In this paper, Bayes estimators for the shape and scale parameters of Gamma distribution under the Entropy loss function have been obtained, assuming Gamma and Exponential priors for the shape and scale parameters respectively. Moment, Maximum likelihood estimators and Lindley’s approximation have been used effectively in Bayesian estimation. Based on Monte Carlo simulation method, those estimators are compared depending on the mean squared errors (MSE’s). The results show that, the performance of the Bayes estimator under Entropy loss function is better than other estimates in all cases.   

The question about the existence of correlation between the parameters A and m of the Paris function is re-examined theoretically for brittle material such as alumina ceramic (Al2O3) with different grain size. Investigation about existence of the exponential function which fit a good approximation to the majority of experimental data of crack velocity versus stress intensity factor diagram. The rate theory of crack growth was applied for data of alumina ceramics samples in region I and making use of the values of the exponential function parameters the crack growth rate theory parameters were estimated.

One of the most important methodologies in operations research (OR) is the linear programming problem (LPP). Many real-world problems can be turned into linear programming models (LPM), making this model an essential tool for today's financial, hotel, and industrial applications, among others. Fuzzy linear programming (FLP) issues are important in fuzzy modeling because they can express uncertainty in the real world. There are several ways to tackle fuzzy linear programming problems now available. An efficient method for FLP has been proposed in this research to find the best answer. This method is simple in structure and is based on crisp linear programming. To solve the fuzzy linear programming problem (FLPP), a new ranking function (R

      This study aims to classify the critical points of functions with 4 variables and 8 parameters, we found the caustic for the certain function with the spreading of the critical points. Finally, as an application, we found the bifurcation solutions for the equation of sixth order with boundary conditions using the Lyapunov-Schmidt method in the variational case.

The comedian scenes which Shakespeare has entered in some of his tragedies(Hamlet, King Lear, and Macbeth), constantly the wrath of conservative critics and theorists of Western Drama, as big violation to Aristotle’s rules of tragedy that is forbidden to insert comedian scene in tragedy. Chapter one deals with the research problem, and its significance, purpose,Boarders and the definition of Comic Relieve. Chapter two comprises the theoretical framework which has displayed Arist-Otle’s conception about the imitation way of heroes characters between tragedy and comedy, the different function of catharsis in each one. Then the research has exposed the economical and theatrical activities in London during Elizabethan age which was looke

In order to get better understanding of asphalt pavement performance, asphalt from five Iraqi refineries (Qayarah, Nassiriyah, Baiji, Samawah and Daurah) were analyzed into five chemical fractions including asphaltenes, polar compounds, first acidaffins, second acidaffins and saturated hydrocarbons where the last four fractions called maltenes. Polar compounds /saturated hydrocarbons ratio (PC/S) and the ratio of the reactive to the unreactive components of the maltenes fraction (durability rating) parameters were determined. The study showed that Baiji asphalt has the best durability over other asphalts, while Qayarah asphalt is considered to have the least durability grade. These results confirm the correlation of the chemical composit

The aim of this paper is to approximate multidimensional functions f∈C(R^s) by developing a new type of Feedforward neural networks (FFNS) which we called it Greedy ridge function neural networks (GRGFNNS). Also, we introduce a modification to the greedy algorithm which is used to train the greedy ridge function neural networks. An error bound are introduced in Sobolov space. Finally, a comparison was made between the three algorithms (modified greedy algorithm, Backpropagation algorithm and the result in [1]).

In this paper, the process for finding an approximate solution of nonlinear three-dimensional (3D) Volterra type integral operator equation (N3D-VIOE) in R³ is introduced. The modelling of the majorant function (MF) with the modified Newton method (MNM) is employed to convert N3D-VIOE to the linear 3D Volterra type integral operator equation (L3D-VIOE). The method of trapezoidal rule (TR) and collocation points are utilized to determine the approximate solution of L3D-VIOE by dealing with the linear form of the algebraic system. The existence of the approximate solution and its uniqueness are proved, and illustrative examples are provided to show the accuracy and efficiency of the model.

Mathematical Subject Classificat

The use of non-parametric models and subsequent estimation methods requires that many of the initial conditions that must be met to represent those models of society under study are appropriate, prompting researchers to look for more flexible models, which are represented by non-parametric models                  

          In this study, the most important and most widespread estimations of the estimation of the nonlinear regression function were investigated using Nadaraya-Watson and Regression Local Ploynomial, which are one of the types of non-linear

Image classification is the process of finding common features in images from various classes and applying them to categorize and label them. The main problem of the image classification process is the abundance of images, the high complexity of the data, and the shortage of labeled data, presenting the key obstacles in image classification. The cornerstone of image classification is evaluating the convolutional features retrieved from deep learning models and training them with machine learning classifiers. This study proposes a new approach of “hybrid learning” by combining deep learning with machine learning for image classification based on convolutional feature extraction using the VGG-16 deep learning model and seven class