Depth of modular invariant rings

It is well-known that the ring of invariants associated to a non-modular representation of a finite group is Cohen-Macaulay and hence has depth equal to the dimension of the representation. For modular representations the ring of invariants usually fails to be Cohen-Macaulay and computing the depth is often very difficult. In this paper¹ we obtain a simple formula for the depth of the ring of invariants for a family of modular representations. This family includes all modular representations of cyclic groups. In particular, we obtain an elementary proof of the celebrated theorem of Ellingsrud and Skjelbred [6].     

Anomalous stability of aqueous boehmite dispersions induced by hydrolyzed aluminium poly-cations

Aqueous dispersions of colloidal boehmite rods turn into strong gels when the concentration of (1–1) electrolyte concentrations becomes exceeds 50 mM. However, after addition of aluminium chlorohydrate (ACH) the rods remain stable up to salt concentrations as high as 2 M. Moreover the boehmite-ACH dispersions with an aspect ratio of 19 quickly separate into an isotropic and a liquid crystal nematic phase above a typical threshold concentration of 2 v/v%. It is known that ACH forms polynuclear cations at mild acidic conditions. The anomalous stability as encountered in these dispersions is explained by assuming that these hydrolyzed poly-cations cause a shift of the charge carrying surface.     

Total Synthesis of Vancomycin Aglycon—Part 2: Synthesis of Amino Acids 1–3 and Construction of the AB-COD-DOE Ring Skeleton

A triazene-based synthetic strategy for the construction of the complex biaryl ethers and a Suzuki coupling reaction were the key steps in the synthesis of precursor 1 of the aglycon of vancomycin, which already contains the complete skeleton of the target compound. The cleavage of the triazene unit from the D ring and the removal of the other protecting groups led to the aglycon of vancomycin. These strategies should be particularly valuable for the synthesis of other naturally occurring glycopeptide antibiotics and offer opportunities for the synthesis of combinatorial libraries of compounds of the vancomycin family for chemical biology studies.     

Particle morphology effects on the performance of PMMA filled with aluminium hydroxide in a variety of fire tests

The effect of aluminium hydroxide particle size and shape has been investigated on the performance of (polymethyl methacrylate) composites in a number of flammability tests. As a subsidiary exercise correlation between the tests has been investigated. The work has shown the expected effect of particle size on performance, with surface area giving the best measure of particle size if non-spherical particles are involved. While the smallest particles always give the best results, the effect varies markedly according to the test and is most pronounced in the ISO ignitability test. Some possible explanations for these effects are proposed but more experiments are needed to choose between them. Correlation between the various tests is generally poor and reliance on any one of them for product development would be unwise.     

Feature-Based Molecular Networks Identification of Bioactive Metabolites from Three Plants of the Polynesian Cosmetopoeia Targeting the Dermal Papilla Cells of the Hair Cycle

The term cosmetopoeia refers to the use of plants in folks’ cosmetics. The aerial parts of Bidens pilosa L., the leaves of Calophyllum inophyllum L. and the fruits of Fagraea berteroana A.Gray ex Benth are traditionally used in French Polynesia for hair and skin care. During the hair cycle, dermal papilla cells and their interaction with epithelial cells are essential to promote hair follicle elongation. The aim of our investigations was the identification of metabolites from these three plants and chemical families responsible for their hair growth activity. A bioactivity-based molecular network was produced by mapping the correlation between features obtained from LC-MS/MS data and dermal papilla cell proliferation, using the Pearson correlation coefficient. The analyses pointed out glycosylated flavonols and phenolic acids from B. pilosa and C. inophyllum, along with C-flavonoids, iridoids and secoiridoids from F. berteroana, as potential bioactive molecules involved in the proliferation of hair follicle dermal papilla cells. Our results highlight the metabolites of the plant species potentially involved in the induction of hair follicle growth and support the traditional uses of these plants in hair care.     

Direct-Space Structure Determination of Covalent Organic Frameworks from 3D Electron Diffraction Data

Structure determination of covalent organic frameworks (COFs) with atomic precision is a bottleneck that hinders the development of COF chemistry. Although three-dimensional electron diffraction (3D-ED) data has been used to solve structures of sub-micrometer-sized COFs, successful structure solution is not guaranteed as the data resolution is usually low. We demonstrate that the direct-space strategy for structure solution, implemented using a genetic algorithm (GA), is a successful approach for structure determination of COF-300 from 3D-ED data. Structural models with different geometric constraints were considered in the GA calculations, with successful structure solution achieved from room-temperature 3D-ED data with a resolution as low as ca. 3.78 Å. The generality of this strategy was further verified for different phases of COF-300. This study demonstrates a viable strategy for structure solution of COF materials from 3D-ED data of limited resolution, which may facilitate the discovery of new COF materials in the future.     

Polymorphism of l‐Tryptophan

A new polymorph of l ‐tryptophan was prepared through crystallization from the gas phase, with structure determination carried out directly from powder XRD data augmented by periodic DFT‐D calculations. The new polymorph (denoted β) and the previously reported polymorph (denoted α) are both based on alternating hydrophilic and hydrophobic layers, but with substantially different hydrogen‐bonding arrangements. The β polymorph exhibits the energetically favourable l 2‐l 2 hydrogen‐bonding arrangement, which is unprecedented for amino acids with aromatic side chains. The specific molecular conformations adopted in the β polymorph facilitate this hydrogen‐bonding scheme while avoiding steric conflict of the side chains.