Numerical range and compact convex sets

Let K be a compact convex subset of the plane, μ be a regular Borel measure with support K and N _μ be the multiplication operator on L ²(μ). In this article we show that \(\overline{W}(N_{\mu})\), the closure of numerical range of N _μ , is K. Also we prove that if K has uncountable many extreme points then the Berberian Hilbert space extension of L ²(μ) is non separable.     

Al(H_2PO_4)_3 as an Efficient and Reusable Catalyst for One-pot Three-component Synthesis of α-Amino Phosphonates under Solvent-free Conditions

Synthesis of α‐amino phosphonates is described under solvent‐free conditions at 100°C from reaction between aldehydes and amines in the presence of trialkyl phosphites using Al(H₂PO₄)₃ as an efficient and reusable heterogeneous catalyst. The advantages of this procedure are short reaction time, flexibility and having high to excellent yields.     

Synthesis of phosphonato esters involving heterocyclic biological bases in a highly diastereoselective and chemoselective route

Abstract  

Synthesis of five phosphonato esters has been accomplished via reaction between dimethyl acetylenedicarboxylate and triphenyl phosphite in the presence of biological compounds such as theophylline, 4-hydroxypyrimidine, 2H-3,1-benzoxazine-2,4(1H)-dione, 2-chloroaniline, or 3-nitroaniline at ambient temperature. The configuration of the compounds was determined on the basis of coupling constants emerging from the Karplus equation.     

Protic ionic liquid [TMG][Ac] as an efficient,homogeneous and recyclable catalyst for Boc protection of amines

An efficient and practical protocol for the chemoselective N-Boc protection of various structurally different aryl, aliphatic and heterocyclic amines was carried out with (Boc)₂O using protic 1, 1, 3, 3-tetra-methylguanidinium acetate (10 mol%) as recyclable catalyst under solvent free condition at ambient temperature. No competitive side reactions (isocyanate, urea and N, N-di-Boc) were observed. α-Amino alcohols afforded the N-Boc-derivative without oxazolidinone formation.     

Synthesis of oxime phosphoranes from reaction between triphenylphosphine and acetylenic esters in the presence of oxime derivatives

A new one-pot, simple and effective procedure is presented for the preparation of O-containing phosphorus ylides by the Michael addition reaction of N-methylpyrrole-2-carbaldehydoxime, pyridin-2-carbaldehydoxime or acetophenonoxime with acetylenic esters.     

Reversed‐phase vortex‐assisted liquid–liquid microextraction: A new sample preparation method for the determination of amygdalin in oil and kernel samples

A novel, simple, and rapid reversed‐phase vortex‐assisted liquid–liquid microextraction coupled with high‐performance liquid chromatography has been introduced for the extraction, clean‐up, and preconcentration of amygdalin in oil and kernel samples. In this technique, deionized water was used as the extracting solvent. Unlike the reversed‐phase dispersive liquid–liquid microextraction, dispersive solvent was eliminated in the proposed method. Various parameters that affected the extraction efficiency, such as extracting solvent volume and its pH, vortex, and centrifuging times were evaluated and optimized. The calibration curve shows good linearity (r² = 0.9955) and precision (RSD < 5.2%) in the range of 0.07–20 μg/mL. The limit of detection and limit of quantitation were 0.02 and 0.07 μg/mL, respectively. The recoveries were in the range of 96.0–102.0% with relative standard deviation values ranging from 4.0 to 5.1%. Unlike the conventional extraction methods for plant extracts, no evaporative and re‐solubilizing operations were needed in the proposed technique.     

Copper/Graphene/Clay Nanohybrid: A Highly Efficient Heterogeneous Nanocatalyst for the Synthesis of Novel 1,2,3‐Triazolyl Carboacyclic Nucleosides via ‘Click’ Huisgen 1,3‐Dipolar Cycloaddition

A very mild and highly efficient synthesis of some novel 1H‐1,2,3‐triazolyl carboacyclic nucleosides via a ‘Click’ Huisgen cycloaddition of N‐propargyl nucleobases and azido alcohols using Cu/aminoclay/reduced graphene oxide nanohybrid (Cu/AC/r‐GO nanohybrid) as nanocatalyst is described. The preparation and characterization of Cu/AC/r‐GO nanohybrid are discussed. This catalyst was characterized by X‐ray diffraction, FT‐IR, TEM, and energy‐dispersive analysis of X‐ray techniques. Cu/AC/r‐GO nanohybrid is a stable and highly efficient heterogeneous nanocatalyst that can be easily prepared, used, and restored from the reaction mixture by simple filtration, and reused for many consecutive trials without significant decrease in activity.     

Novel (4-oxothiazolidine-2-ylidene)benzamide derivatives: synthesis,characterization and crystal structures

Research on Chemical Intermediates - A convenient, one-pot, multicomponent synthesis of new (4-oxothiazolidine-2-ylidene)benzamide derivatives by unsymmetrical thioureas, various amines and methyl...