for which stability switches and the nature of the Hopf bifurcat

After this systematic presentation of the phenomenon of rotation of formulas, ie the construction of the verb and the verb, and the narrated narratives therein differed among the readers, it became clear to us how the difference was clear between reading and the other, and how readers have varied in their readings of the verb, As we have noted through our modest research that the phenomenon of building the verb for the actor and the effect have included the act of both past and present tense, and not limited to a specific time, and this difference in reading was not limited to a particular environment, but beyond To more than one environment This is evidenced by the readings of various readers from the environment of Kufa, Basra, Mecca,

The aim of the current research is to identify the level of organizational culture among the headmasters and teachers of intermediate and secondary schools in Arar city. It also aims to identify the effect of job variables, qualifications, educational stage, and years of experience on the level of organizational culture and its domains. The research sample consisted of 62 participants divided into 7 headmasters and 55 teachers. The researcher used the questionnaire of the organizational culture. The researcher used also statistical methods such as mean, standard deviation, t-test, and One way ANOVA. The results revealed that the level of organizational culture and its four domains were high, and there was no effect of the variables (teac

Previous studies on the synthesis and characterization of metal chelates with uracil by elemental analysis, conductivity, IR, UV-Vis, NMR spectroscopy, and thermal analysis were covered in this review article. Reviewing these studies, we found that uracil can be coordinated through the electron pair on the N1, N3, O2, or O4 atoms. If the uracil was a mono-dentate ligand, it will be coordinated by one of the following atoms: N1, N3 or O2. But if the uracil was bi-dentate ligand, it will be coordinated by atoms N1 and O2, N3 and O2 or N3 and O4. However, when uracil forms complexes in the form of polymers, coordination occurs through the following atoms: N1 and N3 or N1 and O4.

viruses are responsible for a large proportion of lower respiratory tract infections (LRTIs). Other causes of LRTIs are bacteria: Streptococcus pneumoniae, Haemophilus influenzae, Klebsiella pneumoniae, and Staphylococcus aureus being the most common. Sputum samples are commonly used in the microbiological laboratory for diagnosing lower respiratory infections. Objective: The aim of this study to evaluate the causative bacteria and antibiotics sensitivity in culture of sputum samples. Patients Methods: A retrospective study performed in the microbiology department of Al Immamin Al Kahdimin Medical laboratory in Baghdad. The results of sputum cultures collected from the files between 2016 and 2019. A tota

oupling reaction of 4-aminoantipyrene with the (L-Histidine) gave the new bidentate azo ligand.The prepared ligand was identified by FT.IR, UV-Vis and HNMR spectroscopics technique. Treatment of the prepared ligand was done with the following metal ions (Ag+ ,Pb+2 ,Fe+3 ,Cr+3  ) in aqueous ethanol with a1:1 and 1:2  M:L ratio . The prepared complexes were characterized by using FT. IR and UV- VIS spectroscopic method as well as conductivity measurements. Their structures were suggested according to the results obtained.