In this study, a new technique is considered for solving linear fractional Volterra-Fredholm integro-differential equations (LFVFIDE's) with fractional derivative qualified in the Caputo sense. The method is established in three types of Lagrange polynomials (LP’s), Original Lagrange polynomial (OLP), Barycentric Lagrange polynomial (BLP), and Modified Lagrange polynomial (MLP). General Algorithm is suggested and examples are included to get the best effectiveness, and implementation of these types. Also, as special case fractional differential equation is taken to evaluate the validity of the proposed method. Finally, a comparison between the proposed method and other methods are taken to present the effectiveness of the proposal meth

Volterra – Fredholm integral equations (VFIEs) have a massive interest from researchers recently. The current study suggests a collocation method for the mixed Volterra - Fredholm integral equations (MVFIEs)."A point interpolation collocation method is considered by combining the radial and polynomial basis functions using collocation points". The main purpose of the radial and polynomial basis functions is to overcome the singularity that could associate with the collocation methods. The obtained interpolation function passes through all Scattered Point in a domain and therefore, the Delta function property is the shape of the functions. The exact solution of selective solutions was compared with the results obtained

In this study, the flow and heat transfer characteristics of Al₂O₃-water nanofluids for a range of the Reynolds number of 3000, 4500, 6000 and 7500 with a range of volume concentration of 1%, 2%, 3% and 4% are studied numerically. The test rig consists of cold liquid loop, hot liquid loop and the test section which is counter flow double pipe heat exchanger with 1m length. The inner tube is made of smooth copper with diameter of 15mm. The outer tube is made of smooth copper with diameter of 50mm. The hot liquid flows through the outer tube and the cold liquid (or nanofluid) flow through the inner tube. The boundary condition of this study is thermally insulated the outer wall with uniform velocity a

The problem of water scarcity is becoming common in many parts of the world, to overcome part of this problem proper management of water and an efficient irrigation system are needed.  Irrigation with a buried vertical ceramic pipe is known as a very effective in the management of irrigation water.  The two- dimensional transient flow of water from a buried vertical ceramic pipe through homogenous porous media is simulated numerically using the HYDRUS/2D software.  Different values of pipe lengths and hydraulic conductivity were selected.  In addition, different values of initial volumetric soil water content were assumed in this simulation as initial conditions.  Different value

This paper is concerned with the numerical solutions of the vorticity transport equation (VTE) in two-dimensional space with homogenous Dirichlet boundary conditions. Namely, for this problem, the Crank-Nicolson finite difference equation is derived.  In addition, the consistency and stability of the Crank-Nicolson method are studied. Moreover, a numerical experiment is considered to study the convergence of the Crank-Nicolson scheme and to visualize the discrete graphs for the vorticity and stream functions. The analytical result shows that the proposed scheme is consistent, whereas the numerical results show that the solutions are stable with small space-steps and at any time levels.

In this study, low cost biosorbent ̶inactive biomass (IB) granules (dp=0.433mm) taken from drying beds of Al-Rustomia Wastewater Treatment Plant, Baghdad-Iraq were used for investigating the optimum conditions of Pb(II), Cu(II), and Ni(II) biosorption from aqueous solutions. Various physico-chemical parameters such as initial metal ion concentration (50 to 200 mg/l), equilibrium time (0-180 min), pH (2-9), agitation speed (50-200 rpm), particles size (0.433 mm), and adsorbent dosage (0.05-1 g/100 ml) were studied. Six mathematical models describing the biosorption equilibrium and isotherm constants were tested to find the maximum uptake capacities: Langmuir, Freundlich, Redlich–Peterson, Sips, Khan, and Toth models. The best fit to the P

The research aims to derive the efficient industrial plans for Al – shaheed public company under risk by using Target MOTAD as a linear alternative  model for the quadratic programming models.

The results showed that there had been a sort of (trade- off) between risk and the expected gross margins. And if the studied company strives to get high gross margin, it should tolerate risk and vice versa. So the management  of Al- Shaheed Company to be invited to apply the suitable procedures in the production process, in order to get efficient plans that improves it's  performance .

New mixed ligand complexes of New Schiff base 4,4'- ((naphthalen-1-ylimino) methylene) dibenzene-1,3-diol and 8-hydroxy quinoline: Synthesis, Spectral Characterization, Thermal studies and Biological Activities

As one type of resistance furnace, the electrical tube furnace (ETF) typically experiences input noise, measurement noise, system uncertainties, unmodeled dynamics and external disturbances, which significantly degrade its temperature control performance. To provide precise, and robust temperature tracking performance for the ETF, a robust composite control (RCC) method is proposed in this paper. The overall RCC method consists of four elements: First, the mathematical model of the ETF system is deduced, then a state feedback control (SFC) is constructed. Third, a novel disturbance observer (DO) is designed to estimate the lumped disturbance with one observer parameter. Moreover, the stability of the closed loop system including controller

Background: The aim of this study was to measure the radiopacity (RO) of modified microhybrid composite resins by adding 2 types of nanofillers (Zinc Oxide and Calcium Carbonate) in two concentrations 3% and 5% and comparing them to unmodified microhybrid composite resins and to nanofilled composite resin. Materials and Methods: Two types of composite resin were used (Microhybrid composite MH Quadrent anterior shine and Nanofilled composite resin Filtek Z350 XT), for each tested group five disk-shaped specimens (1-mm-thick and 15 mm diameter) were fabricated. The material samples were radiographed together with the aluminum step wedge. The density of the specimens was determined with a transmission densitometer and was expressed in term of