In this work, the modified Lyapunov-Schmidt reduction is used to find a nonlinear Ritz approximation of Fredholm functional defined by the nonhomogeneous Camassa-Holm equation and Benjamin-Bona-Mahony. We introduced the modified Lyapunov-Schmidt reduction for nonhomogeneous problems when the dimension of the null space is equal to two.  The nonlinear Ritz approximation for the nonhomogeneous Camassa-Holm equation has been found as a function of codimension twenty-four.

The aim of this paper is to estimate a nonlinear regression function of the Export of the crude oil Saudi (in Million Barrels) as a function of the number of discovered fields.

 Through studying the behavior of the data we show that its behavior was not followed a linear pattern or can put it in a known form so far there was no possibility to see a general trend resulting from such exports.

We use different nonlinear estimators to estimate a regression function, Local linear estimator, Semi-parametric as well as an artificial neural network estimator (ANN).

The results proved that the (ANN) estimator is the best nonlinear estimator am

     We have presented the distribution of the exponentiated expanded power function (EEPF) with four parameters, where this distribution was created by the exponentiated expanded method created by the scientist Gupta to expand the exponential distribution by adding a new shape parameter to the cumulative function of the distribution, resulting in a new distribution, and this method is characterized by obtaining a distribution that belongs for the exponential family. We also obtained a function of survival rate and failure rate for this distribution, where some mathematical properties were derived, then we used the method of maximum likelihood (ML) and method least squares developed  (LSD)

       We have presented the distribution of the exponentiated expanded power function (EEPF) with four parameters, where this distribution was created by the exponentiated expanded method created by the scientist Gupta to expand the exponential distribution by adding a new shape parameter to the cumulative function of the distribution, resulting in a new distribution, and this method is characterized by obtaining a distribution that belongs for the exponential family. We also obtained a function of survival rate and failure rate for this distribution, where some mathematical properties were derived, then we used the method of maximum likelihood (ML) and method least squares developed  (LSD) to estimate the parameters an

Traffic loading and environmental factors are among the most serious variables that cause the spoilage of flexible pavements and lead to a decrease in their design life. The objective of this study is to investigate the influence of axle load raise and the change in resilient modulus on the flexible pavement design life. Locally, Highway geometric design code for Iraqi building code has assign certain admissible maximum load limits per every axle truck type that should not be overrun. In this paper nine different axle truck loads (8, 9, 10, 11, 12, 13, 14, 15, and 16) tons, single axle with dual tire and, and two different resilient moduli of asphalt pavement were chosen. The evaluation was carried out assuming high temperature to represent

The research deals with Iraq's position of the Lebanese civil war and the Efforts made by Iraq in order to stop the bleeding of this war, the research also deals with the nature of regime in Lebanon and the developments that preceded the war and the positions of the internal and external competing forces, as weu as handling the Iraqi Syrian disagreement and it's impaet on the situation of Lebanon and the war developments.
The research focused on the Iraq's position towards the externd proposed solutions to solve the Lebanese civil war.

The problem of research was to identify after the use of cost technology based on specifications in the validity of determining and measuring the costs of the implementation of contracting, by applying to al-Mansour General Construction Contracting Company as an appropriate alternative to the traditional costing system currently adopted, which is characterized by many shortcomings and weaknesses Which has been reflected in the validity and integrity of the calculations. To solve this problem, the research was based on the premise that: (The application of cost technology based on specifications will result in calculating the cost of the product according to the specification required by the customer, to meet his wishes properly and witho

Praise be to God, who started his book with the praise of himself and prayers and peace be upon those who have no prophet after him and his family and companions and those who followed them with charity until the Day of Judgment.
     For it is known to every researcher in jurisprudence and its origins that the semantics in terms of formulas for assignment are divided into an order and a prohibition, and I have seen it necessary to write a small research on the prohibition, and since this topic is complex, and has a great impact on the difference of scholars, I decided to write on one issue of it And it is the absolute prohibition and its effect on the difference of jurists, and what is meant by the absolute p

Two- dimensional numerical simulations are carried out to study the elements of observing a Dirac point source and a Dirac binary system. The essential features of this simulation are demonstrated in terms of the point spread function and the modulation transfer function. Two mathematical equations have been extracted to present, firstly the relationship between the radius of optical telescope and the distance between the central frequency and cut-off frequency of the optical telescope, secondly the relationship between the radius of the optical telescope and the average frequency components of the modulation transfer function.