Water flow into unsaturated porous media is governed by the Richards’ partial differential equation expressing the mass conservation and Darcy’s laws. The Richards’ equation may be written in three forms,where the dependent variable is pressure head or moisture content, and the constitutive relationships between water content and pressure head allow for conversion of one form into the other. In the present paper, the “moisture-based" form of Richards’ equation is linearized by applying Kirchhoff’s transformation, which
combines the soil water diffusivity and soil water content. Then the similarity method is used to obtain the analytical solution of wetting front position. This exact solution is obtained by means of Lie’s

PDBN Rashid, International Journal of Development in Social Sciences and Humanities, 2023

AASAH Enass J Waheed, Shatha MH Obaid, Research Journal of Pharmaceutical, Biological and Chemical Sciences, 2019 - Cited by 5

In this paper, the dynamical behavior of a three-dimensional fractional-order prey-predator model is investigated with Holling type III functional response and constant rate harvesting. It is assumed that the middle predator species consumes only the prey species, and the top predator species consumes only the middle predator species. We also prove the boundedness, the non-negativity, the uniqueness, and the existence of the solutions of the proposed model. Then, all possible equilibria are determined, and the dynamical behaviors of the proposed model around the equilibrium points are investigated. Finally, numerical simulations results are presented to confirm the theoretical results and to give a better understanding of the dynami

KE Sharquie, GA Ibrahim, AA Noaimi, HK Hamudy, J Saudi Soc Dermatol Dermatol Surg, 2010 - Cited by 2

Background: Fiber-optic endoscopy is an important
investigation of the large intestine, whether or not the
radiologist (barium enema) has discovered a lesion in
the bowel. Colonoscopy affords a unique opportunity
to direct visualization of entire colonic mucosa. At
the same time, the physician can obtain biopsy specimens, remove polyps, and decompress volvuli.
Most experienced endoscopists and well prepared
patients can reach the cecum in over 90% of patients.
If colonoscopy is properly performed, it has a low
risk of complications, such as perforation and bleeding.
Methods: A total of 70 consecutive patients admitted
to Endoscopy department at Al-Kindy Teaching hospital from September- 2008 to July-2009.

The aerodynamic characteristics of general three-dimensional rectangular wings are considered using non-linear interaction between two-dimensional viscous-inviscid panel method and vortex ring method. The potential flow of a two-dimensional airfoil by the pioneering Hess & Smith method was used with viscous laminar, transition and turbulent boundary layer to solve flow about complex configuration of airfoils including stalling effect. Viterna method was used to extend the aerodynamic characteristics of the specified airfoil to high angles of attacks. A modified vortex ring method was used to find the circulation values along span wise direction of the wing and then interacted with sectional circulation obtained by Kutta-Joukowsky the