Noetherianity of some degree two twisted commutative algebras

The resolutions of determinantal ideals exhibit a remarkable stability property: for fixed rank but growing dimension, the terms of the resolution stabilize (in an appropriate sense). One may wonder if other sequences of ideals or modules over coordinate rings of matrices exhibit similar behavior. We show that this is indeed the case. In fact, our main theorem is more fundamental in nature: It states that certain large algebraic structures (which are examples of twisted commutative algebras) are noetherian. These are important new examples of large noetherian algebraic structures, and ones that are in some ways quite different from previous examples.     

A lattice Boltzmann model for diffusion of binary gas mixtures that includes diffusion slip

This paper describes the development of a lattice Boltzmann (LB) model for a binary gas mixture, and applications to channel flow driven by a density gradient with diffusion slip occurring at the wall. LB methods for single component gases typically use a non‐physical equation of state in which the relationship between pressure and density varies according to the scaling used. This is fundamentally unsuitable for extension to multi‐component systems containing gases of differing molecular masses. Substantial variations in the species densities and pressures may exist even at low Mach numbers; hence, the usual linearized equation of state for small fluctuations is unsuitable. Also, existing methods for implementing boundary conditions do not extend easily to novel boundary conditions, such as diffusion slip. The new model developed for multi‐component gases avoids the pitfalls of some other LB models. A single computational grid is shared by all the species, and the diffusivity is independent of the viscosity. The Navier–Stokes equation for the mixture and the Stefan–Maxwell diffusion equation are both recovered by the model. Diffusion slip, the non‐zero velocity of a gas mixture at a wall parallel to a concentration gradient, is successfully modelled and validated against a simple one‐dimensional model for channel flow. To increase the accuracy of the scheme, a second‐order numerical implementation is needed. This may be achieved using a variable transformation method that does not increase the computational time. Simulations were carried out on hydrogen and water diffusion through a narrow channel for varying total pressure and concentration gradients. Copyright © 2011 John Wiley & Sons, Ltd.     

Radiolabelling of TiO<Subscript>2</Subscript> nanoparticles for radiotracer studies

Industrially manufactured titanium dioxide nanoparticles have been successfully radiolabelled with ⁴⁸V by irradiation with a cyclotron-generated proton beam. Centrifugation tests showed that the ⁴⁸V radiolabels were stably bound within the nanoparticle structure in an aqueous medium, while X-ray diffraction indicated that no major structural modifications to the nanoparticles resulted from the proton irradiation. In vitro tests of the uptake of cold and radiolabelled nanoparticles using the human cell line Calu-3 showed no significant difference in the uptake between both batches of nanoparticles. The uptake was quantified by Inductively Coupled Plasma Mass Spectrometry and high resolution γ-ray spectrometry for cold and radiolabelled nanoparticles, respectively. These preliminary results indicate that alterations to the nanoparticles’ properties introduced by proton bombardment can be controlled to a sufficient extent that their further use as radiotracers for biological investigations can be envisaged and elaborated.     

Well‐defined polyisoprene‐grafted silica nanoparticles via the RAFT process

The preparation of well‐defined polyisoprene‐grafted silica nanoparticles (PIP‐g‐SiO₂ NPs) was investigated. Surface initiated reversible addition fragmentation chain transfer (SI‐RAFT) polymerization was used to polymerize isoprene from the surface of 15 nm silica NPs. A high temperature stable trithiocarbonate RAFT agent was anchored onto the surface of particles with controllable graft densities. The polymerization of isoprene mediated by silica anchored RAFT with different densities were investigated and compared to the polymerization mediated by free RAFT agents. The effects of different temperatures, initiators, and monomer feed ratios on the kinetics of the SI‐RAFT polymerization were also investigated. Using this technique, block copolymers of polyisoprene and polystyrene on the surface of silica particles were also prepared. The well‐defined synthesized PIP‐g‐SiO₂ NPs were then mixed with a polyisoprene matrix which showed a good level of dispersion throughout the matrix. These tunable grafted particles have potential applications in the field of rubber nanocomposites. © 2017 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2017 , 55, 1493–1501     

Sulfonated Condensed Polynuclear Aromatic (S-Copna) Resin Catalyzed Selective Oxidation of Sulfides to Sulfoxides or Sulfones Using Hydrogen Peroxide

Abstract

Sulfonated condensed polynuclear aromatic (S-COPNA) resin was found to be a highly efficient, environmentally friendly, recyclable heterogeneous catalyst for the oxidation of alkyl and aryl sulfides to the corresponding sulfoxides or sulfones, in good yields under mild reaction conditions using 30% hydrogen peroxide as an oxidant.

Supplemental materials are available for this article. Go to the publisher's online edition of Phosphorus, Sulfur, and Silicon and the Related Elements for the following free supplemental resource: Synthesis of the S-COPNA resin catalyst. Spectroscopic data for compounds.     

SYNTHESIS OF NEW BENZOSULFOXIDE MACROCYCLIC COMPOUNDS

Bis(dibenzosulfoxo)-27,30,35,38-tetramethyl-24-crown-6, bis(dibenzosulfoxo)-21,24,29,32-tetramethyl-18-crown-4, dibenzosulfoxo-15,18-dimethyl-12-crown-3 and dibenzosulfoxo-12,15-dimethyl-9-crown-2 macrocycles are synthesized by the reaction of 2,2′-sulfinyl-bis(4-methyl phenol)and 1,2-dibromoethane and diethyleneglycol di-p-toluenesulfonate.     

A novel covalent functionalisation of poly (styrene-alt-maleic anhydride) with 4-amino benzo-9-crown-3 ether

The grafting of 4-amino benzo-9-crown-3 ether to poly (styrene-alt-maleic anhydride) has been described. The covalent grafting of crown ether has led to a considerable increase in the solubility of polymer in organic solvents such as dimethyl sulphoxide, dimethylformamide and tetrahydrofuran. The highest solubility was attained in DMF and DMSO. The covalently bonded 4-benzo-9-crown-3 ether allowed the hosting of Li⁺. The covalently grafted crown ether to polymer was identified by infrared spectroscopy and thermogravimetric analysis methods.     

Cup-shaped E,E-stilbenophane: synthesis,crystal structure and supramolecular chemistry

A new E,E-stilbenophane was synthesised and characterised. The crystal structure of this cyclophane shows that this molecule has a cup-shaped structure, which hosts a phenyl ring of neighbouring molecule as guest in its cavity with a π–π distance of about 3.7 Å. Moreover, the NMR spectra and theoretical analysis (gauge-independent atomic orbitals (GIAO) and quantum theory of atoms in molecules (QTAIM)) suggest that the silver recognition by E,E-stilbenophane host molecules is based on cation–π interactions in which the π-electrons of the double bonds play a major role.     

Thermoanalytical study of linkage isomerism in coordination compounds

The non-isothermal differential scanning calorimetry (DSC) experiments revealed that linkage isomerization of both pure trans-[Co(en)₂(ONO)₂]PF₆ (dinitrito isomer) and trans-[Co(en)₂(NO₂)₂]PF₆ (dinitro isomer) occurs in the solid state at elevated temperatures. The process was found to be exothermic for the dinitrito isomer and endothermic for dinitro isomer. The pure isomers could be considered to be in metastable states at ambient temperatures which would be converted to an equilibrium mixture of both isomers (stable state) upon heating. Since the isomerization of both isomers may be described as a two stages process, the corresponding DSC peaks have been resolved into two peaks by means of nonlinear curve fitting tools of PeakFit^® software. The resolution of the peaks helped us to determine enthalpy changes of stepwise isomerization of both isomers. A first-order initial rate and Kissinger methods have been employed to estimate kinetic parameters of the stepwise isomerization reactions. The Kissinger method provided more reliable kinetic results. The high activation energy and positive entropy changes of isomerization of both isomers are considered as indication of a dissociative mechanism in solid state.