On multiplicity in restriction of tempered representations of p-adic groups

Mathematische Zeitschrift - We establish an equality between two multiplicities: one in the restriction of tempered representations of a p-adic group to its closed subgroup with the same derived...     

Activation of α-Fe2O3 for Photoelectrochemical Water Splitting Strongly Enhanced by Low Temperature Annealing in Low Oxygen Containing Ambient

Photoelectrochemical (PEC) water splitting is a promising method for the conversion of solar energy into chemical energy stored in the form of hydrogen. Nanostructured hematite (α-Fe₂O₃) is one of the most attractive materials for a highly efficient charge carrier generation and collection due to its large specific surface area and the short minority carrier diffusion length. In the present work, the PEC water splitting performance of nanostructured α-Fe₂O₃ is investigated which was prepared by anodization followed by annealing in a low oxygen ambient (0.03 % O₂ in Ar). It was found that low oxygen annealing can activate a significant PEC response of α-Fe₂O₃ even at a low temperature of 400 °C and provide an excellent PEC performance compared with classic air annealing. The photocurrent of the α-Fe₂O₃ annealed in the low oxygen at 1.5 V vs. RHE results as 0.5 mA cm⁻², being 20 times higher than that of annealing in air. The obtained results show that the α-Fe₂O₃ annealed in low oxygen contains beneficial defects and promotes the transport of holes; it can be attributed to the improvement of conductivity due to the introduction of suitable oxygen vacancies in the α-Fe₂O₃. Additionally, we demonstrate the photocurrent of α-Fe₂O₃ annealed in low oxygen ambient can be further enhanced by Zn-Co LDH, which is a co-catalyst of oxygen evolution reaction. This indicates low oxygen annealing generates a promising method to obtain an excellent PEC water splitting performance from α-Fe₂O₃ photoanodes.     

Hydrogen production and photocatalytic activity of g-C3N4/Co-MOF (ZIF-67) nanocomposite under visible light irradiation

Herein, cobalt (Co)-based metal–organic zeolitic imidazole frameworks (ZIF-67) coupled with g-C₃N₄ nanosheets synthesized via a simple microwave irradiation method. SEM, TEM and HR-TEM results showed that ZIF-67 were uniformly dispersed on g-C₃N₄ surfaces and had a rhombic dodecahedron shape. The photocatalytic properties of g-C₃N₄/ZIF-67 nanocomposite were evaluated by photocatalytic dye degradation of crystal violet (CV), 4-chlorophenol (4-CP) and photocatalytic hydrogen (H₂) production. In presence of visible light illumination, the photocatalytic dye results showed that 95% CV degradation and 53% 4-CP degradation within 80 min. The H₂ production of the g-C₃N₄/ZIF-67 composite was 2084 μmol g⁻¹, which is 3.84 folds greater than that of bare g-C₃N₄ (541 μmol g⁻¹).     

Generation of single-crystalline domain in nano-scale silicon pillars by near-field short pulsed laser

We observe laser-induced grain morphology change in silicon nanopillars under a transmission electron microscopy (TEM) environment. We couple the TEM with a near-field scanning optical microscopy pulsed laser processing system. This novel combination enables immediate scrutiny on the grain morphologies that the pulsed laser irradiation produces. We find unusual transformation of the tip of the amorphous or polycrystalline silicon pillar into a single crystalline domain via melt-mediated crystallization. On the basis of the three-dimensional finite difference simulation result and the dark field TEM data, we propose that the creation of the distinct single crystalline tip originates from the dominant grain growth initiated at the apex of the non-planar liquid–solid interface. Our microscopic observation provides a fundamental basis for laser-induced conversion of amorphous nanostructures into coarse-grained crystals.     

Synthesis and characterization of a fatty acid self-assembled monolayer on CeO2 nanoparticles: to explore solution-state property of a SAM

Decanoic acid self-assembled monolayer (SAM) in the quasi-crystalline state was prepared on the surface of the cubic CeO₂ nanoparticles (6.5 ± 1.1 nm) by hydrothermal synthesis. The purification method to obtain quasi-crystalline SAM without residual (free) decanoic acid was developed. The SAM was carefully washed (purified) and characterized carefully by FT-IR, TG, DSC, and NMR. The obtained results showed that good agreement with the property of the dry state SAM. The solution state properties of the SAM were also examined by the CeO₂ nanoparticles. It turned out that the quasi-crystalline SAM could be swollen by its good solvents, cyclohexane, and chloroform; however, the quasi-crystalline SAM showed that a size exclusion effect to the solvent, trans-decalin. In addition, it turned out that the molecular motion of the decanoic acids in the SAM was highly restricted even in the swollen state depending on the distance from the grafting point to the CeO₂ surface. The strong osmosis was also observed. The solvent molecules were not easily released from the SAM even after the solvent molecules outside of the SAM were frozen.     

Design variable tolerance effects on the natural frequency variance of constrained multi-body systems in dynamic equilibrium

The design variable tolerance effects on the natural frequency variance of constrained multi-body systems in dynamic equilibrium are investigated in this study. Monte-Carlo simulation is often employed for such investigations, but it is known to have serious drawbacks. Excessive amount of computation time needs to be consumed since a large number of evaluations are usually required for the method. Furthermore, the solution accuracy cannot be always guaranteed in spite of the excessive amount of computation time. In order to overcome such drawbacks, a method employing eigenvalue sensitivity information is proposed to obtain the variance of natural frequency in this study. In order to verify the accuracy and the efficiency of the method, some numerical examples of multi-body systems in dynamic equilibrium are solved and the results are compared to those obtained by an analytical method and Monte-Carlo simulation.     

High‐throughput data dimension reduction via seeded canonical correlation analysis

Canonical correlation analysis (CCA) is one of popular statistical methodologies in multivariate analysis, especially, in studying relation of two sets of variables. However, if sample sizes are smaller than the maximum of the dimensions of two sets of variables, it is not plausible to construct canonical coefficient matrices due to failure of inverting sample covariance matrices. In this article, we develop a two step procedure of CCA implemented in such situation. For this, seeded dimension reduction is adapted into CCA. Numerical studies confirm the approach, and two real data analyses are presented. Copyright © 2014 John Wiley & Sons, Ltd.     

Fast parallel detection of feline panleukopenia virus DNA by multi‐channel microchip electrophoresis with programmed step electric field strength

A multi‐channel microchip electrophoresis using a programmed step electric field strength (PSEFS) method was investigated for fast parallel detection of feline panleukopenia virus (FPV) DNA. An expanded laser beam, a 10× objective lens, and a charge‐coupled device camera were used to simultaneously detect the separations in three parallel channels using laser‐induced fluorescence detection. The parallel separations of a 100‐bp DNA ladder were demonstrated on the system using a sieving gel matrix of 0.5% poly(ethylene oxide) (M_r = 8 000 000) in the individual channels. In addition, the PSEFS method was also applied for faster DNA separation without loss of resolving power. A DNA size marker, FPV DNA sample, and a negative control were simultaneously analyzed with single‐run and one‐step detection. The FPV DNA was clearly distinguished within 30 s, which was more than 100 times faster than with conventional slab gel electrophoresis. The proposed multi‐channel microchip electrophoresis with PSEFS was demonstrated to be a simple and powerful diagnostic method to analyze multiple disease‐related DNA fragments in parallel with high speed, throughput, and accuracy.