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.

this paper presents a novel method for solving nonlinear optimal conrol problems of regular type via its equivalent two points boundary value problems using the non-classical

This paper proposes a new algorithm (F2SE) and algorithm (Alg(n – 1)) for solving the
two-machine flow shop problem with the objective of minimizing total earliness. This
complexity result leads us to use an enumeration solution approach for the algorithm (F2SE)
and (DM) is more effective than algorithm Alg( n – 1) to obtain approximate solution.

The simple and available technique of colorimetry and indirect X-ray fluorescence determination of tetracycline hydrochloride (in the form of colored complex with iron(III) ions) and cyanocobalamine (in the form of the colored thiocyanate complex with cobalt(II) ions) is offered. The analytes were separated from the accompanying components by sorption to polyurethane foam based on ethers. The conditions of sorption separation and measurement of analytical signal of these substances are optimized. The obtained results of tetracycline drugs and injection solution B₁₂ vitamin are in satisfactory agreement with data declared by the manufacturer.

The adsorption of Pb(II) ions onto bentonite and activated carbon was investigated. The effects of pH, initial adsorbent dosage, contact time and temperature were studied in batch experiments. The maximum adsorption capacities for bentonite and activated carbon were 0.0364 and 0.015 mg/mg, respectively. Thermodynamic parameters such as Gibbs free energy change, Enthalpy change and Entropy change have been calculated. These thermodynamic parameters indicated that the adsorption process was thermodynamically spontaneous under natural conditions and the adsorption was endothermic in nature. Experimental data were also tested in terms of adsorption kinetics, the results showed that the adsorption processes followed well pseudo second- order

Abstract:In this paper, some probability characteristics functions (moments, variances,convariance, and spectral density functions) are found depending upon the smallestvariance of the solution of some stochastic Fredholm integral equation contains as aknown function, the sine wave function

Natural bentonite (B) mineral clay was modified by anionic surfactant sodium dodecyl sulfate (SDS) and characterized using different techniques such as: FTIR spectroscopy, scanning electron microscopy (SEM) and X-Ray diffraction (XRD). The bentonite and modified bentonite were used as adsorbents for the adsorption of methyl violet (MV) from aqueous solutions. The adsorption study was carried out at different conditions such as: contact time, pH value and adsorbent weight. The adsorption kinetic described by pseudo– first order and pseudo – second order equilibrium experimental data described by Langmuir, Freundlich and Temkin isotherm models. The thermodynamic parameters standard free energy ( ), standard entropy ( ) standa

The purpose of this research paper is to present the second-order homogeneous complex differential equation   , where   , which is defined on the certain complex domain depends on solution behavior. In order to demonstrate  the relationship between the solution of the second-order of the complex differential equation and its coefficient of function, by studying the solution in certain cases: a meromorphic function, a coefficient of function, and if the solution is considered to be a transformation with another complex solution. In addition, the solution has been provided as a power series with some  applications.

Pharmaceuticals have been widely remaining contaminants in wastewater, and diclofenac is the most common pharmaceutical pollutant. Therefore, the removal of diclofenac from aqueous solutions using activated carbon produced by pyrocarbonic acid and microwaves was investigated in this research. Apricot seed powder and pyrophosphoric acid (45 wt%) were selected as raw material and activator respectively, and microwave irradiation technique was used to prepare the activated carbon. The raw material was impregnated in pyrophosphoric acid at 80◦C with an impregnation ratio of 1: 3 (apricot seeds to phosphoric acid), the impregnation time was 4 h, whereas the power of the microwave was 700 watts with a radiation time of 20 min. A series o