We investigate the interaction of proton with a solid target, describing the wake effects by taking fitted parameters with experimental values of energy loss function ELF for copper using the dielectric function of random phase approximation (RPA). The results exhibited a damped oscillatory behavior in the longitudinal direction behind the projectile. In addition, the wake potential becomes asymmetric around the z-axis with proton velocity values higher than Fermi velocity, as well as it depends on the position of projectile in cylindrical coordinates.

This research aims to clarify the concept of doctrinal rules and adjust its basic terminologies. It further aims to lay down a map for the method of rooting this science by mentioning its rooted sources, in addition to drawing a miniature picture of its history, origin, formation and development. The paper ends with practical models to highlight its importance in rooting the science of nodal rules and facilitating the mentioning of its scattered discussions in a short and comprehensive phrase. The study further illustrates the pioneering role of doctrinal rules science in managing the doctrinal disputes, combining multiple sayings, and in bringing together opposing opinions. The study follows the inductive, descriptive and analytical app

The management of the exchange rate of the most important tools of economic policy because of its wide area in achieving stability and economic growth through the provision of stability in the exchange rate of the currency of the country concerned , as well as the impact and influence of money supply and then treat the economic crisis monetary and reduce the risk of currency exchange rate .For the management of the exchange rate in Iraq has passed through several stages , from installation to link to a basket of currencies to float freely , and we are dealing with in this research regard to the achievements of monetary policy , especially after the enjoyment of independence on according to the Iraqi Central Bank Law No. 56 of 2004 and Ma

 The logistic regression model of the most important regression models a non-linear which aim getting estimators have a high of efficiency, taking character more advanced in the process of statistical analysis for being a models appropriate form of Binary Data.                                                          

Among the problems that appear as a result of the use of some statistical methods I

This study presents a mathematical model describing the interaction of gut bacteria in the participation of probiotics and antibiotics, assuming that some good bacteria become harmful through mutations due to antibiotic exposure. The qualitative analysis exposes twelve equilibrium points, such as a good-bacteria equilibrium, a bad-bacteria equilibrium, and a coexisting endemic equilibrium in which both bacteria exist while being exposed to antibiotics. The theory of the Sotomayor theorem is applied to study the local bifurcation around all possible equilibrium points. It’s noticed that the transcritical and saddle-node bifurcation could occur near some of the system’s equilibrium points, while pitchfork bifurcation cannot be accrued at

The aesthetic contents of data visualization is one of the contemporary areas through which data scientists and designers have been able to link data to humans, and even after reaching successful attempts to model data visualization, it wasn't clear how that reveals how it contributed to choosing the aesthetic content as an input to humanize these models, so the goal of the current research is to use The analytical descriptive approach aims to identify the aesthetic contents in data visualization, which the researchers interpreted through pragmatic philosophy and Kantian philosophy, and analyze a sample of data visualization models to reveal the aesthetic entrances in them to explain how to humanize them. The two researchers reached seve

Based on the theoretical ideas of E. Cassirer, a methodology is developed and an analysis of the painting work by J. Saleem, a representative of modern Iraqi painting, is carried out. While comparing the artistic programme of J. Saleem and the views of E. Cassirer, the methodological potential of the theory of the symbol for the art criticism analysis of the regional painting is clarified. Comparative analysis with the inclusion of the works of B. Buffet, B. Turetsky, J. Miro helps to see the multiple meanings of the same cultural symbol in thematically similar works of different years, created in different socio-cultural circumstances. The article shows that for regions with a shorter history (France, Russia, Spain, etc.), which have lo

The consequences of divorce after separation have several legal and legal provisions among them is that the wife must wait for a certain period specified by the legislator before marrying another, whether her husband left her after the practice of interning or died until the expiration of the period of counting and compensation for arbitrary divorce and the right of the unmarried to live in the marital home and complete her dowry is gold. But it cannot block the object of material and moral damage, especially if it was fired without shortening them and therefore these rights were decided by the provisions of the absolute and remove the effects on its reputation