Vertex operators for non-simply-laced algebras

A vertex operator construction is given for the level one representations of the affine Kac-Moody algebras associated with non-simply-laced finite-dimensional Lie algebras, using free boson and interacting fermion fields. The fermion fields are constructed explicitly and a detailed discussion is given of the theory of the cocycles necessary for this and other vertex operator constructions. The construction is related in detail to the folding of Dynkin diagrams and a generalisation of it yields Freudenthal's magic square.On leave from the Weizmann Institute, Israel     

Fermions and octonions

We analyse further the algebraic structure of dependent fermions, namely ones interrelated by the vertex operator construction. They are associated with special sorts of lattice systems which are introduced and discussed. The explicit evaluation of the relevant cocycles leads to the result that the operator product expansion of the fermions is related in a precise way to one or another of the division algebras given by complex numbers, quaternions or octonions. The latter case is seen to be realised in the light cone formalism of superstring theory.     

Numerical simulation of power law and yield stress fluid flows in double concentric cylinder with slotted rotor and vane geometries

In our previous report, we showed that a rheometer equipped with a double concentric cylinder geometry with slotted rotor could effectively reduce wall slip effects and thus it could be used as an alternative to a rheometer with a vane geometry in yield stress measurements. Here, we use three-dimensional CFD simulation to compare these two geometries for rheological measurements of power law and yield stress fluids. Our results indicate that the double concentric cylinder rheometer with slotted rotor (DCCR/SR) is able to accurately measure rheological properties of a wider spectrum of test fluids than a vane rheometer because of significant reduction of the end and secondary flow effects.     

Deposition of osmium and ruthenium thin films from organometallic cluster precursors

Single‐source organometallic precursors based on a number of homometallic clusters as well as heterometallic cluster RuOs₃(CO)₁₃(µ‐H)₂ have been used for the chemical vapor deposition of osmium films and osmium–ruthenium alloy films, respectively. Copyright © 2009 John Wiley & Sons, Ltd.     

cis‐[(4R,5R)‐4,5‐Bis­(amino­methyl)‐2,2‐di­methyl‐1,3‐dioxolane‐N,N′](malonato‐O,O′)­platinum(II), an anticancer agent

In the title compound, [Pt(C₃H₂O₄)(C₇H₁₆N₂O₂)], the Pt atom is coordinated to two O and two N atoms in a square‐planar arrangement. The two independent mol­ecules, which have very similar structures, are approximately related by pseudo‐twofold screw‐axis symmetry. The six‐membered chelate ring in the leaving ligand assumes a conformation intermediate between the half‐chair and boat forms. The seven‐membered ring in the carrier ligand assumes a twist‐chair conformation and the oxolane ring assumes an envelope conformation. The crystal packing consists of extensive hydrogen‐bonding networks which form two‐dimensional molecular layers, and there are weak van der Waals interactions between these layers.     

Highly Pure Synthesis,Spectral Assignments,and Two‐Photon Properties of Cruciform Porphyrin Pentamers Fused with Benzene Units

Tetrameric porphyrin formation of 2‐hydroxymethylpyrrole fused with porphyrins through a bicyclo[2.2.2]octadiene unit gave bicyclo[2.2.2]octadiene‐fused porphyrin pentamers. Thermal conversion of the pentamers gave fully π‐conjugated cruciform porphyrin pentamers fused with benzene units in quantitative yields. UV/Vis spectra of fully π‐conjugated porphyrin pentamers showed one very strong Q absorption and were quite different from those of usual porphyrins. From TD‐DFT calculations, the HOMO level is 0.49 eV higher than the HOMO?1 level. The LUMO and LUMO+1 levels are very close and are lower by more than 0.27 eV than those of other unoccupied MOs. The strong Q absorption was interpreted as two mutually orthogonal single‐electron transitions (683 nm: 86 %, HOMO→LUMO; 680 nm: 86 %, HOMO→LUMO+1). The two‐photon absorption (TPA) cross section value (σ⁽²⁾) of the benzene‐fused porphyrin pentamer was estimated to be 3900 GM at 1500 nm, which is strongly correlated with a cruciform molecular structure with multidirectional π‐conjugation pathways.     

Delaminated zeolite‐catalysed synthesis of high‐molecular weight polycarbosilane as a low shrinkage SiC precursor

A polycarbosilane (PCS) with a higher number–average molecular weight (2710 vs. 1570), and hence with a higher ceramic yield (74 vs. 68%), compared to a commercial Nipusi type S PCS has been synthesized via the catalytic decomposition of polydimethylsilane at 400 °C using H‐ITQ‐2, a delaminated zeolite with a very high external surface area, as a solid acid. The silicon carbide film fabricated using this PCS was found to show a much lower level (16 vs. 39%) of shrinkage than the commercial PCS‐derived film, together with better mechanical properties, suggesting the potential of its preceramic polymer to produce robust ceramic coatings. © 2007 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 725–732, 2008     

Adhesion comparison of human bone marrow stem cells on a gradient wettable surface prepared by corona treatment

Corona discharge treatment was applied to modify the surface of polyethylene (PE). The wettability of PE surface was gradually increased by power increase of a corona treatment along the PE length, indicating that the hydrophilicity of PE surface increased gradually. The adhesion and proliferation behavior of human bone marrow stem cells (hBMSCs) on the gradient PE surface was evaluated. We found that hBMSCs were adhered to and proliferated on better highly hydrophilic than hydrophobic surfaces. The plot of proliferation rate vs. the water contact angles was parabolic. These results indicate that surface wettability plays an important role in the cell attachment and proliferation.