Schur-multiplicative maps preserving unitarily invariant norms

Characterizations are obtained for maps on real or complex matrices which preserve both the Schur (Hadamard) product and a given unitarily invariant norm.     

A note on rigidity of 3-Sasakian manifolds

Making use of the relations among 3-Sasakian manifolds, hypercomplex manifolds and quaternionic Kähler orbifolds, we prove that complete 3-Sasakian manifolds are rigid.

     

Structure of the hydrogen stabilized MgO(1 1 1)-(1 × 1) surface from low energy electron diffraction (LEED)

A structural study has been performed on the MgO(1 1 1)-(1 × 1) surface by low energy electron diffraction (LEED) using experimental data obtained with a delay-line-detector LEED (DLD-LEED) system to minimize electron damage. It was found that the surface is terminated by a hydroxide layer with the top O-Mg interlayer spacing equal to 1.02 Å, which is close to the spacings between Mg and O planes in bulk brucite crystals (Mg(OH)₂). This is in good agreement with a recent study using photoelectron diffraction (PhD) spectroscopy and density functional theory calculation (DFT) [V.K. Lazarov, R. Plass, H.-C. Poon, D.K. Saldin, M. Weinert, S.A. Chambers, M. Gajdardziska-Josifovska, Phys. Rev. B 71 (2005) 115434]. The second interlayer spacing shows a small expansion of 3% and the third is bulk-like, while the DFT calculation predicted that the spacings below the top one are all bulk-like. This result clearly favors hydroxylation [K. Refson, R.A. Wogelius, D.G. Fraser, M.C. Payne, M.H. Lee, V. Milman, Phys. Rev. B 52 (1995) 10823] as a way of stabilizing the MgO(1 1 1) surface at low temperature over metallization, which has a top layer spacing of 0.86 Å for O termination and 1.25 Å for Mg termination [Lazarov et al. 2005; T. Tsukada, T. Hoshino, Phys. Soc. Jpn. 51 (1982) 2562, J. Goniakowski, C. Noguera, Phys. Rev. B 60 (1999) 16120].     

Fat/water quantitation and differential relaxation time measurement using chemical shift imaging technique

The use of chemical shift imaging for fat and water quantitation and differential measurement of relaxation times for the fat and water component is demonstrated using a hybrid technique. The efficacy of the imaging technique for fat and water quantitation has been tested by comparing the results of imaging to the results of volumetric measurements in phantoms with oil and water homogeneously mixed, fat extraction in ground meat of different grades, and biopsy in preliminary clinical studies. Good correlation is found between the fat and water content measured by imaging and that measured by other means except for the inability to differentiate unsaturated fat protons from water protons. Longitudinal (T1) and transverse (T2) relaxation times for water and fat are also shown to be measurable independently when fat and water signal are suppressed accordingly. The independently measured relaxation times correspond closely to those of the pure samples except that unsaturated protons give decreased water relaxation estimates.     

Waveguide-coupled octagonal microdisk channel add-drop filters

We report planar waveguide-coupled octagonal microdisk channel add-drop filters on silicon nitride-on-silica substrates. Using ray optics, we show that discrete octagonal cavities have wave-front-matched four- and eight-bounce ray orbits. From a planar waveguide-coupled 50-microm-sized octagonal microdisk filter, our experiment demonstrates TM-polarized eight-bounce modes with a coupling efficiency of approximately 56%, Q approximately equal to 1150, and a finesse of approximately 5. Using the two-dimensional finite-difference time-domain method, we obtain qualitative agreement between measurement and simulation of a smaller-sized waveguide-coupled octagonal microdisk filter.     

Fano resonances in prism-coupled multimode square micropillar resonators

We report Fano resonances in a multimode square glass micropillar resonator; the resonances were obtained by using angle-resolved prism coupling. Our experiments reveal characteristically asymmetric line shapes of high-Q resonances and of detuned low-Q resonances in multimode reflection spectra. The asymmetric resonance line shapes evolve for an approximately pi phase within a 0.5 degree range of reflection angles. We model our observed asymmetric multimode resonances by the far-field interference between a light wave that is evanescently coupled with a high-Q mode orbit and a coherent light wave that is refractively coupled with a detuned low-Q mode orbit.     

Synthesis of Some Substituted Naphthalenes as Potential Intermediates for Polyethers and Terpenoids

1-Benzyloxy-5-hydroxynaphthalene and 1,6-dimethyl-5-hydroxynaphthalene were prepared from 5-methoxy--tetralone. 6-Methoxy--tetralone was converted to 1,6-dimethoxy-2-isopropylnaphthalene.     

The DNA double helix fifty years on

This year marks the 50th anniversary of the proposal of a double helical structure for DNA by James Watson and Francis Crick. The place of this proposal in the history and development of molecular biology is discussed. Several other discoveries that occurred in the middle of the twentieth century were perhaps equally important to our understanding of cellular processes; however, none of these captured the attention and imagination of the public to the same extent as the double helix. The existence of multiple forms of DNA and the uses of DNA in biological technologies is presented. DNA is also finding increasing use as a material due to its rather unusual structural and physical characteristics as well as its ready availability.     

Superconductivity and field-induced magnetism in Pr2-xCexCuO4 single crystals

We report muon-spin rotation and relaxation (muSR) measurements on single crystals of the electron-doped high-T(c) superconductor Pr2-xCexCuO4. In a zero external magnetic field, superconductivity is found to coexist with dilute Cu spins that are static on the muSR time scale. In an applied field, we observe a mu(+)-Knight shift that is primarily due to the magnetic moment induced on the Pr ions. Below the superconducting transition temperature T(c), an additional source of local magnetic field appears throughout the volume of the sample. This finding is shown to be consistent with field-induced antiferromagnetic ordering of the Cu spins. Measurements of the temperature dependence of the in-plane magnetic penetration depth lambda(ab) in the vortex state are also presented.