Nonexistence of abelian difference sets: Lander's conjecture for prime power orders

In 1963 Ryser conjectured that there are no circulant Hadamard matrices of order 4$"> and no cyclic difference sets whose order is not coprime to the group order. These conjectures are special cases of Lander's conjecture which asserts that there is no abelian group with a cyclic Sylow -subgroup containing a difference set of order divisible by . We verify Lander's conjecture for all difference sets whose order is a power of a prime greater than 3.

     

The predicted barrier effects in the proximity of tall buildings

A ray model is developed and validated for the prediction of the insertion loss of barriers that are placed in front of a tall building in high-rise cities. The model is based on the theory of geometrical acoustics for sound diffraction at the edge of a barrier and multiple reflections by the barrier and fa?ade surfaces. It is crucial to include the diffraction and multiple reflection effects in the ray model, as they play important roles in determining the overall sound pressure levels for receivers located between the fa?ade and barrier. Comparisons of the ray model with indoor experimental data and wave-based boundary element formulation show reasonably good agreement over a broad frequency range. Case studies are also presented that highlight the significance of positioning the barrier relative to the noise-sensitive receivers in order to achieve improved shielding efficiency of the barrier.     

Absolute potassium cation affinities (PCAs) in the gas phase

The potassium cation affinities (PCAs) of 136 ligands (20 classes) in the gas phase were established by hybrid density functional theory calculations (B3-LYP with the 6-311+G(3df,2p) basis set). For these 136 ligands, 70 experimental values are available for comparison. Except for five specific PCA values-those of phenylalanine, cytosine, guanine, adenine (kinetic-method measurement), and Me(2)SO (by high-pressure mass spectrometric equilibrium measurement)-our theoretical estimates and the experimental affinities are in excellent agreement (mean absolute deviation (MAD) of 4.5 kJ mol(-1)). Comparisons with previously reported theoretical PCAs are also made. The effect of substituents on the modes of binding and the PCAs of unsubstituted parent ligands are discussed. Linear relations between Li+/Na+ and K+ affinities suggest that for the wide range of ligands studied here, the nature of binding between the cations and a given ligand is similar, and this allows the estimation of PCAs from known Li+ and/or Na+ affinities. Furthermore, empirical equations relating the PCAs of ligands with their dipole moments, polarizabilities (or molecular weights), and the number of binding sites were established. Such equations offer a simple method for estimating the PCAs of ligands not included in the present study.     

Spherical growth and surface-quasifree vibrations of Si nanocrystallites in Er-doped Si nanostructures

Si-based Er-doped Si nanostructures were fabricated for exploring efficient light emission from Er ions and Si nanocrystallites. High-resolution transmission electron microscopy observations reveal that Si nanocrystallites are spherically embedded in the SiO2 matrix. Energy-dispersive x-ray analysis indicates that the Er centers are distributed at the surfaces of nanocrystallites surrounded by the SiO2 matrix. Low-frequency Raman scattering investigation shows that Lamb's theory can be adopted to exactly calculate the surface vibration frequencies from acoustic phonons confined in spherical Si nanocrystallites and the matrix effects are negligible.     

A new processing method of CaZn2(OH)6·2H2O powders: Photoluminescence and growth mechanism

In this communication, we report on the formation of calcium hexahydroxodizincate dehydrate, CaZn₂(OH)₆·2H₂O (CZO) powders under microwave-hydrothermal (MH) conditions. These powders were analyzed by X-ray diffraction (XRD), Field-emission gum scanning electron microscopy (FEG-SEM), ultraviolet-visible (UV-vis) absorption spectroscopy and photoluminescence (PL) measurements. XRD patterns confirmed that the pure CZO phase was obtained after MH processing performed at 130 °C for 2 h. FEG-SEM micrographs indicated that the morphological modifications as well as the growth of CZO microparticles are governed by Ostwald-ripening and coalescence mechanisms. UV-vis spectra showed that this material have an indirect optical band gap. The pure CZO powders exhibited an yellow PL emission when excited by 350 nm wavelength at room temperature.     

Finite generation of canonical ring by analytic method

An overview of the analytic proof of the theorem on the finite generation of the canonical ring for the projective algebraic manifold of general type is given.     

Quantitative x-ray phase-contrast imaging using a single grating of comparable pitch to sample feature size

The ability to quantitatively retrieve transverse phase maps during imaging by using coherent x rays often requires a precise grating or analyzer-crystal-based setup. Imaging of live animals presents further challenges when these methods require multiple exposures for image reconstruction. We present a simple method of single-exposure, single-grating quantitative phase contrast for a regime in which the grating period is much greater than the effective pixel size. A grating is used to create a high-visibility reference pattern incident on the sample, which is distorted according to the complex refractive index and thickness of the sample. The resolution, along a line parallel to the grating, is not restricted by the grating spacing, and the detector resolution becomes the primary determinant of the spatial resolution. We present a method of analysis that maps the displacement of interrogation windows in order to retrieve a quantitative phase map. Application of this analysis to the imaging of known phantoms shows excellent correspondence.     

一类Markov链的强逼近

本文给出了一类非时齐的Markov链的强逼近.作为应用,建立了临床试验中Markov链自适应设计的强相合性,重对数律和弱收敛.