The researchers have a special interest in studying  Markov  chains as one of the probability samples which has many applications in different fields. This study comes to deal with the changes issue that happen on budget expenditures by using statistical methods, and Markov chains is the best expression about that as they are regarded reliable  samples in the prediction process. A transitional matrix is built for three expenditure cases (increase ,decrease ,stability) for one of budget expenditure items (base salary) for three directorates (Baghdad ,Nineveh , Diyala) of one  of the ministries. Results are analyzed by applying  Maximum likelihood estimation  and Ordinary least squares  methods resulting

In this reserch Some new substituted and unsubstituted poly imides compounds. were synthesized by reaction of acrylol chloride with different amides (aliphatic and aromatic) in a suitable solvent in the presence amount triethyl amine (Et3N) with heating. The Structure confirmation of all polymers were confirmed using FT-IR,1H-NMR,13C-NMR and UV spectroscopy. Thermal analysis (TG) for some polymers showed their thermal stabilities. Other physical properties including softening points, melting point and solubility of the polymers were also measured

Statistical methods and statistical decisions making were used to arrange and analyze the primary data to get norms which are used with Geographic Information Systems (GIS) and spatial analysis programs to identify the animals production and poultry units in strategic nutrition channels, also the priorities of food insecurity through the local production and import when there is no capacity for production. The poultry production is one of the most important commodities that satisfy human body protein requirements, also the most important criteria to measure the development and prosperity of nations. The poultry fields of Babylon Governorate are located in Abi Ghareg and Al_Kifil centers according to many criteria or factors such as the popu

Many numerical approaches have been suggested to solve nonlinear problems. In this paper, we suggest a new two-step iterative method for solving nonlinear equations. This iterative method has cubic convergence. Several numerical examples to illustrate the efficiency of this method by Comparison with other similar methods is given.

This paper interest to estimation the unknown parameters for generalized Rayleigh distribution model based on censored samples of singly type one . In this paper the probability density function for generalized Rayleigh is defined with its properties . The maximum likelihood estimator method is used to derive the point estimation for all unknown parameters based on iterative method , as Newton – Raphson method , then derive confidence interval estimation which based on Fisher information matrix . Finally , testing whether the current model ( GRD ) fits to a set of real data , then compute the survival function and hazard function for this real data.

A new efficient Two Derivative Runge-Kutta method (TDRK) of order five is developed for the numerical solution of the special first order ordinary differential equations (ODEs). The new method is derived using the property of First Same As Last (FSAL). We analyzed the stability of our method. The numerical results are presented to illustrate the efficiency of the new method in comparison with some well-known RK methods.

     In this article, we aim to define a universal set consisting of the subscripts of the fuzzy differential equation (5) except the two elements  and , subsets of that universal set are defined according to certain conditions. Then, we use the constructed universal set with its subsets for suggesting an analytical method which facilitates solving fuzzy initial value problems of any order by using the strongly generalized H-differentiability. Also, valid sets with graphs for solutions of fuzzy initial value problems of higher orders are found.