The method of operational matrices based on different types of polynomials such as Bernstein, shifted Legendre and Bernoulli polynomials will be presented and implemented to solve the nonlinear Blasius equations approximately. The nonlinear differential equation will be converted into a system of nonlinear algebraic equations that can be solved using Mathematica®12. The efficiency of these methods has been studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as the polynomial degree (n) increases, since the errors decrease. Moreover, the approximate solutions obtained by the proposed methods are compared with the solution of the 4th order Runge-Kutta method (RK4), which gives very

The current study showed that the plants were collected from 23 geographical locations in Brenaj, Wasit, Iraq. The region was characterized by a great diversity of wild plants spread densely in this region. The results were as follows: 32 families, 149 species. Asteraceae was the most widespread with 29 species from the group of dicotyledons, followed by the Fabaceae family (19) species, but there are 13 plant families, with one plant species recorded for each plant family. in Brenaj, Wasit included: Aizoaceae, Capparaceae, Convolvulaceae, Frankeniaceae, Molluginaceae, Papaveraceae, Phyllanthaceae, Primulaceae, Rutaceae, Rubiaceae, Verbenaceae, Zygophyllaceae, Urticaceae, while the plant family Poaceae was most widespread in genera and spec

The proposed design of neural network in this article is based on new accurate approach for training by unconstrained optimization, especially update quasi-Newton methods are perhaps the most popular general-purpose algorithms. A limited memory BFGS algorithm is presented for solving large-scale symmetric nonlinear equations, where a line search technique without derivative information is used. On each iteration, the updated approximations of Hessian matrix satisfy the quasi-Newton form, which traditionally served as the basis for quasi-Newton methods. On the basis of the quadratic model used in this article, we add a new update of quasi-Newton form. One innovative features of this form's is its ability to estimate the energy functio

       We have presented the distribution of the exponentiated expanded power function (EEPF) with four parameters, where this distribution was created by the exponentiated expanded method created by the scientist Gupta to expand the exponential distribution by adding a new shape parameter to the cumulative function of the distribution, resulting in a new distribution, and this method is characterized by obtaining a distribution that belongs for the exponential family. We also obtained a function of survival rate and failure rate for this distribution, where some mathematical properties were derived, then we used the method of maximum likelihood (ML) and method least squares developed  (LSD) to estimate the parameters an

In this paper, the problem of resource allocation at Al-Raji Company for soft drinks and juices was studied. The company produces several types of tasks to produce juices and soft drinks, which need machines to accomplish these tasks, as it has 6 machines that want to allocate to 4 different tasks to accomplish these tasks. The machines assigned to each task are subject to failure, as these machines are repaired to participate again in the production process. From past records of the company, the probability of failure machines at each task was calculated depending on company data information. Also, the time required for each machine to complete each task was recorded. The aim of this paper is to determine the minimum expected ti

The current research tackles the self-efficacy and its relation to the cognitive assessment for the daily disturbances for the University of Baghdad students. Two criteria have been adopted to achieve the objectives of the research. The sample of this study consists of 200 male and female students who were chosen randomly. The data were analyzed statistically, revealing that the university students owned their own self-efficacy as well as a cognitive assessment for the daily disturbances and they recognized them as self-threatening. The results also indicated the existence of a prediction activity in the field of the cognitive assessment to the daily disturbances selection. In light of the acquired results, the study recommends the neces

In this paper we estimate the coefficients and scale parameter in linear regression model depending on the residuals are of type 1 of extreme  value distribution for the largest values . This can be regard as an improvement for the studies with the smallest values . We study two estimation methods ( OLS  & MLE ) where we resort to Newton – Raphson (NR) and Fisher Scoring methods to get MLE estimate because the difficulty of using the usual approach with MLE . The relative efficiency criterion is considered beside to the statistical inference procedures for the extreme value regression model of type 1 for largest values . Confidence interval , hypothesis testing for both scale parameter and regression coefficients

Abstract:                                        

   We can notice cluster data in social, health and behavioral sciences, so this type of data have a link between its observations and we can express these clusters through the relationship between measurements on units within the same group.

    In this research, I estimate the reliability function of cluster function by using the seemingly unrelate