Numerical range of operators acting on Banach spaces

The aim of the paper is to propose a definition of numerical range of an operator on reflexive Banach spaces. Under this definition the numerical range will possess the basic properties of a canonical numerical range. We will determine necessary and sufficient conditions under which the numerical range of a composition operator on a weighted Hardy space is closed. We will also give some necessary conditions to show that when the closure of the numerical range of a composition operator on a small weighted Hardy space has zero.     

The clean and mild synthesis,crystal structure,and intra-molecular hydrogen bond study of substituted new 4,8-dihydropyrano[3,2-b]-pyrans containing chlorokojic acid moiety

Research on Chemical Intermediates - A safe, green and convenient process was developed for the synthesis of a novel group of 4,8-dihydropyrano[3,2-b]-pyrans by dialkyl acetylenedicarboxylates and...     

Efficient highly diastereoselective synthesis of 1,8a-dihydro-7H-imidazo[2,1-b][1,3]oxazines

1-Alkyl imidazoles react smoothly with dialkyl acetylenedicarboxylates in the presence of pyridine carboxaldehydes to diastereoselectively produce 1,8a-dihydro-7H-imidazo[2,1-b][1,3]oxazine derivatives in excellent yields.     

Simple Synthesis of Stable Phosphorus Ylides Derived from Imidazolidine-2-Thione. Efficient One-Pot Synthesis of α-Amino Esters with β-Phosphorus Substituents

Crystalline phosphorus ylides are obtained in nearly quantitative yields from the addition reaction between triphenylphosphine, dialkyl acetylenedicarboxylates, and imidazolidine-2-thione. A dynamic NMR effect is observed in the ¹ H NMR spectrum of the stabilized ylide obtained from dimethyl acetylenedicarboxylate (Δ G ^≠ = 66.6 kJmol^?1 ) and is attributed to restricted rotation around the carbon–carbon partial double bond resulting from the conjugation of the ylide moiety with the adjacent carbonyl group.     

An organic‐inorganic heterogeneous catalyst based on Keplerate polyoxometalates for oxidation of dibenzothiophene derivatives with Hydrogen peroxide

An organic‐inorganic material (NH₄)₂(MimAM)₄₀[Mo₁₃₂O₃₇₂(CH₃COO)₃₀(H₂O)₇₂] have been synthesized by reacting [(NH₄)₄₂[Mo^VI₇₂ Mo^V₆₀O₃₇₂(CH₃COO)₃₀(H₂O)₇₂] with the ionic liquid 3‐Aminoethyl‐1‐methylimidazolium bromide. The catalyst showed remarkably a high catalytic performance in the oxidation of dibenzothiophene (DBT) derivatives with H₂O₂ 35% as a safe and green oxidant. The main parameters affecting the process including catalyst, acid additive, hydrogen peroxide amounts and temperature have been investigated in detail. Sulfur removal of DBT in n‐heptane reached to 98.3% yield at 40 °C using 2.5 mmol H₂O₂ and 100 mg of (NH₄)₂(MimAM)₄₀[Mo₁₃₂O₃₇₂(CH₃COO)₃₀(H₂O)₇₂] after 90 min. Under the optimal conditions, BT (benzothiophene), DBT (dibenzothiophene) and 4,6‐DMDBT (4,6‐dimethyl‐dibenzothiophene) achieved high desulfurization efficiency. Our results showed that the reactivity order of different model sulfur compounds are thiophene <4,6‐dimethyl dibenzothiophene< dibenzothiophene. The catalysts could be easily separated from the reaction solution by simple filtration and recycled for several times without loss of activity.     

Monodisperse CuPt alloy nanoparticles assembled on reduced graphene oxide as catalysts in the transfer hydrogenation of various functional organic groups

We present herein a new nanocatalyst, namely binary CuPt alloy nanoparticles (NPs) supported on reduced graphene oxide (CuPt‐rGO), as a highly active heterogeneous catalyst for the transfer hydrogenation (TH) protocol that is demonstrated to be applicable over the reduction of various unsaturated organic compounds (olefins, aldehydes/ketones and nitroarenes) in aqueous solutions at room temperature. CuPt alloy NPs were synthesized by the co‐reduction of metal (II) acetylacetonates by borane‐tert‐butylamine (BTB) complex in hot oleylamine (OAm) solution and then assembled on reduced graphene oxide (rGO) via ultrasonic‐assisted liquid phase self‐assembly method. The structure of yielded CuPt NPs and CuPt‐rGO nanocatalyst were characterized by TEM, XRD and ICP‐MS. The activity of Cu₇Pt₃‐rGO nanocatalysts were then tested for the THs that were conducted in a commercially available high‐pressure tube using water as sole solvent and ammonia borane as a hydrogen donor at room temperature. The presented catalytic TH protocol was successfully applied over nitroarenes, olefines and aldehydes/ketones, and all the tested compounds were converted to corresponding reduction products with the yields reaching up to 99% under ambient conditions. Moreover, the Cu₇Pt₃‐rGO nanocatalyst was also reusable in the TH by providing 99% yield after five consecutive runs in TH of nitrobenzene as an example.     

Fe3O4@silica‐MCM‐41@DABCO: A novel magnetically reusable nanostructured catalyst for clean in situ synthesis of substituted 2‐aminodihydropyrano[3,2‐b]pyran‐3‐cyano

DABCO (1,4‐diazabicyclo[2.2.2]octane)‐modified magnetite with silica‐MCM‐41 shell (Fe₃O₄@silica‐MCM‐41@DABCO) as an effective, magnetic and novel heterogeneous reusable nanocatalyst was synthesized and analysed using various techniques. Evaluation of the catalytic activity of this nanocatalyst was performed in the clean synthesis of substituted 2‐aminodihydropyrano[3,2‐b]pyran‐3‐cyano in high yields via in situ reaction of azido kojic acid, malononitrile and various aldehydes.     

A fully discrete Galerkin method for Abel-type integral equations

In this paper, we present a Galerkin method for Abel-type integral equation with a general class of kernel. Stability and quasi-optimal convergence estimates are derived in fractional-order Sobolev norms. The fully-discrete Galerkin method is defined by employing simple tensor-Gauss quadrature. We develop a corresponding perturbation analysis which allows to keep the number of quadrature points small. Numerical experiments have been performed which illustrate the sharpness of the theoretical estimates and the sensitivity of the solution with respect to some parameters in the equation.     

Novel nanocomposite membranes based on polybenzimidazole and Fe<Subscript>2</Subscript>TiO<Subscript>5</Subscript> nanoparticles for proton exchange membrane fuel cells

In this work, Fe₂TiO₅ nanoparticles were used for improving the proton conductivity, and water and acid uptake of polybenzimidazole (PBI)-based proton exchange membranes. The nanocomposite membranes have been prepared using different amounts of Fe₂TiO₅ nanoparticles and dispersed into a PBI membrane with the solution-casting method. The prepared membranes were then physico-chemically and electrochemically characterized for use as electrolytes in high-temperature PEMFCs. The PBI/Fe₂TiO₅ membranes (PFT) showed a higher acid uptake and proton conductivity compared with the pure PBI membranes. The highest acid uptake (156 %) and proton conductivity (78 mS/cm at 180 °C) were observed for the PBI nanocomposite membranes containing 4 wt% of Fe₂TiO₅ nanoparticles (PFT₄). The PFT₄ composite membrane showed 380 mW/cm² power density and 760 mA/cm² current density in 0.5 V at 180 °C at dry condition. The above results indicated that the PFT₄ nanocomposite membranes could be utilized as proton exchange membranes for high-temperature fuel cells.