In this paper, we present a Branch and Bound (B&B) algorithm of scheduling (n) jobs on a single machine to minimize the sum total completion time, total tardiness, total earliness, number of tardy jobs and total late work with unequal release dates. We proposed six heuristic methods for account upper bound. Also to obtain lower bound (LB) to this problem we modified a (LB) select from literature, with (Moore algorithm and Lawler's algorithm).  And some dominance rules were suggested. Also, two special cases were derived. Computational experience showed the proposed (B&B) algorithm was effective in solving problems with up to (16) jobs, also the upper bounds and the lower bound were effective in restr

The removal of commercial orange G dye from its aqueous solution by adsorption on tobacco leaves (TL) was studied in respect to different factor that affected the adsorption process. These factors including the tobacco leaves does, period of orange G adsorption, pH, and initial orange G dye concentration .Different types of isotherm models were used to describe the orange G dye adsorption onto the tobacco leaves. The experimental results were compared using Langmuir, and frundlich adsorption isotherm, the constants for these two isotherm models was determined. The results fitted frundlich model with value of correlation coefficient equal to (0.981). The capacity of adsorption for the orange G dye was carried out using various kinetic models

Unconfined Compressive Strength is considered the most important parameter of rock strength properties affecting the rock failure criteria.  Various research have developed rock strength for specific lithology to estimate high-accuracy value without a core.  Previous analyses did not account for the formation's numerous lithologies and interbedded layers. The main aim of the present study is to select the suitable correlation to predict the UCS for hole depth of formation without separating the lithology. Furthermore, the second aim is to detect an adequate input parameter among set wireline to determine the UCS by using data of three wells along ten formations (Tanuma, Khasib, Mishrif, Rumaila, Ahmady, Maudud, Nahr Um

This paper provides a four-stage Trigonometrically Fitted Improved Runge-Kutta (TFIRK4) method of four orders to solve oscillatory problems, which contains an oscillatory character in the solutions. Compared to the traditional Runge-Kutta method, the Improved Runge-Kutta (IRK) method is a natural two-step method requiring fewer steps. The suggested method extends the fourth-order Improved Runge-Kutta (IRK4) method with trigonometric calculations. This approach is intended to integrate problems with particular initial value problems (IVPs) using the set functions  and   for trigonometrically fitted. To improve the method's accuracy, the problem primary frequency  is used. The novel method is more accurate than the conventional Runge-Ku

     In this research, several estimators concerning the estimation are introduced. These estimators are closely related to the hazard function by using one of the nonparametric methods namely the kernel function for censored data type with varying bandwidth and kernel boundary. Two types of bandwidth are used:  local bandwidth and global bandwidth. Moreover, four types of boundary kernel are used namely: Rectangle, Epanechnikov, Biquadratic and Triquadratic and the proposed function was employed with all kernel functions. Two different simulation techniques are also used for two experiments to compare these estimators. In most of the cases, the results have proved that the local bandwidth is the best for all the

          In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

In this study, the quality assurance of the linear accelerator available at the Baghdad Center for Radiation Therapy and Nuclear Medicine was verified using Star Track and Perspex. The study was established from August to December 2018. This study showed that there was an acceptable variation in the dose output of the linear accelerator. This variation was ±2% and it was within the permissible range according to the recommendations of the manufacturer of the accelerator (Elkta).

The manuscript should contain an abstract. The abstract should be self-contained and citation-free and should not exceed 200 words. The abstract should state the purpose, approach, results and conclusions of the work.  The author should assume that the reader has some knowledge of the subject but has not read the paper. Thus, the abstract should be intelligible and complete in it-self (no numerical references); it should not cite figures, tables, or sections of the paper. The abstract should be written using third person instead of first perso The fast microwave assisted pyrolysis (FMWAP) of water hyacinth (WH) for biochar production is investigated. Taguchi’s method was used to optimize FMWAP parameters. The effects of microwave