This paper introduces a relationship between the independence of polynomials associated with the links of the network, and the Jacobian determinant of these polynomials. Also, it presents a way to simplify a given communication network through an algorithm that splits the network into subnets and reintegrates them into a network that is a general representation or model of the studied network. This model is also represented through a combination of polynomial equations and uses Groebner bases to reach a new simplified network equivalent to the given network, which may make studying the ability to solve the problem of network coding less expensive and much easier.

Abstract:

     The research aims to shed light on the Corona pandemic and its repercussions on the global economy in general, and on the activities of Iraqi economic units in particular. It also aims to show the impact of the auditor’s reporting on the effects of the Corona pandemic on economic units and its reflection on the quality of his reporting. To achieve the objectives of the research, the researcher prepared a questionnaire according to the five-point Likert scale and took into account in its preparation compatibility with the characteristics of the study community, and that the target community for this questionnaire are the economic units listed in the Iraq Stock Exchange that have complet

This paper presents a grey model GM(1,1) of the first rank and a variable one and is the basis of the grey system theory , This research dealt  properties of grey model and a set of methods to estimate parameters of the grey model GM(1,1)  is the least square Method (LS) , weighted least square method (WLS), total least square method (TLS) and gradient descent method  (DS). These methods were compared based on two types of standards: Mean square error (MSE), mean absolute percentage error (MAPE), and after comparison using simulation the best method was applied to real data represented by the rate of consumption of the two types of oils a Heavy fuel (HFO) and diesel fuel (D.O) and has been applied several tests to

In this paper, we derived an estimators and parameters of Reliability and Hazard function of new mix distribution ( Rayleigh- Logarithmic) with two parameters and increasing failure rate using Bayes Method with Square Error Loss function and Jeffery and conditional probability random variable of observation. The main objective of this study is to find the efficiency of the derived of Bayesian estimator compared to the to the Maximum Likelihood of this function using Simulation technique by Monte Carlo method under different Rayleigh- Logarithmic parameter and sample sizes. The consequences have shown that Bayes estimator has been more efficient than the maximum likelihood estimator in all sample sizes with application