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

Each book has a specific style in which its author walks on it from its beginning to its end, and the Holy Qur’an is a book that compiled many methods that were indicative of its miracle, and that it is one unit even though it has been astrologer for twenty-three years.
There is no doubt that knowledge of the Qur’anic methods is one of the pillars of the approach that deals with any of the Qur’an, and the multiplicity of Qur’anic methods is a fact that has many causes. It has been expressed by the Qur’anic discharge and the conjugation of verses to bring them to different methods, and on multiple forms such as nominal, actual, singular Qur’an, presentation, delay, deletion, mention, abbreviation and redundancy. The Qur'ani

During the two last decades ago, audio compression becomes the topic of many types of research due to the importance of this field which reflecting on the storage capacity and the transmission requirement. The rapid development of the computer industry increases the demand for audio data with high quality and accordingly, there is great importance for the development of audio compression technologies, lossy and lossless are the two categories of compression. This paper aims to review the techniques of the lossy audio compression methods, summarize the importance and the uses of each method.

 Research Summary

It highlights the importance of assessing the demand for money function in Iraq through the understanding of the relationship between him and affecting the variables by searching the stability of this function and the extent of their influence in the Iraqi dinar exchange rate in order to know the amount of their contribution to the monetary policies of the Iraqi economy fee, as well as through study behavior of the demand for money function in Iraq and analyze the determinants of the demand for money for the period 1991-2013 and the impact of these determinants in the demand for money in Iraq.

And that the problem that we face is how to estimate the total demand for money in

In this paper we use non-polynomial spline functions to develop numerical methods to approximate the solution of 2nd kind Volterra integral equations. Numerical examples are presented to illustrate the applications of these method, and to compare the computed results with other known methods.

A non-polynomial spline (NPS) is an approximation method that relies on the triangular and polynomial parts, so the method has infinite derivatives of the triangular part of the NPS to compensate for the loss of smoothness inherited by the polynomial. In this paper, we propose polynomial-free linear and quadratic spline types to solve fuzzy Volterra integral equations (FVIE) of the 2nd kind with the weakly singular kernel (FVIEWSK) and Abel's type kernel. The linear type algorithm gives four parameters to form a linear spline. In comparison, the quadratic type algorithm gives five parameters to create a quadratic spline, which is more of a credit for the exact solution. These algorithms process kernel singularities with a simple techniqu