an efficient and simple one-pot approach for the synthesis of 3,4-dihydropyrimidin-2-(1h)-one derivatives using antimony trichloride (sbcl3) as a mild catalyst by means of three-component biginelli reaction between β-keto esters, aldehyde derivatives and urea/thiourea under thermal and solvent-free conditions with excellent yields and short reaction times is reported. this methodology offers se...

‎in this paper‎, ‎a numerical procedure for an inverse problem of‎ ‎simultaneously determining an unknown coefficient in a semilinear ‎parabolic equation subject to the specification of the solution at‎ ‎an internal point along with the usual initial boundary conditions ‎is considered‎. ‎the method consists of expanding the required‎ ‎approximate solution as the elements of the inverse quadrati...

Microbial electrolysis cell (MEC) is one of the promising and cutting-edge technologies for generating hydrogen from wastewater through biodegradation of organic waste by exoelectrogenic microbes. In the MECs, the operational parameters, such as applied voltage (Eap), anode surface area, anode-cathode distance, and N2/CO2 volume ratio have a significant impact on the hydrogen yield and producti...

this article proposes a direct method for solving three types of integral equations with time delay. by using operational matrix of integration, integral equations can be reduced to a linear lower triangular system which can be directly solved by forward substitution. numerical examples shows that the proposed scheme have a suitable degree of accuracy.