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 study aims to reach a common point that achieves a balance between two interests, which are generally in conflict with the public interest and the interest of the individual owner of private property, by extrapolating the provisions of the constitutional judiciary that include the protection of private property, and this protection extends to every right of financial value and is not limited to a specific type, but It included everything that can be estimated with money, as ownership is no longer an advantage for the owner, but rather has become a right for him and a social function. The tax is imposed on what is derived from it, but if there is a need to prejudice it, the conditions, limits and restrictions expressly stipulated in the

Systole merazvensis sp. n. from Iraq, is described, figuri4 and differentiated from ,other species of the genus Systok.

The antimicrobial activity of two naphthoquinone semicarbazone derivatives (Two newly synthesized compounds) have been studied by using tube — diluation and disc plate technique. The effect of those derivatives upon pathogenic microorganism iso-lated from specimen(urine iwounds,stool, swabs, throat ....etc) have been studied also in comparison with the antibiotics (amikacin,ampicillin, carbencillin, cephalothin, cefoxitin,clindamycin ,erythromycin,gentamycin,penicillin,tetracylin and tri-methoprim. It was shown that derivative(1) had more effective against micro organ-ism than derivative(11).

Compaction curves are widely used in civil engineering especially for road constructions, embankments, etc. Obtaining the precise amount of Optimum Moisture Content (OMC) that gives the Maximum Dry Unit weight g_dmax. is very important, where the desired soil strength can be achieved in addition to economic aspects.

In this paper, three peak functions were used to obtain the OMC and g_dmax. through curve fitting for the values obtained from Standard Proctor Test. Another surface fitting was also used to model the Ohio’s compaction curves that represent the very large variation of compacted soil types.

The results showed very good correlation between the values obtained from some publ

The advancements in Information and Communication Technology (ICT), within the previous decades, has significantly changed people’s transmit or store their information over the Internet or networks. So, one of the main challenges is to keep these information safe against attacks. Many researchers and institutions realized the importance and benefits of cryptography in achieving the efficiency and effectiveness of various aspects of secure communication.This work adopts a novel technique for secure data cryptosystem based on chaos theory. The proposed algorithm generate 2-Dimensional key matrix having the same dimensions of the original image that includes random numbers obtained from the 1-Dimensional logistic chaotic map for given con

This study examined the imperative construction: the command, the interrogative, the prohibition, the call, and the wish. In the Diwan of Al-Shamakh bin Dirar; where the poetic verses were monitored in each of the topics of the student's creation, and the rhetorical meanings that he came out with. What is new in this study is that it is the first to study the demanded composition in the poetry of a glorious poet, Al-Shammakh bin Dirar Al-Dhubyani. As his poetry did not receive such a study, it sought to employ what was written by rhetoric scholars, in an attempt to explore the demanded composition in the poetry of Al-Shamakh. The study adopted the descriptive analytical approach, which is based on counting the number of times the poet us