Hydrogeology of Wadi Qudaid Area, Northeast Jeddah, West Central Arabian Shield, Saudi Arabia

The study area is a part of the Arabian Shield rocks of west central part of Saudi Arabia (150 km to the northeast of Jeddah). Geologically, the study area comprises five main geologic units i.e. 1) Layered basic volcanics and related volcaniclastics which are composed mainly from intercalated basalts and andesites and the related volcaniclastic derivatives, 2) Acidic volcanics and related volcaniclastics which are composed from layered and laminated dark and light acidic to intermediate igneous rocks, quartz and chert and marbles, 3) The Tertiary sedimentary succession which of volcaniclastic red beds and the intercalated clays;5) Tertiary volcanics of Harrart, and 4) The Quaternary wadi fill deposits which are composed from friable pebble supported conglomerates, sandstones and clays. Hydrogeologically, the groundwater aquifer of Wadi Qudaid is present mainly in two main horizons i.e. i) unconfined shallow aquifer (13 - 37 m) within the well porous and permeable conglomerates of the Quaternary Wadi deposits, ii) The deep confined aquifer of the bedded tuffaceous sandstones and mudstone of the Tertiary sedimentary succession of Ash Shumaysi Formation. The water samples are analyzed for major elements i.e. Ca, Mg, Na, Cl, SO4, HCO3 and the results show the normal content of these elements. The study related the addition and depletion of many elements during the running trip of the groundwater from the northeast (recharge area) to the southwest (downstream) area.

Restricted Three-Body Problem in Different Coordinate Systems

In this paper of the series, the equations of motion for the spatial circular restricted three-body problem in sidereal spherical coordinates system were established. Initial value procedure that can be used to compute both the spherical and Cartesian sidereal coordinates and velocities was also developed. The application of the procedure was illustrated by numerical example and graphical representations of the variations of the two sidereal coordinate systems.

Symbolic and Graphical Computations of a Class of Slightly Perturbed Equations

In this paper, a class of slightly perturbed equations of the form F(x)= ξ -x+αΦ(x) will be treated graphically and symbolically, where Φ(x) is an analytic function of x. For graphical developments, we set up a simple graphical method for the real roots of the equation F(x)=0 illustrated by four transcendental equations. In fact, the graphical solution usually provides excellent initial conditions for the iterative solution of the equation. A property avoiding the critical situations between divergent to very slow convergent solutions may exist in the iterative methods in which no good initial condition close to the root is available. For the analytical developments, literal analytical solutions are obtained for the most celebrated slightly perturbed equation which is Kepler’s equation of elliptic orbit. Moreover, the effect of the orbital eccentricity on the rate of convergence of the series is illustrated graphically.