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.

Current search problem manifested and widows who community harsh to bear hardships and pains، The goals of continuing the sustainability of life and take responsibility, and especially in light of the difficult circumstances in which Iraq is going through, and the displacement of murder and terrorism, which generated huge numbers of widows and orphans Because of the loss of a breadwinner and which became women and children are the most harm to the victim and as a result of wars and armed tendencies So this research is an important and vital topic opens our horizons important for overlapping roles of women widows and their impact on the achievement and status of Iraqi women and that as long as aptly characterized and their ability to end

The study sought to identify the attitudes of PhD students towards establishing the field of educational administration. The study followed the descriptive survey method. The questionnaire was used to collect information from the study community consisting of (95) male and female students in the department of educational administration and Planning. Among the most important results about students ’attitudes towards establishing the educational administration field are the following: 1) identifying the necessity of establishing the educational administration field. 2) Encouraging students to attend seminars and scientific conferences in Islamic rooting. 3) there are no statistically significant differences in the attitudes of doctoral s

The objective of this study is to highlight the skills of office managers and it's impact on the effectiveness of time management in the institutes and faculties of middle technical university and a group of cognitive and practical aims. The managers skills forms mthe modern trend and the main source to provide organizations with highly skilled managers with distinctive performance and because of the sharp changes in the environment which today's organizations works in it , business organizations generally and managers especially realise the importance of time management and it's role in achieving competitive advantage . The problem of this study raised from this point which reflect the extent of departments managers realisation

Background: Alveolar ridge expansion is proposed when the alveolar crest thickness is ≤5 mm. The screw expansion technique has been utilized for many years to expand narrow alveolar ridges. Recently, the osseodensification technique has been suggested as a reliable technique to expand narrow alveolar ridges with effective width gain and as little surgical operating time as possible. The current study aimed to compare osseodensification and screw expansion in terms of clinical width gain and operating time. Materials and methods: Forty implant osteotomies were performed in deficient horizontal alveolar ridges (3–5 mm). A total of 19 patients aged 21–59 years were randomized into two groups: the screw expansion group, which invo

The topological indices of the "[(µ3-2, 5-dioxyocyclohexylidene)-bis ((2-hydrido)-nonacarbonyltriruthenium]” were studied within the quantum theory of atoms in the molecule (QTAIM), clusters are
analyzed using the density functional theory (DFT). The estimated topological variables accord with prior
descriptions of comparable transition metal complexes. The Quantum Theory of Atom, in molecules
investigation of the bridging core component, Ru3H2, revealed critical binding points (chemical bonding)
between Ru (1) and Ru (2) and Ru (3). Consequently, delocalization index for this non-bonding interaction
was calculated in the core of Ru3H2, the interaction is of the (5centre–5electron) class.

The interest of many companies has become dealing with the tools and methods that reduce the costs as one of the most important factors of successful companies, and became the subject of the attention of many economic units because of the impact on the profits of company, and since the nineties of the last century the researchers and writers gave great attention to this subject, especially in light of the large competition and rapid developments in cost management techniques, as well as the wide and significant change in production methods that have been directed towards achieving customer satisfaction, all this and more driven by economic units in all sectors whether it is service or productivity to find methods that would reduc

In this research velocity of moving airplane from its recorded digital sound is introduced. The data of sound file is sliced into several frames using overlapping partitions. Then the array of each frame is transformed from time domain to frequency domain using Fourier Transform (FT). To determine the characteristic frequency of the sound, a moving window mechanics is used, the size of that window is made linearly proportional with the value of the tracked frequency. This proportionality is due to the existing linear relationship between the frequency and its Doppler shift. An algorithm was introduced to select the characteristic frequencies, this algorithm allocates the frequencies which satisfy the Doppler relation, beside that the tra