Optimal Eighth Order Iterative Methods

We develop an eighth order family of methods, consisting of three steps and three parameters, for solving nonlinear equations. Per iteration the methods require four evaluations (three function evaluations and one evaluation of the first derivative). Convergence analysis shows that the family is eighth-order convergent which is also substantiated through the numerical work. Computational results ascertain that family of methods are efficient and demonstrate equal or better performance as compared with other well known methods.     

Homotopy analysis Sumudu transform method for time—fractional third order dispersive partial differential equation

In this article, we apply the newly introduced numerical method which is a combination of Sumudu transforms and Homotopy analysis method for the solution of time fractional third order dispersive type PDE equations. It is also discussed generalized algorithm, absolute convergence and analytic result of the finite number of independent variables including time variable.     

Stereoselective and facile total synthesis of (+)-goniodiol,a styryllactone from carbohydrates

The stereoselective synthesis of (+)-goniodiol, a cytotoxic styryllactone, has been accomplished in 10 steps starting from inexpensive and readily available d-manitol and δ-gluconolactone involving the direct and straightforward reaction conditions of Grignard addition, chain elongation, and hydroboration, thus making the synthesis simple and convenient.     

An efficient synthesis of pyrazole chalcones under solvent free conditions at room temperature

An easy,safe,solvent free and effective method for the synthesis of pyrazole-substituted chalcones has been achieved by grinding pyrazole aldehydes and acetophenones in the presence of activated barium hydroxide(C-200) in high yield within short span of time.All reactions were carried out just by grinding the two reactants in the presence of activated barium hydroxide(C-200). Results are also compared with sodium hydroxide and potassium hydroxide.     

Polymerization of lactide and synthesis of block copolymer catalyzed by copper(Ⅱ) Schiff base complex

In the present investigation, the novel copper Schiff base complex was synthesized and its catalytic activity was evaluated for the ring-opening polymerization (ROP) of lactide and block polymerization of poly(lactide) with poly(ethylene glycol)methyl ether.     

Discovery of new mutually orthogonal bioorthogonal cycloaddition pairs through computational screening

Density functional theory (DFT) calculations and experiments in tandem led to discoveries of new reactivities and selectivities involving bioorthogonal sydnone cycloadditions. Dibenzocyclooctyne derivatives (DIBAC and BARAC) were identified to be especially reactive dipolarophiles, which undergo the (3 + 2) cycloadditions with N-phenyl sydnone with the rate constant of up to 1.46 M^–1 s^–1. Most significantly, the sydnone-dibenzocyclooctyne and norbornene-tetrazine cycloadditions were predicted to be mutually orthogonal. This was validated experimentally and used for highly selective fluorescence labeling of two proteins simultaneously.