Frameworks, Symmetry and Rigidity

Symmetry equations are obtained for the rigidity matrix of a bar-joint framework in R^d. These form the basis for a short proof of the Fowler-Guest symmetry group generalisation of the Calladine-Maxwell counting rules. Similar symmetry equations are obtained for the Jacobian of diverse framework systems, including constrained point-line systems that appear in CAD, body-pin frameworks, hybrid systems of distance constrained objects and infinite bar-joint frameworks. This leads to generalised forms of the Fowler-Guest character formula together with counting rules in terms of counts of symmetry-fixed elements. Necessary conditions for isostaticity are obtained for asymmetric frameworks, both when symmetries are present in subframeworks and when symmetries occur in partition-derived frameworks.Comment: 5 Figures. Replaces Dec. 2008 version. To appear in IJCG

Rigidity of Frameworks Supported on Surfaces

A theorem of Laman gives a combinatorial characterisation of the graphs that admit a realisation as a minimally rigid generic bar-joint framework in \bR^2. A more general theory is developed for frameworks in \bR^3 whose vertices are constrained to move on a two-dimensional smooth submanifold \M. Furthermore, when \M is a union of concentric spheres, or a union of parallel planes or a union of concentric cylinders, necessary and sufficient combinatorial conditions are obtained for the minimal rigidity of generic frameworks.Comment: Final version, 28 pages, with new figure

Ocean color, a three component system?

This study measures the concentrations of phytoplankton chlorophyll and yellow substance in the coastal waters of the Gulf of Maine. Sea surface observations attempt to delineate the principal biochemical parameters responsible for sea surface color. It is shown that the reddish-brown water changed to a blue-green in the open gulf

Quantification of apolipoprotein E receptors in human brain-derived cell lines by real-time polymerase chain reaction

Apolipoprotein (apo) E4 is a risk factor for Alzheimer's disease (AD) and other neurodegenerative diseases, compared to wild-type apoE3. The mechanism(s) is unknown. One possibility, demonstrated in peripheral tissue cell lines, is that apoE stimulates nitric oxide synthase (NOS) via a receptor-dependent signalling pathway and that apoE4 generates inappropriate amounts of nitric oxide (NO) compared to apoE3. Prior to biochemical investigations, we have quantified the expression of several candidate receptor genes, including low-density lipoprotein-receptor (LDL-r) family members and scavenger receptor class B, types I and II (SR-BI/II), as well as the three NOS isoenzymes and protein kinase B (Akt), in 38 human cell lines, of which 12 derive from brain. Expression of apoE receptor 2 (apoER2), a known signalling receptor in brain, was readily detected in SH-SY-5Y and CCF-STTG1 cells, common models of neurons and astrocytes, respectively, and was highest in H4 neuroglioma, NT-2 precursor cells and IMR-32 neuroblastoma cells. Transcripts of the other lipoprotein receptors were widely, but variably, distributed across the different cell types. Of particular note was the predominant expression of SR-BII over SR-BI in many of the brain-derived cells. As the C-terminus of SR-BII, like apoER2, contains potential SH3 signalling motifs, we suggest that in brain SR-BII functions as a signal transducer receptor. (c) 2004 Elsevier Inc. All rights reserved

Ion-tracer anemometer

Gas velocity measuring instrument measures transport time of ion-trace traveling fixed distance between ionization probe and detector probe. Electric field superimposes drift velocity onto flow velocity so travel times can be reduced to minimize ion diffusion effects

Stereoelectronic effects on the binding of neutral Lewis bases to CdSe nanocrystals

Using P-31 nuclear magnetic resonance (NMR) spectroscopy, we monitor the competition between tri-nbutylphosphine (Bu3P) and various amine and phosphine ligands for the surface of chloride terminated CdSe nanocrystals. Distinct P-31 NMR signals for free and bound phosphine ligands allow the surface ligand coverage to be measured in phosphine solution. Ligands with a small steric profile achieve higher surface coverages (Bu3P = 0.5 nm(-2), Me2P-n-octyl = 2.0 nm(-2), NH2Bu = >3 nm(-2)) and have greater relative binding affinity for the nanocrystal (binding affinity: Me3P > Me2P -n-octyl similar to Me2P -n-octadecyl > Et3P > Bu3P). Among phosphines, only Bu 3 P and Me2P-n-octyl support a colloidal dispersion, allowing a relative surface binding affinity (K-rel) to be estimated in that case (K-rel = 3.1). The affinity of the amine ligands is measured by the extent to which they displace Bu3P from the nanocrystals (K-rel: H2NBu similar to N-n-butylimidazole > 4-ethylpyridine > Bu3P similar to HNBu2 > Me2NBu > Bu3N). The affinity for the CdSe surface is greatest among soft, basic donors and depends on the number of each ligand that bind. Sterically unencumbered ligands such as imidazole, pyridine, and n-alkylamines can therefore outcompete stronger donors such as alkylphosphines. The influence of repulsive interactions between ligands on the binding affinity is a consequence of the high atom density of binary semiconductor surfaces. The observed behavior is distinct from the self-assembly of straight-chain surfactants on gold and silver where the ligands are commensurate with the underlying lattice and attractive interactions between aliphatic chains strengthen the binding