High-pressure synthesis, crystal structure, and electromagnetic properties of CdRh2O4: an analogous oxide of the postspinel mineral MgAl2O4

The postspinel mineral MgAl(2)O(4) exists only under the severe pressure conditions in the subducted oceanic lithosphere in the Earth's deep interior. Here we report that its analogous oxide CdRh(2)O(4) exhibits a structural transition to a quenchable postspinel phase under a high pressure of 6 GPa at 1400 °C, which is within the general pressure range of a conventional single-stage multianvil system. In addition, the complex magnetic contributions to the lattice and metal nonstoichiometry that often complicate investigations of other analogues of MgAl(2)O(4) are absent in CdRh(2)O(4). X-ray crystallography revealed that this postspinel phase has an orthorhombic CaFe(2)O(4) structure, thus making it a practical analogue for investigations into the geophysical role of postspinel MgAl(2)O(4). Replacement of Mg(2+) with Cd(2+) appears to be effective in lowering the pressure required for transition, as was suggested for CdGeO(3). In addition, Rh(3+) could also contribute to this reduction, as many analogous Rh oxides of aluminous and silicic minerals have been quenched from lower-pressure conditions.     

VISUAL PIGMENTS—10. SPECTROSCOPY AND PHOTOPHYSICAL DYNAMICS OF RETINOL AND RETINYL ETHER

Abstract— The absorption and emission spectra, lifetimes and quantum yields of all-trans retinol have been examined as a function of solvent and temperature. In addition, the spectroscopy of retinyl ether and 2 other polyene alcohols have been determined. Based on the results obtained, we conclude that the singlet excited state of retinol and retinyl cther is of a forbidden character and of the type loosely called ¹A^-_g. Retinol forms a dimer in an alkane solvent when cooling from 298 to 77 K. A general structure for the dimer is proposed.     

Characterization of rankings generated by linear discriminant analysis

Pairwise linear discriminant analysis can be regarded as a process to generate rankings of the populations. But in general, not all rankings are generated. We give a characterization of generated rankings. We also derive some basic properties of this model.     

Tail probabilities of the limiting null distributions of the Anderson–Stephens statistics

For the purpose of testing the spherical uniformity based on i.i.d. directional data (unit vectors) z_i, i=1,…,n, Anderson and Stephens (Biometrika 59 (1972) 613–621) proposed testing procedures based on the statistics S_max=max_u S(u) and S_min=min_u S(u), where u is a unit vector and nS(u) is the sum of squares of u′z_i's. In this paper, we also consider another test statistic S_range=S_max−S_min. We provide formulas for the P-values of S_max, S_min, S_range by approximating tail probabilities of the limiting null distributions by means of the tube method, an integral-geometric approach for evaluating tail probability of the maximum of a Gaussian random field. Monte Carlo simulations for examining the accuracy of the approximation and for the power comparison of the statistics are given.     

Some Geometry of the Cone of Nonnegative Definite Matrices and Weights of Associated X2 Distribution

Consider the test problem about matrix normal mean M with the null hypothesis M = O against the alternative that M is nonnegative definite. In our previous paper (Kuriki (1993, Ann. Statist., 21, 1379–1384)), the null distribution of the likelihood ratio statistic has been given in the form of a finite mixture of ² distributions referred to as X² distribution. In this paper, we investigate differential-geometric structure such as second fundamental form and volume element of the boundary of the cone formed by real nonnegative definite matrices, and give a geometric derivation of this null distribution by virtue of the general theory on the X² distribution for piecewise smooth convex cone alternatives developed by Takemura and Kuriki (1997, Ann. Statist., 25, 2368–2387).     

On the Eigenstates of the Elliptic Calogero–Moser Model

It is known that the trigonometric Calogero–Sutherland model is obtained by the trigonometric limit (–1) of the elliptic Calogero–Moser model, where (1, ) is a basic period of the elliptic function. We show that for all square-integrable eigenstates and eigenvalues of the Hamiltonian of the Calogero–Sutherland model, if exp(2–1) is small enough then there exist square-integrable eigenstates and eigenvalues of the Hamiltonian of the elliptic Calogero–Moser model which converge to the ones of the Calogero–Sutherland model for the 2-particle and the coupling constant l is positive integer cases and the 3-particle and l=1 case. In other words, we justify the regular perturbation with respect to the parameter exp(2–1). With some assumptions, we show analogous results for N-particle and l is positive integer cases.     

Energy transfer between excitons and plasmons in semiconductor-metal hybrid nanostructures

We summarized our recent optical studies on semiconductor nanoparticle (NP) based hybrid nanostructures: isolated CdSe NPs on Au substrates, close-packed CdSe NP monolayers on Au substrates, and close-packed monolayers of mixed CdSe/Au NPs. Luminescence properties of semiconductor-metal hybrid nanostructures were studied by space-resolved optical imaging spectroscopy and time-resolved luminescence spectroscopy. The luminescence spectra and dynamics of isolated and assembled NPs depend on the local environments. We discuss exciton-plasmon interactions in semiconductor-metal hybrid nanostructures.     

Observation of charged excitons in hole-doped carbon nanotubes using photoluminescence and absorption spectroscopy

We report the first observation of trions (charged excitons), three-particle bound states consisting of one electron and two holes, in hole-doped carbon nanotubes at room temperature. When p-type dopants are added to carbon nanotube solutions, the photoluminescence and absorption peaks of the trions appear far below the E11 bright exciton peak, regardless of the dopant species. The unexpectedly large energy separation between the bright excitons and the trions is attributed to the strong electron-hole exchange interaction in carbon nanotubes.