The mystery of perpendicular fivefold axes and the fourth dimension in intermetallic structures

The structures of eight related known intermetallic structure types are the impetus to this paper: Li21Si5, Mg44Rh7, Zn13(Fe,Ni)2, Mg6Pd, Na6Tl, Zn91Ir11, Li13Na29Ba19, and Al69Ta39. All belong to the F43m space group, have roughly 400 atoms in their cubic unit cells, are built up at least partially from the gamma-brass structure, and exhibit pseudo-tenfold symmetric diffraction patterns. These pseudo-tenfold axes lie in the {110} directions, and thus present a paradox. The {110} set is comprised of three pairs of perpendicular directions. Yet no 3D point group contains a single pair of perpendicular fivefold axes (by Friedel's Law, a fivefold axis leads to a tenfold diffraction pattern). The current work seeks to resolve this paradox. Its resolution is based on the largest of all 4D Platonic solids, the 600-cell. We first review the 600-cell, building an intuition discussing 4D polyhedroids (4D polytopes). We then show that the positions of common atoms in the F43m structures lie close to the positions of vertices in a 3D projection of the 600-cell. For this purpose, we develop a projection method that we call intermediate projection. The introduction of the 600-cell resolves the above paradox. This 4D Platonic solid contains numerous orthogonal fivefold rotations. The six fivefold directions that are best preserved after projection prove to lie along the {110} directions of the F43m structures. Finally, this paper shows that at certain ideal projected cluster sizes related to one another by the golden mean (tau=(1+ radical 5)/2), constructive interference leading to tenfold diffraction patterns is optimized. It is these optimal values that predominate in actual F43m structures. Explicit comparison of experimental cluster sizes and theoretically derived cluster sizes shows a clear correspondence, both for isolated and crystalline pairs of projected 600-cells.     

Mechanisms of nozzle type reactor operation with gas removal

A nozzle type reactor with provision for gas removal has been studied for the neutralisation of dodecylbenzene sulphonic acid with sodium carbonate solution. Gas was removed via a central air core so that the product was essentially foam-free. The rate of mixing and the chemical reaction between dodecylbenzene sulphonic acid and sodium carbonate solution, were observed to be much faster than the liquid residence time so complete conversion into the product was achieved within seconds. Some gas bubbles were entrained in the product: however these were negligible compared with the bulk of the gas bubbles expelled at the top of the reactor. The criteria for gas removal was that the time for bubbles to travel to the air core under the prevailing centripetal force was less than the liquid phase residence time in the reactor. Mathematical models were therefore proposed to predict the equilibrium bubble diameter and the time for bubble travel to the core. Predicted times were found to be very much less than the average residence time.     

A measurement of the branching ratio∑ +→pγ/∑ +→pπ 0⋆

In an experiment performed in the CERN SPS hyperon beam we have obtained a value for the branching ratio $${{\Sigma ^ + \to p\gamma } \mathord{\left/ {\vphantom {{\Sigma ^ + \to p\gamma } {\Sigma ^ + \to p\pi }}} \right. \kern-\nulldelimiterspace} {\Sigma ^ + \to p\pi }}^0 of\left( {2.46_{ - 0.35}^{ + 0.30} } \right) \times 10^{ - 3} ,$$ corresponding to a branching ratio $${{\Sigma ^ + \to p\gamma } \mathord{\left/ {\vphantom {{\Sigma ^ + \to p\gamma } {\Sigma ^ + \to all}}} \right. \kern-\nulldelimiterspace} {\Sigma ^ + \to all}}of\left( {1.27_{ - 0.18}^{ + 0.16} } \right) \times 10^{ - 3} .$$ This result is discussed in the context of present understanding of hyperon radiative decays.     

Diels-Alder cycloaddition of acetylene gas to a polycyclic aromatic hydrocarbon bay region

The direct conversion of a polycyclic aromatic hydrocarbon bay region to a new, unsubstituted benzene ring by Diels-Alder cycloaddition of acetylene gas is reported for the first time. At 140 °C in dimethylformamide, under 1.8 atm pressure of acetylene gas, 7,14-dimesitylbisanthene is slowly converted to 7,14-dimesitylbenzo[ghi]bisanthene (21% conversion in 48 h).     

New butyrolactone and other metabolites from the bark of Endlicheria arenosa against of the phytopathogen Colletotrichum tamarilloi

In this work, screening of Lauraceae species for their antifungal activity against Collectotrichum tamarilloi was carried out and the ethanol extract derived from the bark of Endlicheria arenosa was found to be the best candidate. From the ethanolic extract of the bark of E. arenosa, the hexane and chloroform fractions were found to be active, from these five fatty acids were identified and two lactones were isolated. The most active fatty acid was the dodecanoic acid with a minimal inhibitory concentration (MIC) of 78.0 μM. The butyrolactone 3R,4R-licunolide A, it has not previously reported, and licunolide B show both the lowest MIC (55.3 μM). This is the first report of compounds of natural origin as growth inhibitors of C. tamarilloi.     

Unboundedness in Integer and Discrete Programming L.P. Relaxations

Commercial branch and bound codes for solving the general mixed integer linear programming problem commence by solving the linear programming relaxation of the submitted problem, terminating if the relaxation is unbounded. It is assumed that the submitted problem is either unbounded or has no feasible solutions. It is shown that the assumption is correct for all integer programming problems which can be submitted to the currently available codes (though counter examples which cannot be so submitted are given), but that the assumption is generally incorrect for discrete linear programming problems (using for example the special ordered set construct). Sufficient conditions on formulations to ensure its correctness are given. One possible formulation approach, applicable to special ordered set situations, is discussed.     

Isolation and separation of tall fescue and ryegrass alkaloids.

Bases were extractable from dried, powdered grass material by percolation with methanol. The bases were removed from the methanol by cation-exchange resins and subsequently removed from the resins. Isolation of bases by these methods eliminated the problems associated with the use of large quantities of chlorinated solvents and formation of emulsions found in previously described isolation methods. The bases were separated by paper and thin-layer chromatography (TLC). TLC and a spectrodensitometer were used to quantify the principal alkaloids in crude extracts of tall fescue samples. This procedure recovered all of the alkaloids in spiked samples, and the standard deviation for perlolidine and perloline in tall fescue samples was 3% or less of the mean value.     

BioSimGrid: towards a worldwide repository for biomolecular simulations

BioSimGrid is a database for biomolecular simulations, or, a "Protein Data Bank extended in time" for molecular dynamics trajectories. We describe the implementation details: architecture, data schema, deposition, and analysis modules. We encourage the simulation community to explore BioSimGrid and work towards a common trajectory exchange format.     

Organocobalt complexes IX. The insertion of acetylenes into butenolide complexes; crystal structure of a dicobalt complex with a novel five-carbon bridge

Preparative thin layer chromatography has yielded the first-pure insertion products from acetylenes and butenolide dicobalt hexacarbonyls; the structure of one such product has been determined by X-ray crystallography and a related formulation is suggested for the other isomer formed in comparable amounts.