An application of weighted Hardy spaces to the Navier–Stokes equations

In this article, we consider the mapping properties of convolution operators with smooth functions on weighted Hardy spaces H^p(w)$H^p(w)$ with w   belonging to Muckenhoupt class _A∞$A_{\infty }$. As a corollary, one obtains decay estimates of heat semigroup on weighted Hardy spaces. After a weighted version of the div–curl lemma is established, these estimates on weighted Hardy spaces are applied to the investigation of the decay property of global mild solutions to Navier–Stokes equations with the initial data belonging to weighted Hardy spaces.     

Variable Lebesgue norm estimates for BMO functions. II

The paper concerns characterization of BMO in terms of Banach function spaces. In particular, we are interested in characterizing BMO by using the variable Lebesgue norm.     

An epsilon-based measure of efficiency in DEA – A third pole of technical efficiency

In DEA, we have two measures of technical efficiency with different characteristics: radial and non-radial. In this paper we compile them into a composite model called “epsilon-based measure (EBM).” For this purpose we introduce two parameters which connect radial and non-radial models. These two parameters are obtained from the newly defined affinity index between inputs or outputs along with principal component analysis on the affinity matrix. Thus, EBM takes into account diversity of input/output data and their relative importance for measuring technical efficiency.     

Mössbauer spectroscopy of the high-pressure phase of pure iron;ɛ-Fe

Hyperfine Interactions - First off-line tests at the ion trap facility SHIPTRAP took place. The facility is being set up to deliver very clean and cooled beams of singly-charged recoil ions (Rare...     

Dependence of single-molecule conductance on molecule junction symmetry

The symmetry of a molecule junction has been shown to play a significant role in determining the conductance of the molecule, but the details of how conductance changes with symmetry have heretofore been unknown. Herein, we investigate a naphthalenedithiol single-molecule system in which sulfur atoms from the molecule are anchored to two facing gold electrodes. In the studied system, the highest single-molecule conductance, for a molecule junction of 1,4-symmetry, is 110 times larger than the lowest single-molecule conductance, for a molecule junction of 2,7-symmetry. We demonstrate clearly that the measured dependence of molecule junction symmetry for single-molecule junctions agrees with theoretical predictions.     

Conductive characteristics of radical‐bearing polythiophenes using a microcomb‐shaped electrode

The electric conductivity of π‐conjugated and radical‐bearing polymers, i.e., polythiophenes bearing pendant galvinoxyl and phenoxyl radical groups, was measured using a microcomb‐shaped electrode. The electric conductivity was found to be enhanced by the radical content in the polymer. The infrared (IR) and Raman spectroscopies suggested a structural change from an aromatic form to a quinoid one in the polythiophene backbone by the phenoxyl radical generation. The effect of the pendant galvinoxyl radical's unpaired electron on the electric conductivity of the polythiophene was discussed by comparing the conductivity of a radical‐bearing polystyrene and a polythiophene mixed with low‐molecular radical molecules. Copyright © 2007 John Wiley & Sons, Ltd.     

Collective dynamics of supercritical water

Inelastic X-ray scattering experiments on sub- and supercritical water were performed to investigate collective dynamics of this unique solvent. Analysis within a generalized Langevin formalism shows that the positive dispersion of the sound velocity, as compared to the hydrodynamic value, first decreases (1.0<ρ<0.8 g cm⁻³) at all measured momentum transfers (1.3-10.7 nm⁻¹), and then increases (0.7<ρ<0.26 g cm⁻³) again only at higher momentum transfers. We suggest the initial decrease is due to approaching the percolation limit in the number of hydrogen bonds, and the subsequent increase is due to the formation of rigid dimers in sub- and supercritical water.     

Theory of RIXS in strongly correlated electron systems: Mott gap excitations in cuprates

We theoretically examine the momentum dependence of resonant inelastic X-ray scattering (RIXS) spectrum for one-dimensional and two-dimensional cuprates based on the single-band Hubbard model with realistic parameter values. The spectrum is calculated by using the numerical diagonalization technique for finite-size clusters. We focus on excitations across the Mott gap and clarify spectral features coming from the excitations as well as the physics behind them. Good agreement between the theoretical and existing experimental results clearly demonstrates that the RIXS is a potential tool to study the momentum-dependent charge excitations in strongly correlated electron systems.