An upper bound for the representation dimension of group algebras with elementary abelian Sylow p-subgroups

Abstract

In this article, we present an upper bound on the representation dimension of the group algebra of a group with an elementary abelian Sylow p-subgroup. Specifically, if k is a field of characteristic p and G is a group with elementary abelian Sylow p-subgroup P, we prove that the representation dimension of kG is bounded above by the order of P. Key to proving this theorem is the separable equivalence between the two algebras and some nice properties of Mackey decomposition.     

The application of chiroptical spectroscopy (circular dichroism) in quantifying binding events in lanthanide directed synthesis of chiral luminescent self-assembly structures

The binding of asymmetrical and optically pure tridentate ligands (L = 1(S) and 1(R)) containing one carboxylic group and 2-naphthyl as an antenna to lanthanide ions (M = La(iii) and Eu(iii)) was studied in CH₃CN, showing the successive formation of M:L, M:L₂ and M:L₃ stoichiometric species in solution. The europium complexes EuL₃ were also synthesised, structurally characterised and their photophysical properties probed in CH₃OH and CH₃CN. The changes in the chiroptical properties of both 1(S) and 1(R) were used (by circular dichroism (CD) spectroscopy) to monitor the formation of these chiral self-assemblies in solution. While circularly polarised luminescence (CPL) showed the formation of Eu(1(S))₃ and Eu(1(R))₃ as enantiomers, with high luminescence dissymmetry factors (g _lum), fitting the CD changes allowed for binding constants to be determined that were comparable to those seen in the analyses of absorbance and luminescence changes.     

Interactive effects between aerofoils and time independent flow perturbations

A technique is developed to assess the interdependent effects of an aerofoil in the vicinity of, immersed in or passing through, a shear flow. The two former cases in which there is no time-dependency are analogous to an aircraft wing and slipstream combination, while the latter case may be likened to a compressor rotor blade responding to a circumferential distortion. In the model, however, no time-dependent terms are included.A case study is made of an aerofoil of known geometry passing through a combined pressure/temperature distortion of stated initial geometry. The changes both in the streamline patterns of the distortion and of the pressure distribution are indicated and it is seen that the resulting lift response of the aerofoil bears some resemblance to that measured on rotating blades in compressors with circumferential flow conditions.     

Strain analysis for extrusion of powder metals

A method is described for determining the strain distribution during axisymmetric extrusion of powder metals. Density variations in these materials are included in the analysis. The method examines these changes together with the laminar flow pattern to determine strain rates and, ultimately, strains.     

A review of turbomachinery tip gap effects : Part 1: Cascades

This two part review covers experiments examining the effects of blade tip gaps encountered in turbomachines and the methods by which the synthesised data are currently used in turbomachine design and analysis. Data gained since the 1930's are subdivided for convenience into cascade (Part 1) and rotating machinery¹ (Part 2) data, with a further subdivision into diffusing, or compressor type flows and accelerating, or turbine type flows. The overall trend is that an increasing tip gap, whose effect can reach over most or all of the blade height, reduces turbomachine performance. There is some evidence among the compressor and compressor cascade data that an optimum gap exists when the opposing effects of secondary flows and tip leakage with rotor/wall relative movement tend to balance. Turbine data are, in general, more regular than the body of compressor data, possibly because of the enhanced effect of, usually, undefined boundary layers in diffusing flow in the latter. Comment is made in Part 2 on the predictive and design models reported in the literature     

De Novo Design of Xeno‐Metallo Coiled Coils

Bioinorganic chemists aspire to achieve the same exquisite and highly controlled inorganic chemistry featured in biology. An exciting mimetic approach involves the use of miniature artificial protein scaffolds designed de novo (often based on the coiled coil (CC) scaffold), for reproducing native metal ion sites and their function. Recently, there is increased interest, instead, in the design of xeno‐metal sites within CC assemblies. This involves incorporating either non‐biological metal ions, cofactors or non‐proteinogenic amino acid ligands for metal ion coordination, whilst retaining a minimal CC protein scaffold. Using this approach, one should be able to create functional designs with unique and unusual properties, which combine the advantages of both biology and ‘traditional’ non‐biological inorganic chemistry. It is the recent progress with respect to the design of xeno‐metallo CCs which will be discussed in this Focus Review.     

Selective nucleophilic chemistry in the synthesis of 5-carbamoyl-3-sulfanylmethylisoxazole-4-carboxylic acids

The solution-phase syntheses of 5-carbamoyl-3-sulfanylmethylisoxazole-4-carboxylic acids were accomplished from dimethyl 3-chloromethylisoxazole-4,5-dicarboxylate by selective nucleophilic chemistry. For example, treatment of this trifunctionalized core with 3-bromobenzylamine and subsequent X-ray analysis identified the sole product as methyl 5-(3-bromobenzylcarbamoyl)-3-chloromethylisoxazole-4-carboxylate. Subjecting this amide/ester to thiophenol in the presence of 1 N NaOH completed the two-step transformation of this versatile starting material to the targeted 5-carbamoyl-3-sulfanylmethylisoxazole-4-carboxylic acid. Employing various amines and thiophenols, this chemistry was applied in the generation of a 90-compound library of druglike isoxazoles.     

Effect of matrix on recovery of biogenic amines in fish

Biogenic amines, such as putrescine, cadaverine, and histamine, in fish can be indicators of spoilage and/or safety. Methanol extraction used for AOAC Official Methods 996.07 and 977.13 has resulted in low amine recoveries in fish. Extraction methodology was evaluated to improve recovery from fish tissue. Samples were evaluated for recovery of known quantities of biogenic amines added to tissue prior to extraction. Addition of 25% 0.4 N HCI to the 75% methanol-water extraction solvent (according to AOAC Official Methods 996.07 and 977.13) resulted in higher recoveries (P < 0.05) of the biogenic amines. Putrescine recovery increased from 44 +/- 2 to 100 +/- 14% in flounder and scup, and from 53 +/- 21 to 119 +/- 27% in mackerel and butterfish; cadaverine recovery increased from 47 +/- 4 to 106 +/- 15% (flounder/scup) and 58 +/- 24 to 113 +/- 9% (mackerel/butterfish); histamine recovery increased from 54 +/- 13 to 89 +/- 28% (mackerel). MeOH extraction resulted in comparable recovery from canned tuna, indicating that protein denaturation from processing may eliminate possible matrix interference. Acidification of the solvent resulted in a more complete extraction of the added amines to fresh/frozen fish tissue. This finding could indicate that current extraction procedures may cause biogenic amines to be underestimated.     

Enantioselective regulation of a metal complex in reversible binding to serum albumin: dynamic helicity inversion signalled by circularly polarised luminescence

The helicity of the (SSS)-Delta enantiomer of a terbium and europium(iii) complex is inverted on reversible binding to 'drug site II' of serum albumin, signalled by a switch in its circularly polarised emission; no such behaviour occurs with the (RRR)-Lambda complexes, thereby defining a unique chiroptical probe of albumin binding.