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.     

Spectral Assignment of Phenanthrene Derivatives Based on 6H-Dibenzo[C,E][1,2] Oxaphosphinine 6-Oxide by NMR and Quantum Chemical Calculations

Abstract

Organophosphorus compounds such as 6H-dibenzo[c,e][1,2]oxaphosphinine 6-oxide (DOPO, 1) and its derivatives are important and versatile compounds for a broad field of applications. However, a thorough spectral assignment is often subordinate to its chemical properties. This article presents and unambiguously attributes the ¹H and ¹³C NMR spectra of DOPO (1), selected products yielded from the Atherton–Todd reaction (2–4), DOPO-HQ (5) as well as sulfur derivatives (6–7) via a set of 1D- and 2D-NMR experiments. The complex P-C and P-H coupling patterns are discussed and compared with the derivatives possessing different chemical environments around the phosphorus atom. In addition, we compared our results with density functional theory calculations. Even though the prediction of NMR data of organophosphorus compounds via molecular modeling is limited, this study presents a method that yields good results for this class of heterocycles. This knowledge should help to quickly assign NMR spectroscopic data of other DOPO (1) derivatives and can be extrapolated to organophosphorus compounds in general.

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: NMR Spectra of Compounds 1-7 (Figures S1 - S15).     

PHOSPHORUS-NITROGEN COMPOUNDS. PART 52.1 THE SYNTHESIS OF SOME 1,3,2-BENZODIAZAPHOSPHORINE 2-OXIDES AND 2-SULPHIDES

Abstract

The reactions of 4-methyl-2-[N-(p-toluidinyl)methyl]aniline with phosphorus oxychloride, thiophosphoryl chloride, and their derivatives yield 1,3,2-benzodiazaphosphorine 2-oxides and 2-sulphides. Their ¹H NMR and infrared spectra are discussed. Related 1,3,2-benzodiazophosphorine and 1,3,2-dibenzodiazaphosphocine 2-oxides and 2-sulphides are compared.     

NMR Characterization of Substituted Aromatic Poly (Ether Sulofone)s

Abstract

The synthesis of a variety of substituted bisphenol A polysulfones, including nitro, amino, aminomethyl, ethyl, and methyl derivatives, is described. Nuclear magnetic resonance (NMR) (both proton and carbon, and several 2-D experiments) data confirm conclusions on the substitution site based on arguments on inductive effects in the phenyl rings. The proton ortho to the oxygen in the bisphenol A (BPA) residue is replaced in electrophilic substitution reactions. The degree of substitution was also calculated from the NMR results. The ethyl and methyl derivatives were expected, from the starting reactants, to each have a BPA ring substituted. The NMR data showed that, on the average, this is true. The nitro derivative also has substitution in every BPA ring, while the amino and aminomethyl derivatives have only intermittent BPA rings substituted. Measured degrees of substitution (DS) varied from 0.11 to 2.25.     

A two-step stimulus-response cell-SELEX method to generate a DNA aptamer to recognize inflamed human aortic endothelial cells as a potential in vivo molecular probe for atherosclerosis plaque detection

Aptamers are single-stranded oligonucleotides that are capable of binding wide classes of targets with high affinity and specificity. Their unique three-dimensional structures present numerous possibilities for recognizing virtually any class of target molecules, making them a promising alternative to antibodies used as molecular probes in biomedical analysis and clinical diagnosis. In recent years, cell-systematic evolution of ligands by exponential enrichment (SELEX) has been used extensively to select aptamers for various cell targets. However, aptamers that have evolved from cell-SELEX to distinguish the “stimulus-response cell” have not previously been reported. Moreover, a number of cumbersome and time-consuming steps involved in conventional cell-SELEX reduce the efficiency and efficacy of the aptamer selection. Here, we report a “two-step” methodology of cell-SELEX that successfully selected DNA aptamers specifically against “inflamed” endothelial cells. This has been termed as stimulus-response cell-SELEX (SRC-SELEX). The SRC-SELEX enables the selection of aptamers to distinguish the cells activated by stimulus of healthy cells or cells isolated from diseased tissue. We report a promising aptamer, N55, selected by SRC-SELEX, which can bind specifically to inflamed endothelial cells both in cell culture and atherosclerotic plaque tissue. This aptamer probe was demonstrated as a potential molecular probe for magnetic resonance imaging to target inflamed endothelial cells and atherosclerotic plaque detection.

Sodium Bismuthate Mediated Oxidation of Allylic and Benzylic Alcohols

A simple and readily available oxidation of primary allylic and benzylic alcohols to the corresponding aldehydes is carried out by sodium bismuthate in acetic acid.     

Regiospecific Preparation of 5-Acylaminotetralones

A Beckmann Rearrangement/Friedel-Crafts strategy was utilized to prepare 5-amidotetralones in high yield.     

Laterally dibenzyloxy-branched nematogens with large nematic range and rich solid polymorphism

Mesogenic compounds containing four rings in the core usually have very high melting points. However, when two identical lateral benzyloxy groups are introduced on the same side of one of the central rings, the melting point is lowered dramatically and a large nematic range is retained. This range is affected by the bulkiness of the para-substituents in the lateral rings. Methyl groups can be introduced in the ortho- or meta-positions with a consequent decrease in the melting temperature without much affecting the nematic range. These compounds exhibit a rich solid polymorphism which is certainly related to the effect of the conformations of the lateral substituent on the molecular arrangment in the solid phase. Some preliminary NMR experiments on the nematic phase indicate that the molecular long axis coincides with the core axis, whereas the para-axis of the lateral fragment makes an angle close to the magic angle with respect to the molecular long axis.