The Littlewood-Richardson rule for wreath products with symmetric groups and the quiver of the category F≀FIn

We give a new proof for the Littlewood-Richardson rule for the wreath product F?S_n where F is a finite group. Our proof does not use symmetric functions but use more elementary representation theoretic tools. We also derive a branching rule for inducing the natural embedding of F?S_n to F?S_n+1. We then apply the generalized Littlewood-Richardson rule for computing the ordinary quiver of the category F?FI_n where FI_n is the category of all injective functions between subsets of an n-element set.     

Electrowetting without electrolysis on self-healing dielectrics

An electrowetting system with protection against dielectric breakdown is presented. It comprises an electrolyte and a Parylene-C film deposited on an aluminum electrode. The system demonstrates virtually instantaneous self-healing (within 100 ms) after dielectric breakdown under both DC and certain AC electrowetting conditions. DC current response during electrowetting on intentionally damaged Parylene-C is presented. Also presented is a characterization of DC offset voltages and duty cycle percentages required for electrolysis free AC electrowetting between 10 Hz and 4 kHz.     

A computational study of tert-butylbenzenium ions

A computational study of tert-butylbenzenium ions has been performed. Structures and energies of the various isomers and the transition states for their interconversions have been determined. The existence of a stable π-electron complex (called A1) between a tert-butyl cation and a benzene molecule has been confirmed. Other minimum points on the potential energy surface corresponding to π-complexes were found, but the barriers for transforming these complexes into the stable π-electron complex A1 are so low that the transformation into the stable structure can take place at all temperatures. The structures were evaluated at the DFT-B3LYP level of theory. The energies were evaluated with the Gaussian-3 (G3B3) and CBS (CBS-QB3) composite methodologies. A discussion of published experimental data in view of the computational results is given. It is pointed out that it should be possible to show the presence of the π-complex by IR spectroscopy. The computations show that the π-complex has a very strong IR band in an otherwise empty region.     

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