Weighted Gaussian entropy and determinant inequalities

Aequationes mathematicae - We produce a series of results extending information-theoretical inequalities (discussed by Dembo–Cover–Thomas in 1988–1991) to a weighted version of...     

Suzuki–Miyaura coupling catalyzed by palladium nanoparticles biosynthesized using Glycyrrhiza glabra as reducing and stabilyzing agent

An unprecedented environmentally friendly method has been developed for the synthesis of palladium nanoparticles supported on Glycyrrhiza glabra. The synthesized nanoparticles were utilized in Suzuki–Miyaura reaction between different aryl halides and aryl bronic acid in aqueous media. This heterogeneous catalyst can be reused and recycled repeatedly more than five times with only slight loss of its initial catalytic efficiency. This reaction carrid out under atmospheric pressure with high efficiency, unique and simple work‐up procedure and excellent yields.     

Silica Sulfuric Acid,an Efficient and Recyclable Solid Acid Catalyst for the Synthesis of 4,4′-(Arylmethylene)bis (1H-pyrazol-5-ols)

Silica sulfuric acid (SSA) is employed as a recyclable catalyst for the condensation reaction of aromatic aldehydes with 3-methyl-l-phenyl-5-pyrazolone. This condensation reaction is performed in a mixture (1:1 v/v) of water–ethanol at 70 °C, giving 4,4′-alkylmethylene-bis(3-methyl-5-pyrazolones) in 75–93% yields.

Silica‐bonded S‐sulfonic Acid as a Recyclable Catalyst for Synthesis of 2,3‐Dihydroquinazolin‐4(1H)‐ones

2,3‐Dihydroquinazolin‐4(1H)‐one derivatives were synthesized via a one‐pot, three component reaction of isatoic anhydride and an aromatic aldehyde with ammonium acetate or primary amine catalyzed by silica‐bonded S‐sulfonic acid in ethanol at 80°C. The reaction work‐up is simple and the catalyst is easily separated from the products by filtration. The heterogeneous catalyst was recycled for ten runs upon the condensation reaction of isatoic anhydride and 4‐chlorobenzaldehyde with ammonium acetate without losing its catalytic activity.     

A novel strategy for the synthesis of 6H-chromeno [4, 3-b] quinoline by intramolecular Heck cyclization

A novel procedure for the synthesis of various derivatives of 6H-chromeno [4, 3-b] quinolines from intramolecular Heck reaction of 2-chloro-3-(phenoxymethyl) quinolines is described in this study. Intramolecular cyclization of N-alkylated indoles was efficiently investigated as well. The reaction is catalyzed by bis (triphenylphosphine) palladium (II) dichloride in acetonitrile at 80 °C.     

Facile preparation of highly stable and active hybrid palladium nanoparticles: effectual,reusable and heterogeneous catalyst for coupling reactions

Palladium nanoparticles were supported on a bed of Fe₃O₄@‐NH₂@Murexide using a simple and efficient method, and characterized using Fourier transform infrared spectroscopy, X‐ray diffraction, scanning and transmission electron microscopies and inductively coupled plasma optical emission spectrometry. The catalytic system showed great efficiency in cross‐coupling reaction of aryl iodides and arylboronic acid and in Sonogashira cross‐coupling reaction in the green solvent EtOH–H₂O (1:1). The isolation and recovery of the catalyst were simple and facile and it could be used for several successive Suzuki–Miyaura coupling and Sonogashira cross‐coupling reactions. Copyright © 2016 John Wiley & Sons, Ltd.     

A novel three-component method for the synthesis of triazolo[1,2-a]indazole-triones

An efficient synthesis of triazolo[1,2-a]indazole-1,3,8-trione derivatives based on the three-component condensation of urazole, dimedone and aromatic aldehydes under solvent-free conditions is described.     

Basic inequalities for weighted entropies

The concept of weighted entropy takes into account values of different outcomes, i.e., makes entropy context-dependent, through the weight function. In this paper, we establish a number of simple inequalities for the weighted entropies (general as well as specific), mirroring similar bounds on standard (Shannon) entropies and related quantities. The required assumptions are written in terms of various expectations of weight functions. Examples are weighted Ky Fan and weighted Hadamard inequalities involving determinants of positive-definite matrices, and weighted Cramér-Rao inequalities involving the weighted Fisher information matrix.     

Silica-bonded S-Sulfonic Acid: A Recyclable Catalyst for the Synthesis of Trisubstituted Imidazoles under Solvent-free Conditions

Trisubstituted imidazoles have been synthesized in high yields in the presence of silica‐bonded S‐sulfonic acid as a catalyst. The reaction was carried out at 130°C under solvent‐free conditions. The reaction work‐up is simple and the catalyst is easily separated from the products by filtration.