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

optical properties of pure poly(vinyl Alcohol) films and poly(vinyl Alcohol) doped with methyl red were study, different percentage prepared with constant thickness using casting technique. Absorption, Transmission spectra have been recorded in order to study the optical parameters such as absorption coefficient, energy gap, refractive index, Extinction coefficient and dispersion parameters were measured in the wavelength range (200-800)nm. This study reveals that the optical properties of PVA affect by increasing the impurity concentration.

     Transformation and many other substitution methods have been used to solve non-linear differential fractional equations. In this present work, the homotopy perturbation method to solve the non-linear differential fractional equation with the help of He’s Polynomials is provided as the transformation plays an essential role in solving differential linear and non-linear equations. Here is the α-Sumudu technique to find the relevant results of the gas dynamics equation in fractional order. To calculate the non-linear fractional gas dynamical problem, a consumer method created on the new homotopy perturbation a-Sumudu transformation method (HP TM) is suggested. In the Caputo type, the derivative is evaluated. a-Sumudu homotopy pe

Humans knew writing and to blog motivated by the need for registration and documentation, and tried from the very beginning of research to find the most suitable material for this purpose, he used many different materials in form, nature, and composition, so it is written on the mud by the ancient Sumerian people in different forms and when the text is long Numbered as the pages of the book at the present time, this research will deal with the damage to manuscripts and then find ways to address them.

Self-criticism is that a person confronts himself with his mistakes in order to reform and develop them for the better, motivate them and inspire hope in them to push them forward and continue to give in this life. The Holy Qur’an teaches us, through the models it cited in its verses, that this is through repentance, a feeling of remorse, and a determination to leave mistakes, and quit disobedience and sins, etc., and all this is done through constructive criticism, and at the same time, one must realize his strengths. , in order to succeed in preserving it and employing it in the right path that pleases God, His Messenger, himself and his society. This has been explained through an introduction, two topics and a conclusion, and God is t

In this paper Hermite interpolation method is used for solving linear and non-linear second order singular multi point boundary value problems with nonlocal condition. The approximate solution is found in the form of a rapidly convergent polynomial. We discuss behavior of the solution in the neighborhood of the singularity point which appears to perform satisfactorily for singular problems. The examples to demonstrate the applicability and efficiency of the method have been given.

The Ash'aris and their position on faith, An Ideological Study

Omed AbdulQader rasool               

College of Islamic Sciences/Salahaddin University-Erbil

Abstract

The concept of faith is very complex, and there are a lot of talk about it among the major Islamic groups such as the Kharijites, the Mu'tazila, the Jahmiyya and others, because of its great importance, and the worldly and eschatological effects it entails according to the elements of faith such as recognition, ratification and action.

The researcher chose one sect, which is the