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 study used three methods such as Williamson-hall, size-strain Plot, and Halder-Wagner to analysis x-ray diffraction lines to determine the crystallite size and the lattice strain of the nickel oxide nanoparticles and then compare the results of these methods with two other methods. The results were calculated for each of these methods to the crystallite size are (0.42554) nm, (1.04462) nm, and (3.60880) nm, and lattice strain are (0.56603), (1.11978), and (0.64606) respectively were compared with the result of Scherrer method (0.29598) nm,(0.34245),and the Modified Scherrer (0.97497). The difference in calculated results Observed for each of these methods in this study.

Background: Determination of local bone mineral density (BMD) immediately after implant insertion play an important role in implant success rate, may offer comprehensive description of the bone, and give enough information to the surgeon prior to implant insertion and at follow up status. The aim of the present study is to evaluate the changes of local bone density in the dental implant recipient sites by using computerized tomography. Material and method: The sample consisted of (20) dental implants recipient sites, bone density assessment was done twice, immediately after implants insertion and after six months. Results: The mean HU of the bone around the implant insertion site, immediately after implant placement was 552.28 HU, and inc

Reliability analysis methods are used to evaluate the safety of reinforced concrete structures by evaluating the limit state function 𝑔(𝑋𝑖). For implicit limit state function and nonlinear analysis , an advanced reliability analysis methods are needed. Monte Carlo simulation (MCS) can be used in this case however, as the number of input variables increases, the time required for MCS also increases, making it a time consuming method especially for complex problems with implicit performance functions. In such cases, MCS-based FORM (First Order Reliability Method) and Artificial Neural Network-based FORM (ANN FORM) have been proposed as alternatives. However, it is important to note that both MCS-FORM and ANN-FORM can also be time-con

To evaluate the effectiveness of different microwave irradiation exposure times on the disinfection of dental stone samples immersed in different solutions, and its affect on the dimensional accuracy and surface porosity. Dental stone casts were inoculated with an isolate of Bacillus subtilis to examine the efficiency of microwave irradiation as a disinfection method while immersed in different solutions; water, 40% sodium chloride, or without immersion for different durations. Dimensional accuracy and surface porosity were also evaluated. Significant reduction in colony counts of Bacillus subtilis were observed after 5 minutes of microwave irradiation of immersed dental casts in water and NaCl solution. No evidence of growth was observed a

Background: Immediate implant placement in the maxillary anterior region was challenging, especially with the jumping gap and limited primary implant stability. Objective: To assess the autogenous dentin graft biomaterial's ability to improve the esthetic outcomes of an immediately inserted implant. Methods: Twenty patients with non-restorable retained roots in the maxillary non-molar region surrounded by natural sound teeth were included in this study after a complete clinical and radiological examination, including patient health and clinical fitness for the immediate dental implant procedure. A single dental implant was inserted for each patient, and the resulting jump distance was filled with the mineralized dentin graft and co

Foundations supporting reciprocating engines, radar towers, turbines, large electric motors, and generators, etc. are subject to vibrations caused by unbalanced machine forces as well as the static weight of the machine. If these vibrations are excessive, they may damage the machine or cause it not to function properly. In the case of block foundation, if changes in size and mass of the foundation do not lead to a satisfactory design, a pile foundation may be used. In this study, the dynamic response of piles and pile Groups in dry sand is investigated experimentally. The analysis involves the displacement response under harmonic excitation. In addition, a numerical modeling by using finite element method with a three-dimensional formula

Three cohesionless free flowing materials of different density were mixed in an air fluidized bed to study the mixing process by calculating performance of mixing index according to Rose equation (1959) and to study the effect of four variables (air velocity, mixing time, particle size of trace component and concentration of trace component) on the mixing index and as well as on mixing performance. It was found that mixing index increases with increasing the air velocity, mixing time and concentration of trace component until the optimum value. Mixing index depends on the magnitude of difference in particle size The first set of experiments (salt then sand then cast iron) give higher mixing index and better performance of mixing than the