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.
In this research, some robust non-parametric methods were used to estimate the semi-parametric regression model, and then these methods were compared using the MSE comparison criterion, different sample sizes, levels of variance, pollution rates, and three different models were used. These methods are S-LLS S-Estimation -local smoothing, (M-LLS)M- Estimation -local smoothing, (S-NW) S-Estimation-NadaryaWatson Smoothing, and (M-NW) M-Estimation-Nadarya-Watson Smoothing.
The results in the first model proved that the (S-LLS) method was the best in the case of large sample sizes, and small sample sizes showed that the
... Show MoreThis study is conducted to verify the efficienecy of local Ninivite rock when used in the treatment of drinking water in plants operating currently in the country in order to develop the situation of these stations to cope with the increase in population. Also, this will limit the pollutian which are increasing in the country's rivers.
(Euphrates and Tigris). These rivers are the sources to feed all water treatment plants in the country. The idea is the develop or the modify these stations by replacing part of top layer of sand filters used in these stations with Ninivite rock to operate as filters composed of two medium. The efficiency of this rock is compared with other materials used successfully worldwide in this area, such a
... Show MoreThe study aimed to know the effect of the use alcoholic ethanol extraction of Boswellia Carterii In prolonging the period of preservation cooled ground meat in 4C for 6 days, it has been mixing ground meat with 150,300,450 mg/ml of alcoholic extract Consecutive, Where (0 was the control sample), All samples were stored separately for 0 , 3 , 6 days in Refrigerator temperature 4 C, Conducted by some microbial tests, Results have shown that mixing the ground meat with Boswellia Carterii extraction Led to prolong the storage of meat for 6 days at 4 C .and the Best result came when adding alcoholic ethanol extract of Boswellia Carterii by 450mg/ml Which Equal 0.9 g ,that reducing microbial load more higher than 150&300 mg/ml. All of thes
... Show MoreThe transition structure is considered as the most important hydraulic structure controlling the w/s transtion, morever it decrease the scouring of outlet structure.
seven experiment samples for transition structure was used in this research at different angles ( 10° - 90° ).
It was shown that froud number has a clear effect on the depth of the scouring, morever the high discharge rates cause an increase of the ratio between the length of the scour and its depth.
In order to select the best flaring angle it was shown that the angle of 40° has the most discharge rate, least structure length and least angle scour depth, with the firmly of t
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