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

Sliding Mode Controller (SMC) is a simple method and powerful technique to design a robust controller for nonlinear systems. It is an effective tool with acceptable performance. The major drawback is a classical Sliding Mode controller suffers from the chattering phenomenon which causes undesirable zigzag motion along the sliding surface. To overcome the snag of this classical approach, many methods were proposed and implemented. In this work, a Fuzzy controller was added to classical Sliding Mode controller in order to reduce the impact chattering problem. The new structure is called Sliding Mode Fuzzy controller (SMFC) which will also improve the properties and performance of the classical Sliding Mode control

In this paper Heun method has been used to find numerical solution for first order nonlinear functional differential equation. Moreover, this method has been modified in order to treat system of nonlinear functional differential equations .two numerical examples are given for conciliated the results of this method.

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

The spectral characteristics and the nonlinear optical properties of the mixed donor (C-480) acceptor (Rh-6G) have been determined. The spectral characteristics are studied by recording their absorption and fluorescence spectra. The nonlinear optical properties were measured by z-scan technique, using Q-switched Nd: YAG laser with 1064 nm wavelength. The results showed that the optimum concentration of acceptor is responsible for increasing the absorption and the emission bandwidth of donor to full range and to 242 nm respectively by the energy transfer process, also the efficiency of the process was increased by increasing the donor and acceptor concentration. The obtained nonlinear properties results of the mixture C-480/ Rh-6G showed

The Halabja earthquake occurred on 12/11/2017 in Iraq, with a magnitude of 7.3 Mw, which happened in the Iraqi-Iranian borders. This earthquake killed and injured many people in the Kurdish region in the north of the country. There is no natural disaster more dangerous than earthquake, especially it occurs without warning, great attention must be paid to the impact of earthquakes on the soil and preparing for a wave of earthquakes. Numerical modeling using specific elements is considered a powerful tool to investigate the required behavior of structures in Geotechnical engineering, and the main objective of this is to assess the response of the Al-Wand dam to the Halabja earthquake, as this dam is located in an area that has been su

Background: One of the most common complications of dentures is its ability to fracture, so the aim of this study was to reinforce the high impact denture base with carbon nanotubes in different concentrations to improve the mechanical and physical properties of the denture base. Materials and methods: Three concentrations of carbon nanotubes was used 0.5%, 1%, 1.5% in a pilot study to see the best values regarding transverse strength, impact, hardness and roughness test, 1 wt% was the best concentration, so new samples for control group and 1wt% carbon nanotubes and the previous tests were of course repeated. Results: There was a significant increase in impact strength and transverse strength when we add carbon nanotubes in 1wt%, compared

The study in duded isolation and identification of microbial isolates from oral cavity to 10 volunteers, diagnosed within the three groups: Staphylococcus aureus, Staphylococcus epidermidis, Streptococcus spp. and Candida albicans . The sensitivity test of all isolates bacteria Streptococcus spp. , S. aureus and S. epidermidis showed high resistance to Ampicillin(100)%,followed Methicillin (88.88)% and Amoxicillin / clavulanic acid(77.77)%, while the resistance for each of Vancomycin and Amoxicillin were (66.66)%, and the resistance to Erythromycin and Pencillin (55.55)% to each of them. The results showed less resistance to Trimethoprim (22.22)% and Cefalotine (11.11)% of all bacteria isolate. Investigation of the pre

An increasing trend to use probiotic and study their effects on the pathogens has been conductor where they are defined as live micro-organisms that give a health benefit to the host when ingested in sufficient quantities, including the yeast Saccharomyces boulardii In addition research show that a magnetic field (MF) has a biological effect. This study aims to investigate the effects of magnetic field on the inhibitory action of Saccharomyces boulardii against bacteria isolated from urinary tract infection, Study the sensitivity of bacterial isolates to antibiotics after diagnosis by microscopic, Cultural and biochemical examinations as well as Api20 E examinations were used gram negative bacteria , Most isolates were resistant to an