Accelerating cosmologies from spacelike branes

We point out that the recently proposed model of a flat four-dimensional universe with accelerated expansion in string or M theory is a special case of time-dependent solutions that the author found under the name of spacelike (S) branes. We also show that similar accelerating models can be obtained from S branes if the internal space is chosen to be hyperbolic or flat spaces.     

Giant optical activity in quasi-two-dimensional planar nanostructures

We examine the spectral dependence in the visible frequency range of the polarization rotation of two-dimensional gratings consisting of chiral gold nanostructures with subwavelength features. The gratings, which do not diffract, are shown to exhibit giant specific rotation (approximately 10(4) degrees/mm) of polarization in direct transmission at normal incidence. The rotation is the same for light incident on the front and back sides of the sample. Such reciprocity indicates three dimensionality of the structure arising from the asymmetry of light-plasmon coupling at the air-metal and substrate-metal interfaces. The structures thus enable polarization control with quasi-two-dimensional planar objects. However, in contradiction with recently suggested interpretation of experiments on larger scale but otherwise similar structures, the observed polarization phenomena violate neither reciprocity nor time-reversal symmetry.     

Mirror symmetry and

We show that counting functions of covers of are equal to sums of integrals associated to certain `Feynman' graphs. This is an analogue of the mirror symmetry for elliptic curves.

     

Liquid crystalline nanosheet colloids with controlled particle size obtained by exfoliating single crystal of layered niobate k(4)nb(6)o(17)

Colloidally dispersed niobate nanosheets with the thickness of 1.8 nm and controlled mean lateral sizes of 0.15-7.8 mum were prepared and their liquid crystallinity was examined. The nanosheet colloids with different lateral sizes were obtained by exfoliation of single crystals of layered niobate K4Nb6O17 and subsequent ultrasonication. Naked-eye and microscope observations of the nanosheet colloids between crossed polarizers revealed liquid crystallinity of the sols characterized by birefringence as functions of the lateral sizes and concentration of the nanosheets. The nanosheet colloids with smaller lateral sizes (0.15-1.9 mum) varied from isotropic to biphasic (isotropic + liquid crystalline), and finally to fully liquid crystalline states as the colloid concentration increased. The phase transition concentrations (from isotropic to biphasic and biphasic to liquid crystalline) decreased with increasing aspect ratio (lateral-to-thickness ratio) of the nanosheets, almost in accordance with the prediction by Onsager theory, indicating that the liquid crystallinity is explained basically by excluded-volume effect between the nanosheets. On the other hand, the colloids with larger lateral sizes (6.2 and 7.8 mum) stably kept liquid crystalline state even at very low concentration (5.1 x 10-6 in volume fraction), which was much lower than that expected from the theory.     

Creation of magnetic cerasomes through electroless plating and their manipulation using external magnetic fields

Magnetic cerasome, an artificial cell membrane having ultrathin magnetic metal layers on the surface, was prepared through electroless plating of magnetic metal alloy onto an organic–inorganic vesicular nanohybrid “cerasome.” Morphological and functional characteristics of the magnetic cerasome were evaluated using various physical measurements: scanning and transmission electron microscopies, energy-dispersive X-ray spectroscopy, electron tomography, and vibrating sample magnetometry. The results proved that high morphological stability of the cerasome was important for constructing the magnetic lipid vesicle and that insertion of an alkylated metal ligand into the cerasome was essential to the magnetic metal alloy deposition on the cerasome surface. Fluorescence microscopic observations revealed that the magnetic cerasomes were collected reversibly on the slide glass surface and manipulated depending on external motion of a magnet. The potential use of the magnetic cerasomes as a novel vesicular nanohybrid is also described in this report.     

A concise synthesis of (S)-N-ethoxycarbonyl-alpha-methylvaline

A practical and efficient protocol for the three-step synthesis of (S)-N-ethoxycarbonyl-alpha-methylvaline 3 is described which utilizes readily available commercial starting materials. The key transformations involve resolution-crystallization of tartrate salt 6 followed by a one-pot procedure for the preparation of 3 which is isolated as the dicyclohexylamine salt in 45% overall yield and in 91-95% ee.     

A practical ortho-rearrangement of silyl group of ortho-bromophenyl silyl ethers using magnesium(0)

A practical synthesis of ortho-silyl-substituted phenol from ortho-bromophenyl silyl ethers without using RLi is described. Various ortho-bromophenyl silyl ethers are treated with commercially available Mg turnings, which are easy to handle in air, and transfer of the silyl group to the ortho-position occurs in good to high yields. Selective mono-magnesiation of 2,6-dibromophenyl silyl ether is observed even in the presence of excess Mg, and ortho-bromo-6-silylphenol is obtained as the predominant product. The obtained ortho-silyl-substituted phenol is formylated with (CH₂O)_n/MgCl₂/Et₃N, and then condensation with a diamine leads to a silyl-substituted salen-type ligand in a good yield. This scheme is suitable for the large scale synthesis of silyl-substituted salen-type ligands bearing imine groups.     

On the existence of multiple positive solutions of quasilinear elliptic eigenvalue problems

We study a quasilinear elliptic problem