The equation of Kepler is used to solve different problems associated with celestial mechanics and the dynamics of the orbit. It is an exact explanation for the movement of any two bodies in space under the effect of gravity. This equation represents the body in space in terms of polar coordinates; thus, it can also specify the time required for the body to complete its period along the orbit around another body. This paper is a review for previously published papers related to solve Kepler’s equation and eccentric anomaly. It aims to collect and assess changed iterative initial values for eccentric anomaly for forty previous years. Those initial values are tested to select the finest one based on the number of iterations, as well as the

Polycaprolactone is one of the natural biodegradable polymers mainly used in bioplastics production for packaging, usually composed of non-toxic compounds and biodegradable. The aim was to examine the role of zinc oxide (ZnO) nanopowder on the,wettability , thermal and anti-bacterial effect nanocomposites.  Pure PCL and PCL-based bio- nanocomposites doped with various ratios of ZnO nanoparticles from 0% to 5wt% were prepared through the arrangement of throwing procedure.  The results show that wettability properties in relation to ideal PCL and that they were increasingly hydrophobic from 57º.8 to 69º.53 because add ZnO  nanocomposites,the thermal stability between 300 and 400 ° C makes them perfect for the application

It is well known that the spread of cancer or tumor growth increases in polluted environments. In this paper, the dynamic behavior of the cancer model in the polluted environment is studied taking into consideration the delay in clearance of the environment from their contamination. The set of differential equations that simulates this epidemic model is formulated. The existence, uniqueness, and the bound of the solution are discussed. The local and global stability conditions of disease-free and endemic equilibrium points are investigated. The occurrence of the Hopf bifurcation around the endemic equilibrium point is proved. The stability and direction of the periodic dynamics are studied. Finally, the paper is ended with a numerical simul

In this paper, a Cholera epidemic model is proposed and studied analytically as well as numerically. It is assumed that the disease is transmitted by contact with Vibrio cholerae and infected person according to dose-response function. However, the saturated treatment function is used to describe the recovery process. Moreover, the vaccine against the disease is assumed to be utterly ineffective. The existence, uniqueness and boundedness of the solution of the proposed model are discussed. All possible equilibrium points and the basic reproduction number are determined. The local stability and persistence conditions are established. Lyapunov method and the second additive compound matrix are used to study the global stability of the system.

It is proposed and studied a prey-predator system with a Holling type II functional response that merges predation fear with a predator-dependent prey's refuge. Understanding the impact of fear and refuge on the system's dynamic behavior is one of the objectives. All conceivable steady-states are investigated for their stability. The persistence condition of the system has been established. Local bifurcation analysis is performed in the Sotomayor sense. Extensive numerical simulation with varied parameters was used to explore the system's global dynamics. A limit cycle and a point attractor are the two types of attractors in the system. It's also interesting to note that the system exhibits bi-stability between these 2 types of attractors.

The aim of this study was to compare the effect of conventional implant site preparation technique and a combination of conventional/piezosurgery preparation on implant stability measured at different time intervals, insertion torque, and preparation time. A randomized controlled study was designed, it included 26 patients who received 54 dental implants randomly assigned to 2 groups; in the control group, implants were installed after conventional preparation with drills whereas the study group received implants after mixed conventional/piezosurgery preparation. The outcome variables included: implant stability measured immediately after implant insertion, at 8 weeks and 16 weeks postoperatively, insertion torque and preparation time. All