An efficient modification and a novel technique combining the homotopy concept with  Adomian decomposition method (ADM) to obtain an accurate analytical solution for Riccati matrix delay differential equation (RMDDE) is introduced  in this paper  . Both methods are very efficient and effective. The whole integral part of ADM is used instead of the integral part of homotopy technique. The major feature in current technique gives us a large convergence region of iterative approximate solutions .The results acquired by this technique give better approximations for a larger region as well as previously. Finally, the results conducted via suggesting an efficient and easy technique, and may be addressed to other non-linear problems.

Stumpff functions are an infinite series that depends on the value of z. This value results from multiplying the reciprocal semi-major axis with a universal anomaly. The purpose from those functions is to calculate the variation of the universal parameter (variable) using Kepler's equation for different orbits. In this paper, each range for the reciprocal of the semi-major axis, universal anomaly, and z is calculated in order to study the behavior of Stumpff functions C(z) and S(z). The results showed that when z grew, Stumpff functions for hyperbola, parabola, and elliptical orbits were also growing. They intersected and had a tendency towards zero for both hyperbola and parabola orbits, but for elliptical orbits, Stumpff functions

In this paper, a new technique is offered for solving three types of linear integral equations of the 2nd kind including Volterra-Fredholm integral equations (LVFIE) (as a general case), Volterra integral equations (LVIE) and Fredholm integral equations (LFIE) (as special cases). The new technique depends on approximating the solution to a polynomial of degree  and therefore reducing the problem to a linear programming problem(LPP), which will be solved to find the approximate solution of LVFIE. Moreover, quadrature methods including trapezoidal rule (TR), Simpson 1/3 rule (SR), Boole rule (BR), and Romberg integration formula (RI) are used to approximate the integrals that exist in LVFIE. Also, a comparison between those methods i

           Exposure to lead results in significant accumulation in most of vital organs, and free radical damage has been proposed as a cause of lead-induced tissue damage, where oxidative stress is a likely molecular mechanism. This study was designed to evaluate therapeutic effects of melatonin in lead-induced organ toxicity in rats. The therapeutic effects of melatonin on lead induced toxicity in rats were evaluated using 36 rats, which were allocated into 3 groups and treated as follows: Group I, includes 12 rats injected subcutaneously with 0.2 ml physiological saline for 30 days, followed by treatment with a daily dose of 20mg/kg melatonin, administrated I.P for the successive 30 da

A simple, accurate and sensitive spectrophotometric way is used to determine Bisacodyl in pure and pharmaceutical preparations. The proposed method depends on using 2,4-Dinitrophenylhydrazine as chromogenic reagent . The method was based on the oxidative coupling reaction of Bisacodyl with 2,4-Dinitrophenylhydrazine with Sodium periodate in the presence of sodium hydroxide as alkaline media to form red water soluble dye product , that has a maximum absorption at ?max 522nm . Beer ,s law is obeyed in the concentration of (2.00–20.00) ?g.ml -1 .The molar absorptivity is (6505) L.mol-1.cm-1,a sandall sensitivity of(0.0555) ?g.cm-2), correlation coefficient of (0.9970) , Limitof detection (LOD) (0.0312 ?g.ml-1), limit of Quantitation (LOQ) (

Quick and accurate quaternary mixture resolution of furosemide (FURO), carbamazepine (CARB), diazepam (DIAZ) and carvedilol (CARV) by using derivative spectrophotometric method was performed. FURO and CARV were determined by means of first (D1), second (D2), third (D3) and fourth (D4) derivative spectrophotometric methods, CARB was determined by using D1, D2, D3 derivatives, while D1 and D2 were used for the determination of DIAZ. The recommended methods were verified using laboratory prepared mixtures and then successfully applied for the pharmaceutical formulations analysis of the cited drugs. The results obtained revealed the efficiency of the proposed methods as quantitative tool of analysis of the quaternary mixture with no requirement

This paper aims to propose a hybrid approach of two powerful methods, namely the differential transform and finite difference methods, to obtain the solution of the coupled Whitham-Broer-Kaup-Like equations which arises in shallow-water wave theory. The capability of the method to such problems is verified by taking different parameters and initial conditions. The numerical simulations are depicted in 2D and 3D graphs. It is shown that the used approach returns accurate solutions for this type of problems in comparison with the analytic ones.