In this paper, a new technique is offered for solving three types of linear integral equations of the 2^nd 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

The theory of probabilistic programming  may be conceived in several different ways. As a method of programming it analyses the implications of probabilistic variations in the parameter space of linear or nonlinear programming model. The generating mechanism of such probabilistic variations in the economic models may be due to incomplete information about changes in demand, pro­duction and technology, specification errors about the econometric relations presumed for different economic agents, uncertainty of various sorts and the consequences of imperfect aggregation or disaggregating of economic variables. In this Research we discuss the probabilistic programming problem when the coefficient b_i is random variable

One of the troublesome duties in chemical industrial units is determining the instantaneous drop size distribution, which is created between two immiscible liquids within such units. In this work a complete system for measuring instantaneous droplet size is constructed. It consists of laser detection system (1mW He-Ne laser), drop generation system (turbine mixer unit), and microphotography system. Two immiscible liquids, water and kerosene were mixed together with different low volume fractions (0.0025, 0.02) of kerosene (as a dispersed phase) in water (as a continuous phase). The experiments were carried out at different rotational speed (1180- 2090 r.p.m) of the turbine mixer. The Sauter mean diameter of the drops was determined by la

Soil compaction is one of the most harmful elements affecting soil structure, limiting plant growth and agricultural productivity. It is crucial to assess the degree of soil penetration resistance to discover solutions to the harmful consequences of compaction. In order to obtain the appropriate value, using soil cone penetration requires time and labor-intensive measurements. Currently, satellite technologies, electronic measurement control systems, and computer software help to measure soil penetration resistance quickly and easily within the precision agriculture applications approach. The quantitative relationships between soil properties and the factors affecting their diversity contribute to digital soil mapping. Digital soil maps use

Aim To develop a low-density polyethylene–hydroxyapatite (HA-PE) composite with properties tailored to function as a potential root canal filling material. Methodology Hydroxyapatite and polyethylene mixed with strontium oxide as a radiopacifier were extruded from a single screw extruder fitted with an appropriate die to form fibres. The composition of the composite was optimized with clinical handling and placement in the canal being the prime consideration. The fibres were characterized using infrared spectroscopy (FTIR), and their thermal properties determined using differential scanning calorimetry (DSC). The tensile strength and elastic modulus of the composite fibres and gutta-percha were compared, dry and after 1 month storage in

In this study predication of crop coefficient (Kc) values through growing season for cucumber plant was conducted. A field experiment was carried out at AL Yusufiyah Township, in the Governorate of Baghdad, (latitude: 33°09' N, longitude: 44°24' E, and altitude: 34 m) in medium loam soil. The plant was cultivated inside the greenhouse under subsurface trickle irrigation system with soil water retention technology (SWRT) during the growing season 2017. Crop coefficient values were guessed from the direct method of measurements of daily crop evapotranspiration, while reference evapotranspiration was obtained from Agricultural Meteorology Project - Station of Baghdad - Abu-Ghraib.  The obtained results were showed that crop coeffici

Mass transfer was examined at a stationary rectangular copper electrode (cathode) by using the reduction of cupric ions as the electrochemical reaction. The influence of electrolyte temperature (25, 45, and 65 ^oC), and cupric ions concentration (4, 8, and 12 mM) on mass transfer coefficient were investigated by using limiting current technique. The mass transfer coefficient and hence the Sherwood number was correlated as Sh =

Abstract: The power and the size of the final spot of the laser beam reaching the target are very important requirements in most of the laser applications and fields such as medical, military, and scientific, so studying laser propagation in the atmosphere is a very important topic. The propagation of the laser beam through the atmosphere is subject to several attenuation processes that deplete the power and expand the beam. Through the simulation results of the free electron laser within the visible region of the electromagnetic spectrum (400-700nm), it was found that the attenuation increases with decreasing wavelength. Laser propagation in the presence of rain and snow leads to a very large loss of power compared to propagation i