This paper is concerned with the oscillation of all solutions of the n-th order delay differential equation . The necessary and sufficient conditions for oscillatory solutions are obtained and other conditions for nonoscillatory solution to converge to zero are established.
The aim of this study was to investigate antibiotic amoxicillin removal from synthetic pharmaceutical wastewater. Titanium dioxide (TiO2) was used in photocatalysis treatment method under natural solar irradiation in a tubular reactor. The photocatalytic removal efficiency was evaluated by the reduction in amoxicillin concentration. The effects of antibiotics concentration, TiO2 dose, irradiation time and the effect of pH were studied. The optimum conditions were found to be irradiation time 5 hr, catalyst dosage 0.6 g/L, flow rate 1 L/min and pH 5. The photocatalytic treatment was able to destruct the amoxicillin in 5 hr and induced an amoxicillin reduction of about 10% with 141.8 kJ/L accumulate
... Show MoreUreteric obstruction is rarely noted in cases of gastric cancer. Its involvement by distant metastasis from gastric adenocarcinoma without direct invasion is an exceptionally unusual occurrence. This is the story of a 58-year-old man who arrived at the emergency department with acute flank pain and fever. He was initially diagnosed with obstructive pyelonephritis after the discovery of a new onset, complete ureteric obstruction on the left side. Subsequent investigations and follow-up revealed the presence of gastric adenocarcinoma with possible ureteric metastasis bilaterally, flank pain and hydronephrosis were the first and only presentations of gastric cancer. The rarity of the condition and the unusual presentation encouraged us to r
... Show MoreDegenerate parabolic partial differential equations (PDEs) with vanishing or unbounded leading coefficient make the PDE non-uniformly parabolic, and new theories need to be developed in the context of practical applications of such rather unstudied mathematical models arising in porous media, population dynamics, financial mathematics, etc. With this new challenge in mind, this paper considers investigating newly formulated direct and inverse problems associated with non-uniform parabolic PDEs where the leading space- and time-dependent coefficient is allowed to vanish on a non-empty, but zero measure, kernel set. In the context of inverse analysis, we consider the linear but ill-pose
The method of operational matrices is based on the Bernoulli and Shifted Legendre polynomials which is used to solve the Falkner-Skan equation. The nonlinear differential equation converting to a system of nonlinear equations is solved using Mathematica®12, and the approximate solutions are obtained. The efficiency of these methods was studied by calculating the maximum error remainder ( ), and it was found that their efficiency increases as increases. Moreover, the obtained approximate solutions are compared with the numerical solution obtained by the fourth-order Runge-Kutta method (RK4), which gives a good agreement.
The Korteweg-de Vries equation plays an important role in fluid physics and applied mathematics. This equation is a fundamental within study of shallow water waves. Since these equations arise in many applications and physical phenomena, it is officially showed that this equation has solitary waves as solutions, The Korteweg-de Vries equation is utilized to characterize a long waves travelling in channels. The goal of this paper is to construct the new effective frequent relation to resolve these problems where the semi analytic iterative technique presents new enforcement to solve Korteweg-de Vries equations. The distinctive feature of this method is, it can be utilized to get approximate solutions for travelling waves of
... Show MoreShatt Al-Hilla was considered one of the important branches of Euphrates River that supplies irrigation water to millions of dunams of planted areas. It is important to control the velocity and water level along the river to maintain the required level for easily diverting water to the branches located along the river. So, in this research, a numerical model was developed to simulate the gradually varied unsteady flow in Shatt AL-Hilla. The present study aims to solve the continuity and momentum (Saint-Venant) equations numerically to predict the hydraulic characteristics in the river using Galerkin finite element method. A computer program was designed and built using the programming language FORTRAN-77. Fifty kilometers was consid
... Show MoreUsing zooplankton as bioindicators, this study evaluates the ecological condition of the Euphrates River in Iraq's Babylon Province. Site 1 (North Hillah, next to the old Babylon ruins), Site 2 (Hillah city center), Site 3 (South Hillah, close to Al-Mahaweel), and Site 4 (near Al-Kifl town) were the four monitoring locations chosen along the river. The highest and lowest averages of the measured physical and chemical factors indicate temperature (25.1°-29.4°), pH (7.2-7.9), electrical conductivity (EC) (940 µS/cm-1241µS/cm), total dissolved solids TDS (591 mg/L-789mg/L), dissolved oxygen (DO) (5.6 mg/ l-7.1 mg/L), biological oxygen demand (BOD5) (2.4mg/L-4.2 mg/L), nitrate (1.3 mg/L–3.2 mg/L), nitrite (0.04 mg/L–0.13 mg/L),
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