Linear Independence of q-Analogues of Certain Classical Constants

Let K be ? or an imaginary quadratic number field, and q ∈ K an integer with ¦q¦ > 1. We give a quantitative version of Σ_n≥1 a_n/(qⁿ ? 1) ? K for non-zero periodic sequences (a_n) in K of period length ≤ 2. As a corollary, we get a quantitative version of the linear independence over K of 1, the q-harmonic series, and a q-analogue of log 2. A similar result on 1, the q-harmonic series, and a q-analogue of ζ(2) is also proved. Mathematics Subject Classification (2000): 11J72, 11J82     

Feasibility of low-voltage cathodic electroluminescence at oxide-covered aluminum electrodes for trace metal determinations in aqueous solutions

Metal-catalyzed electroluminescence is generated at an oxide-covered aluminum electrode during the reduction of oxygen, potassium peroxodisulfate, and especially hydrogen peroxide in aqueous solutions. The feasibility of this electroluminescence for the determination of copper (5 × 10^?9 M) and thallium (> 10^?10 M) is demonstrated.     

Symmetrization of functions in Sobolev spaces and the isoperimetric inequality

A positive measurable function f on R^d can be symmetrized to a function f^* depending only on the distance r, and with the same distribution function as f. If the distribution derivatives of f are Radon measures then we have the inequality f^*f, where f is the total mass of the gradient. This inequality is a generalisation of the classical isoperimetric inequality for sets. Furthermore, and this is important for applications, if f belongs to the Sobolev space H¹,P then f^* belongs to H¹,P and f^*_pf_p.     

Time-dependent density functional approach for the calculation of inelastic x-ray scattering spectra of molecules

We apply time-dependent density functional theory to study the valence electron excitations of molecules and generalize the typically used time-propagation scheme and Casida's method to calculate the full wavevector dependent response function. This allows the computational study of dipole-forbidden valence electron transitions and the dispersion of spectral weight as a function of the wavevector. The method provides a novel analysis tool for spectroscopic methods such as inelastic x-ray scattering and electron energy loss spectroscopy. We present results for benzene and CF(3)Cl and make a comparison with experimental results.     

On the spline collocation method for the single layer equation related to time-fractional diffusion

The boundary element spline collocation method is studied for the time-fractional diffusion equation in a bounded two-dimensional domain. We represent the solution as the single layer potential which leads to a Volterra integral equation of the first kind. We discretize the boundary integral equation with the spline collocation method on uniform meshes both in spatial and time variables. In the stability analysis we utilize the Fourier analysis technique developed for anisotropic pseudodifferential equations. We prove that the collocation solution is quasi-optimal under some stability condition for the mesh parameters. We have to assume that the mesh parameter in time satisfies (h_t=c h^\frac2a)(h_t=c h^{\frac{2}{\alpha}}), where (h) is the spatial mesh parameter.     

Electrogenerated chemiluminescence of fluorescein in aqueous alkaline solutions

Fluorescein is shown to emit light when electrolyzed either anodically or cathodically using potential pulses, in aqueous alkaline solutions at a platinum electrode.     

X‐ray‐Raman‐scattering‐based EXAFS beyond the dipole limit

X‐ray Raman scattering (XRS) provides a bulk‐sensitive method of measuring the extended X‐ray absorption fine structure (EXAFS) of soft X‐ray absorption edges. Accurate measurements and data analysis procedures for the determination of XRS‐EXAFS of polycrystalline diamond are described. The contributions of various angular‐momentum components beyond the dipole limit to the atomic background and the EXAFS oscillations are incorporated using self‐consistent real‐space multiple‐scattering calculations. The properly extracted XRS‐EXAFS oscillations are in good agreement with calculations and earlier soft X‐ray EXAFS results. It is shown, however, that under certain conditions multiple‐scattering contributions to XRS‐EXAFS deviate from those in standard EXAFS, leading to noticeable changes in the real‐space signal at higher momentum transfers owing to non‐dipole contributions. These results pave the way for the accurate application of XRS‐EXAFS to previously inaccessible light‐element systems.     

ERKALE—A flexible program package for X‐ray properties of atoms and molecules

ERKALE is a novel software program for computing X‐ray properties, such as ground‐state electron momentum densities, Compton profiles, and core and valence electron excitation spectra of atoms and molecules. The program operates at Hartree–Fock or density‐functional level of theory and supports Gaussian basis sets of arbitrary angular momentum and a wide variety of exchange‐correlation functionals. ERKALE includes modern convergence accelerators such as Broyden and ADIIS and it is suitable for general use, as calculations with thousands of basis functions can routinely be performed on desktop computers. Furthermore, ERKALE is written in an object oriented manner, making the code easy to understand and to extend to new properties while being ideal also for teaching purposes. © 2012 Wiley Periodicals, Inc.     

Intrinsic and 1-aminonaphthalene-4-sulfonate-specific extrinsic lyoluminescences of X-ray irradiated sodium chloride

1-Aminonaphthalene-4-sulfonate (ANS)-specific extrinsic lyoluminescence (LL) of X-ray irradiated sodium chloride is observed at 425 nm when the irradiated salt is dissolved in an aqueous solution of ANS. The paper discusses, in detail, the mechanism of the ANS-specific LL and its analytical applicability. Also, the intrinsic LL of X-ray irradiated sodium chloride is studied. Hydrated electron as well as hole scavenger experiments support the proposal that in the case of the intrinsic LL of X-ray irradiated sodium chloride, trapped electrons (mainly F-center electrons) are released and hydrated whereas trapped holes (V-centers) remain surface-bound and are only partially hydrated before recombination occurs. These hydrated electrons and dissolving solid surface-bound hole centers, which are probably only partially hydrated, are able to act as reducing and oxidizing agents, respectively, in the luminophore oxidation-initiated reductive excitation pathway of ANS. Solution additives (halides and pseudohalides) show that in the chemiluminescence processes in question, oxidizing agents will follow the Marcus theory of electron transfer reactions. The LL method described allows the determination of ANS in the concentration range ≈10⁻¹¹ − 10⁻⁷ M. This suggests that aminonaphthalene derivatives can be used as label molecules in high sensitivity lyoluminobioaffinity assays.