The Wang-Ball polynomials operational matrices of the derivatives are used in this study to solve singular perturbed second-order differential equations (SPSODEs) with boundary conditions. Using the matrix of Wang-Ball polynomials, the main singular perturbation problem is converted into linear algebraic equation systems. The coefficients of the required approximate solution are obtained from the solution of this system. The residual correction approach was also used to improve an error, and the results were compared to other reported numerical methods. Several examples are used to illustrate both the reliability and usefulness of the Wang-Ball operational matrices. The Wang Ball approach has the ability to improve the outcomes by minimi

In this paper, Touchard polynomials (TPs) are presented for solving Linear Volterra integral equations of the second kind (LVIEs-2k) and the first kind (LVIEs-1k) besides, the singular kernel type of this equation. Illustrative examples show the efficiency of the presented method, and the approximate numerical (AN) solutions are compared with one another method in some examples. All calculations and graphs are performed by program MATLAB2018b.

A new method based on the Touchard polynomials (TPs) was presented for the numerical solution of the linear Fredholm integro-differential equation (FIDE) of the first order and second kind with condition. The derivative and integration of the (TPs) were simply obtained. The convergence analysis of the presented method was given and the applicability was proved by some numerical examples. The results obtained in this method are compared with other known results.

In this research, Haar wavelets method has been utilized to approximate a numerical solution for Linear state space systems. The solution technique is used Haar wavelet functions and Haar wavelet operational matrix with the operation to transform the state space system into a system of linear algebraic equations which can be resolved by MATLAB over an interval from 0 to . The exactness of the state variables can be enhanced by increasing the Haar wavelet resolution. The method has been applied for different examples and the simulation results have been illustrated in graphics and compared with the exact solution.

Abstract

Heavy-duty diesel vehicle idling consumes fossil fuel and reduces atmospheric quality at idle period, but its restriction cannot simply be proscribed. A comprehensive tailpipe emissions database to describe idling impacts is not yet available. This paper presents a substantial data set that incorporates results from DI multi-cylinders Fiat diesel engine. Idle emissions of CO, hydrocarbon (HC), oxides of nitrogen (NOx), smoke opacity, carbon dioxide (CO₂) and noise have been reported, when three EGR ratios (10, 20 and 30%) were added to suction manifold.

CO₂ concentrations increased with increasing idle time and engine idle speed, but it didn’t show clear effect for IT adva

In the recent decade, injection of nanoparticles (NPs) into underground formation as liquid nanodispersions has been suggested as a smart alternative for conventional methods in tertiary oil recovery projects from mature oil reservoirs. Such reservoirs, however, are strong candidates for carbon geo-sequestration (CGS) projects, and the presence of nanoparticles (NPs) after nanofluid-flooding can add more complexity to carbon geo-storage projects. Despite studies investigating CO2 injection and nanofluid-flooding for EOR projects, no information was reported about the potential synergistic effects of CO2 and NPs on enhanced oil recovery (EOR) and CGS concerning the interfacial tension (γ) of CO2-oil system. This study thus extensively inves

In this study, the behavior of screw piles models with continuous helix was studied by conducting laboratory experimental tests on a single screw pile that has several aspect ratios (L/D) under the influence of static axial compression loads. The screw piles were inserted in a soft soil that has a unit weight of 18.72 kN/m3 and moisture content of 30.19%. Also, the soil has a liquid limit of 55% and a plasticity index of 32%. A physical laboratory model was designed to investigate the ultimate compression capacity of the screw pile and measure the generated porewater pressure during the loading process. The bedding soil was prepared according to the field unit weight and moisture content and the failure load was assumed correspondin

Background: Pharmacy internship programmes are driven by most developed countries to outweigh the ongoing growth in the pharmacy career which encourages pharmacists to play a significant role as healthcare providers.    Objectives: This study examines pharmacy students' perception, satisfaction, challenges, and limitations with the internship curriculum.    Method: A cross-sectional study was conducted using an online survey with different elements to examine students' perceptions of various aspects.    Result: Most students reported a positive impression regarding their internships, however, they were less satisfied with the allowance for filling prescriptions and compounding also, the college's follow-up was inadequate. F

The effective surface area of drug particle is increased by a reduction in the particle size. Since dissolution takes place at the surface of the solute, the larger the surface area, the further rapid is the rate of drug dissolution. Ketoprofen     is class II type drug according to (Biopharmaceutics Classification System BCS) with low solubility and high permeability. The aim of this investigation was to increase the solubility and hence the dissolution rate by the preparation of ketoprofen     nanosuspension using solvent evaporation method. Materials like PVP K30, poloxamer 188, HPMC E5, HPMC E15, HPMC E50, Tween 80 were used as stabilizers in perpetration of differ