A Convenient and Selective Palladium‐Catalyzed Aerobic Oxidation of Alcohols

An efficient procedure for the oxidation of primary and secondary alcohols to aldehydes and ketones, respectively, with molecular oxygen under ambient conditions has been achieved. By applying catalytic amounts of Pd(OAc)₂ in the presence of tertiary phosphine oxides (O?PR₃) as ligands, a variety of substrates are selectively oxidized without formation of ester byproducts. Spectroscopic investigations and DFT calculations suggest stabilization of the active palladium(II) catalyst by phosphine oxide ligands.     

The parameter uniform numerical method for singularly perturbed parabolic reaction–diffusion problems on equidistributed grids

This article presents the study of singularly perturbed parabolic reaction–diffusion problems with boundary layers. To solve these problems, we use a modified backward Euler finite difference scheme on layer adapted nonuniform meshes at each time level. The nonuniform meshes are obtained by equidistribution of a positive monitor function, which involves the second-order spatial derivative of the singular component of the solution. The equidistributing monitor function at each time level allows us to use this technique to non-linear parabolic problems. The truncation error and the stability analysis are obtained. Parameter–uniform error estimates are derived for the numerical solution. To support the theoretical results, numerical experiments are carried out.     

Pd-mediated synthesis of 2-arylquinolines and tetrahydropyridines from modified Baylis-Hillman adducts

We synthesized 2-arylquinolines and tetrahydropyridines via palladium-mediated Heck type reactions starting from the Baylis-Hillman adducts. 2-Arylquinolines were prepared via the Heck type cyclization followed by concomitant aerobic oxidation.     

Chemo-enzymatic synthesis of both enantiomers of rugulactone

The synthesis of both the (R)- and (S)-enantiomers of the natural product rugulactone has been achieved. Candida rugosa lipase hydrolyzes the butyrate ester of the protected 3-hydroxy homoallylic alcohol with very high enantioselectivity (E = 244) and provides the key intermediates with high enantiomeric purity (ee 98–99%) and excellent yields.     

Asymmetric synthesis of Goniothalesdiol A from (R)-2,3-O-cyclohexylidine glyceraldehyde

Goniothalesdiol A 1 has been synthesized from (R)-2,3-O-cyclohexylidine glyceraldehyde with high stereoselectivity and 22% overall yield in 11 simple steps. The key features of the synthetic strategy include the stereocontrolled allylation of (R)-2,3-O-cyclohexylidine glyceraldehydes; the cross-metathesis with a Grubbs’s second generation catalyst, and the intramolecular base-catalyzed oxy-Michael addition for the formation of the tetrahydropyran ring.     

An exploration of fractal-based prognostic model and comparative analysis for second wave of COVID-19 diffusion

Nonlinear Dynamics - The coronavirus disease 2019 (COVID-19) pandemic has fatalized 216 countries across the world and has claimed the lives of millions of people globally. Researches are being...     

Fractional Calculus on Fractal Interpolation for a Sequence of Data with Countable Iterated Function System

In recent years, the concept of fractal analysis is the best nonlinear tool towards understanding the complexities in nature. Especially, fractal interpolation has flexibility for approximation of nonlinear data obtained from the engineering and scientific experiments. Random fractals and attractors of some iterated function systems are more appropriate examples of the continuous everywhere and nowhere differentiable (highly irregular) functions, hence fractional calculus is a mathematical operator which best suits for analyzing such a function. The present study deals the existence of fractal interpolation function (FIF) for a sequence of data \({\{(x_n,y_n):n\geq 2\}}\) with countable iterated function system, where \({x_n}\) is a monotone and bounded sequence, \({y_n}\) is a bounded sequence. The integer order integral of FIF for sequence of data is revealed if the value of the integral is known at the initial endpoint or final endpoint. Besides, Riemann–Liouville fractional calculus of fractal interpolation function had been investigated with numerical examples for analyzing the results.     

Regio- and stereoselective synthesis of methyl 5-methylenetetrahydropyran-3-carboxylates from Baylis-Hillman adducts via allyltributylstannane-mediated radical cyclization

Two types of regioisomeric methyl 5-methylenetetrahydropyran-3-carboxylate derivatives 3a-c and 6a-c were synthesized stereoselectively starting from the Baylis-Hillman adducts via the allyltributylstannane-mediated vinyl radical cyclization as the key step.