Muirhead-Rado inequality for compact groups

Muirhead’s majorization inequality was extended by Rado to the case of arbitrary permutation groups. We further generalize this inequality to compact groups and their linear representations over the reals. We characterize saturation of the inequality, and describe the saturation condition in detail for the case of actions on Hermitian operators. Supported in part by the National Science Foundation and the Center for the Mathematics of Information.     

Pt coated Cr2O3 thin films for resistive gas sensors

The resistive response of atomic layer deposited thin epitaxial α-Cr₂O₃(0 0 1) films, to H₂ and CO in air, was studied. The films were covered with Pt nanoislands formed by electron-beam evaporation of a sub-monolayer amount of the material. The gas measurements were performed at 250°C and 450°C. These temperatures led to different proportion of chemical states, Pt²⁺ and Pt⁴⁺, to which the Pt oxidized. The modification was ascertained by the X-ray photoelectron spectroscopy method. As a result of the modification, the response was fast at 250°C, but slowed at 450°C. A disadvantageous abundance of Pt⁴⁺ arising at 450°C in air could be diminished by high-vacuum annealing thus restoring the response properties of the system at 250°C.      

A second generation dendrimer incorporating nine S2N2-donor macrocycles and its palladium(II) complex

A new second generation dendrimer incorporating nine S2N2-donor macrocyclic units that bind nine Pd(II) cations is reported.     

sigma-donor,pi-donor,and anion competition in pi-complexation of alkali metal cations

Removal of or replacement of one of two phenylethyl sidearms on azalariats leads to clear evidence for cation-pi interactions with the remaining sidearm.     

Supramolecular stabilization of N(2)H(7)(+)

The cation N(2)H(7)(+) has been stabilized in a largely hydrophobic supramolecular environment and characterized in the solid state. The cation is situated in the bowl-shaped cavity of calix[4]arene. All of the hydrogen atoms are clearly discernible owing to high-quality X-ray data as well as lack of disorder and symmetry-imposed ambiguity. It appears that electrostatic interactions play a critical role in stabilizing the structure.     

SENSITIZATION OF PHOTOCONDUCTIVE EFFECTS IN ZINC OXIDE*,†

Abstract— The current status of research on sensitized photoconductive effects in zinc oxide is reviewed. The various types of chemical and spectral photosensitization processes observed in polycrystalline specimens can be explained qualitatively with a generalized electron acceptor molecule (EAM) model. in which electronegative surface agents trap zinc oxide conduction electrons in the dark and illumination causes a release of the trapped electrons. The EAM may be an adsorbed gas or vapor, adsorbed dye molecules, or an aggregated dye film, depending on the particular photoeffect.     

Studies of interface phonons

The vibrational modes localized at the interface between two distinct crystals have been studied for a simple crystal model obeying all of the invariance conditions required for models used in studies of dynamical properties of crystal surfaces, and giving rise to Rayleigh surface waves. The two crystals are assumed to be semi-infinite simple cubic and to have the same lattice parameter a. They differ by their mass (M and M_A) and the central force interactions between first (K and K_a) and second nearest neighbors $\text{1}\text{2}\text{K}$ and $\text{1}\text{2}\text{K}{}_{\mathrm{A}}$. The interface is obtained by coupling the (001) free surfaces of these distinct crystals by central force intractions (K^'). We find that the variation of the interaction conditions (K^') at the interface and of the $\text{(}\text{K}\text{M}\text{)}\text{(}\text{K}{}_{\mathrm{A}}\text{M}{}_{\mathrm{A}}\text{)}$ parameter has the following qualitative effects on the properties of surface and bulk phonons. When (K^') increases from zero to a finite value, the frequencies of the surface phonons increase and are splitted in the case of two identical crystals. One can say that the surface phonons are transformed into interface modes. For some values of $\text{K}{}^{\mathrm{\text{'}}}\text{K}$ and $\text{(}\text{K}\text{M}\text{)}\text{(}\text{K}{}_{\mathrm{<mtext>A</mtext>}}\text{M}{}_{\mathrm{<mtext>A</mtext>}}\text{)}$ parameters these interface phonons may be admixed with bulk phonons and thus become virtual interface states.