In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods is produced. Finally, for more explanation, an algorithm is proposed and applied for testing examples to illustrate the effectiveness of the new technique.

The need to create the optimal water quality management process has motivated researchers to pursue prediction modeling development. One of the widely important forecasting models is the sessional autoregressive integrated moving average (SARIMA) model. In the present study, a SARIMA model was developed in R software to fit a time series data of monthly fluoride content collected from six stations on Tigris River for the period from 2004 to 2014. The adequate SARIMA model that has the least Akaike's information criterion (AIC) and mean squared error (MSE) was found to be SARIMA (2, 0, 0) (0,1,1). The model parameters were identified and diagnosed to derive the forecasting equations at each selected location. The correlat
... Show MoreIn this work, optical system with different aperture shapes (circular, square, elliptical and triangle aperture) has been used for efficiency evaluation when the system involved moving factor in ideal case (aberration free). The optical system evaluate far moving object, therefore the image forming at image plane due to point spread function (image formula of incoherently illuminated point object). A mathematical treatment has been used to getting results by Gaussian numerical calculations method. The results show priority of circular aperture when optical system that submits of moving factor.
Metasurface polarizers are essential optical components in modern integrated optics and play a vital role in many optical applications including Quantum Key Distribution systems in quantum cryptography. However, inverse design of metasurface polarizers with high efficiency depends on the proper prediction of structural dimensions based on required optical response. Deep learning neural networks can efficiently help in the inverse design process, minimizing both time and simulation resources requirements, while better results can be achieved compared to traditional optimization methods. Hereby, utilizing the COMSOL Multiphysics Surrogate model and deep neural networks to design a metasurface grating structure with high extinction rat
... Show MoreThe effluent quality improvement being discharged from wastewater treatment plants is essential to maintain an environment and healthy water resources. This study was carried out to evaluate the possibility of intermittent slow sand filtration as a promising tertiary treatment method for the sequencing batch reactor (SBR) effluent. Laboratory scale slow sand filter (SSF) of 1.5 UC and 0.1 m/h filtration rate, was used to study the process performance. It was found that SSF IS very efficient in oxidizing organic matter with COD removal efficiency up to 95%, also it is capable of removing considerable amounts of phosphate with 76% and turbidity with 87% removal efficiencies. Slow sand filter efficiently reduced the mass of suspended
... Show MoreInthisstudy,FourierTransformInfraredSpectrophotometry(FTIR),XRay Diffraction(XRD)andlossonignition(LOI),comparativelyemployedtoprovideaquick,relativelyinexpensiveandefficientmethodforidentifyingandquantifyingcalcitecontentofphosphateoresamplestakenfromAkashatsiteinIraq.Acomprehensivespectroscopicstudyofphosphate-calcitesystemwasreportedfirstintheMid-IRspectra(4004000cm-1)usingShimadzuIRAffinity-1,fordifferentcutsofphosphatefieldgradeswithsamplesbeneficiatedusingcalcinationandleachingwithorganicacidatdifferenttemperatures.Thenusingtheresultedspectratocreateacalibrationcurverelatesmaterialconcentrationstotheintensity(peaks)ofFTIRabsorbanceandappliesthiscalibrationtospecifyphosphate-calcitecontentinIraqicalcareousphosphateore.Theirpeakswereass
... Show MoreIn this paper, the memorization capability of a multilayer interpolative neural network is exploited to estimate a mobile position based on three angles of arrival. The neural network is trained with ideal angles-position patterns distributed uniformly throughout the region. This approach is compared with two other analytical methods, the average-position method which relies on finding the average position of the vertices of the uncertainty triangular region and the optimal position method which relies on finding the nearest ideal angles-position pattern to the measured angles. Simulation results based on estimations of the mobile position of particles moving along a nonlinear path show that the interpolative neural network approach outperf
... Show MoreIn this study, hexadecyltrimethylammonium bromide (HDMAB) - bentonite was synthesized by placing alkylammonium cation onto bentonite. Adsorption of textile dye such as direct Yellow 50 on natural bentonite and HDMAB -bentonite was investigated. The effects of pH, contact time,dosage clay and temperature were investigated experimentally .The Langmuir and Freundlish isotherms equations were applied to the data and values of parameters of these isotherm equations were evaluated. The study indicated that using 0.2 g of HDMAB (hexadecyltrimethylammonium bromide) lead to increase the percentage removal(R%) from 78% for pure bentonite to 99 %. The optimum pH value for the adsorption experiments was found to be pH=3 and therefore all the experim
... Show MoreIn this work, the Whittaker wave functions were used to study the nuclear density distributions and elastic electron scattering charge form factors for proton-rich nuclei and their corresponding stable nuclei (10,8B, 13,9C, 14,12N and 19,17F). The parameters of Whittaker’s basis were fixed to generate the experimental values of available size radii. The Whittaker basis was connected to harmonic-oscillator basis through boundary condition at match point. The nuclear shell model was opted with pure configuration for all studied nuclei to compute aforementioned studied quantities except 10