Geometric characterizations of centroids of simplices

We study the centroid of a simplex in space. Primary attention is paid to the relationships among the centroids of the different k-skeletons of a simplex in n-dimensional space. We prove that the 0-dimensional skeleton and the n-dimensional skeleton always have the same centroid. The centroids of the other skeleta are generically different (as we prove), but there are remarkable instances where they coincide in pairs. They never coincide in triples for regular pyramids.     

Turn-on fluorescence in tetraphenylethylene-based metal-organic frameworks: an alternative to aggregation-induced emission

Coordinative immobilization of functionalized tetraphenylethylene within rigid porous metal-organic frameworks (MOFs) turns on fluorescence in the typically non-emissive tetraphenylethylene core. The matrix coordination-induced emission effect (MCIE) is complementary to aggregation-induced emission. Despite the large interchromophore distances imposed by coordination to metal ions, a carboxylate analogue of tetraphenylethylene anchored by Zn(2+) and Cd(2+) ions inside MOFs shows fluorescence lifetimes in line with those of close-packed molecular aggregates. Turn-on fluorescence by coordinative ligation in a porous matrix is a powerful approach that may lead to new materials made from chromophores with molecular rotors. The potential utility of MCIE toward building new sensing materials is demonstrated by tuning the fluorescence response of the porous MOFs as a function of adsorbed small analytes.     

Solvents showing the external heavy atom effect in phosphorimetry

Ten solvents containing heavy atoms were examined for suitability for use in the external heavy atom effect for routine phosphorimetry. In previous work only iodine-containing solvent systems have been used, and the incongruity of enhancement results for structurally similar compounds suggests that the ultraviolet transmission characteristics of the solvent systems may be responsible for fractional enhancements. In this study the effect of chlorine-, bromine-, and iodine-containing solvent systems on phosphorescence and fluorescence intensities was investigated. Generally, chlorine-, and bromine-containing solvent systems showed a significant improvement in phosphorimetric enhancements with slightly longer lifetimes than in solvent systems containing iodine. As expected from their smaller spin-orbit coupling, chlorine-containing solvent systems yield smaller enhancements than bromine-containing solvent systems. Solvent systems containing bromine seem to offer the best compromise between ultraviolet transmission characteristics and large spin-orbit coupling constants.     

Pulse propagation in particulate suspensions

The propagation of finite pulses of high-frequency in a suspension composed of a distribution of incompressible particles in an incompressible fluid is examined by using the technique of modulated simple-wave theory. The differential equation which governs the propagation of high-frequency pulses is derived and its consequences are examined. The properties of small amplitude high-frequency pulses are examined in detail.