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

In this paper, for the first time we introduce a new four-parameter model called the Gumbel- Pareto distribution by using the T-X method. We obtain some of its mathematical properties. Some structural properties of the new distribution are studied. The method of maximum likelihood is used for estimating the model parameters. Numerical illustration and an application to a real data set are given to show the flexibility and potentiality of the new model.

     The variational iteration method is used to deal with linear and nonlinear differential equations. The main characteristics of the method lie in its flexibility and ability to accurately and easily solve nonlinear equations. In this work, a general framework is presented for a variational iteration method for the analytical treatment of partial differential equations in fluid mechanics. The Caputo sense is used to describe fractional derivatives. The time-fractional Kaup-Kupershmidt (KK) equation is investigated, as it is the solution of the system of partial differential equations via the Boussinesq-Burger equation. By comparing the results that are obtained by the variational iteration method with those obtained by the two-dim

     The Exponentiated Lomax Distribution is considered one of the most commonly used continuous distribution which has a major role in analysing and modelling life time data. Therefore, A family was formed for the Exponential Lomax Distribution by introducing two new distributions as special case of the Exponentiated Lomax Distribution: (Modified Exponentiated Lomax Distribution (MELD) and Restricted Exponentiated Lomax Distribution (RELD. Furthermore, to assess the usefulness and flexibility, the two distributions were applied upon simulation study besides real application with real data set. The simulation results clearly shown the flexible performance of the maximum likelihood estimators for the parameter. Also, the real applicat

Ferritin is a key organizer of protected deregulation, particularly below risky hyperferritinemia, by straight immune-suppressive and pro-inflammatory things. , We conclude that there is a significant association between levels of ferritin and the harshness of COVID-19. In this paper we introduce a semi- parametric method for prediction by making a combination between NN and regression models. So, two methodologies are adopted, Neural Network (NN) and regression model in design the model; the data were collected from مستشفى دار التمريض الخاص for period 11/7/2021- 23/7/2021, we have 100 person, With COVID 12 Female & 38 Male out of 50, while 26 Female & 24 Male non COVID out of 50. The input variables of the NN m

This paper examines a new nonlinear system of multiple integro-differential equations containing symmetric matrices with impulsive actions. The numerical-analytic method of ordinary differential equations and Banach fixed point theorem are used to study the existence, uniqueness and stability of periodic solutions of impulsive integro-differential equations with piecewise continuous functions. This study is based on the Hölder condition in which the ordering ,  and  are real numbers between 0 and 1.

     In this article, a new efficient approach is presented to solve a type of partial differential equations, such (2+1)-dimensional differential equations non-linear, and nonhomogeneous. The procedure of the new approach is suggested to solve important types of differential equations and get accurate analytic solutions i.e., exact solutions. The effectiveness of the suggested approach based on its properties compared with other approaches has been used to solve this type of differential equations such as the Adomain decomposition method, homotopy perturbation method, homotopy analysis method, and variation iteration method. The advantage of the present method has been illustrated by some examples.

     Magnesium oxide nanoparticles (MgO NPs) were synthesized by a green method using the peels of Persimmon extract as the reducing agent , magnesium nitrate, and NaOH. This method is eco-friendly and non-toxic. In this study, an ultrasound device was used to reduce the particle size, with the impact on the energy gap was set at the beginning at 5.39 eV and then turned to 4.10 eV. The morphological analysis using atomic force microscopy (AFM)  showed that the grain size for MgO NPs was 67.70 nm which became 42.33 nm after the use of the ultrasound. The shape of the particles was almost spherical and became cylindrical.  In addition the Field-Emission Scanning Electron Microscopy (FESEM) analysis sh

The Korteweg-de Vries equation plays an important role in fluid physics and applied mathematics. This equation is a fundamental within study of shallow water waves. Since these equations arise in many applications and physical phenomena, it is officially showed that this equation has solitary waves as solutions, The Korteweg-de Vries equation is utilized to characterize a long waves travelling in channels. The goal of this paper is to construct the new effective frequent relation to resolve these problems where the semi analytic iterative technique presents new enforcement to solve Korteweg-de Vries equations. The distinctive feature of this method is, it can be utilized to get approximate solution

Analysis of variance (ANOVA) is one of the most widely used methods in statistics to analyze the behavior of one variable compared to another. The data were collected from a sample size of 65 adult males who were nonsmokers, light smokers, or heavy smokers. The aim of this study is to analyze the effects of cigarette smoking on high-density lipoprotein cholesterol (HDL-C) level and determine whether smoking causes a reduction  in this level, by using the completely randomized design (CRD) and Kruskal- Wallis method. The results showed that the assumptions of the one- way ANOVA are not satisfied, while, after transforming original data by using log transformation, they are satisfied. From the results, a significantly