In this paper, we introduce a new class of Weighted Rayleigh Distribution based on two parameters, one is the scale parameter and the other is the shape parameter introduced in Rayleigh distribution. The main properties of this class are derived and investigated . The moment method and least square method are used to obtain estimators of parameters of this distribution. The probability density function,   survival function, cumulative distribution and hazard function are derived and found. Real data sets are collected to investigate two methods that depend on in this study. A comparison is made between two methods of estimation and clarifies that MLE method is better than the OLS method by using the mea

This paper deals with founding an estimation of best approximation of unbounded functions which satisfied weighted Lipschitz condition with respect to the convex polynomials by means of weighted moduli of smoothness of fractional order  , ( , ) p f t . In addition we prove some properties of weighted moduli of smoothness of fractional order.

In 2020 one of the researchers in this paper, in his first research, tried to find out the Modified Weighted Pareto Distribution of Type I by using the Azzalini method for weighted distributions, which contain three parameters, two of them for scale while the third for shape.This research compared the distribution with two other distributions from the same family; the Standard Pareto Distribution of Type I and the Generalized Pareto Distribution by using the Maximum likelihood estimator which was derived by the researchers for Modified Weighted Pareto Distribution of Type I, then the Mont Carlo method was used–that is one of the simulation manners for generating random samples data in different sizes ( n= 10,30,50), and in di

Background: The surgical treatment of pilonidal sinus varies from wide excision and laying the wound open or excision with primary closure or excision with the use of skin graft in some special cases.
Objectives: The objectives of this study is to determine the efficacy of treating non complicated pilonidal sinus disease with minimal excision and primary closure technique, complications and recurrence rate.
Patients and methods: This is a prospective study conducted in shahid ahmed ismaiel hospital in rania – As sulaimania IRAQ during the period from December 2013 to January 2016 and was carried on one hundred (100) consecutive patients with non complicated non recurrent pilonidal sinus patients who were treated with minimal exci

The research seeks to identify the factors affecting the monopoly and the possibility of measuring the phenomenon of economic ( monopolistic profit) accounted for and that the importance of research topic arising from the transformation of the majority of developing countries to the market economy, which represents the image of the capitalist economy, which is a monopoly, a stages that economy in its various forms, whether Market Worldwide sales monopoly or monopoly, which generates absolute monopolistic profits, which more or less affect on the overall economy of those countries than they should study the phenomenon of monopoly and its impact on the economies of those countries that still love to find her site reinforces its pos

 In this paper we study the effect of the number of training samples for  Artificial neural networks ( ANN ) which is necessary for training process of feed forward neural network  .Also we design 5 Ann's and train 41 Ann's which illustrate how good the training samples that represent the actual function for Ann's.

In this paper, a Cournot oligopoly with isoelastic demand function and constant marginal cost is considered. The local stability conditions of the Cournot equilibrium are determined for four models with different decision mechanisms. In the first model, firms adjust their outputs using the best reply response with naive expectations. The second model is a generalization of the first one, where firms have adaptive expectations. Meanwhile, the third and fourth models adopt the bounded rationality and local monopolistic approximation, respectively. The results show that, in the case of identical firms, the Cournot equilibrium is always stable when the firms adopt the local monopolistic approximation mechanism.

For a connected topological space M we define the homeomorphism and period noncoincidence indices of M, each of them is topological invariant reflecting the abundance of fixed point free self homeomorphisms and periodic point free self maps defined on M respectively. We give some results for computing each of these indices and we give some examples and some results relating these indices with Hoffman index.