Asymptotic behaviour of the least squares estimator of the mean of AR(1) models

The aim of the paper is to investigate the limit behaviour of the least squares estimator of the shift parameter of nearly unstable, nearly stable, and nearly explosive AR(1) models. Both zero start and stationary cases are treated. Connection with the maximum likelihood estimator of the shift parameter of continuous time AR(1) processes is also discussed.     

The influence of glass coating on the single domain wall potential in amorphous glass-coated Fe-based microwires

The effect of the glass coating on the single domain wall potential in amorphous glass-coated Fe-based microwire has been studied by the switching field distribution technique. The thermoactivated mechanism model is used to describe the thermally activated switching through the complex energy barrier in amorphous FeSiB microwires. Glass removal leads to the increase of the probability of the thermally activated switching pointing to the decrease of the energy barrier.     

X-ray photoelectron spectroscopy and differential capacitance study of thiol-functional polysiloxane films on gold supports

Polymeric molecules containing multiple thiol groups (polythiols) provide tenacious attachment to metal surfaces such as gold. Polythiol films are also well suited for subsequent derivatization with biomacromolecules through remnant free thiol groups of the film. In this study, 1-3 nm thick layers of a commercial polythiol, poly((mercaptopropyl)methylsiloxane) (PMPMS), are investigated with X-ray photoelectron spectroscopy (XPS) and electrochemical impedance spectroscopy. XPS is used to reveal the surface coverage of thiolate-Au bonds between the polythiol and the metal support, which is found to be approximately 30% lower than that in alkanethiol self-assembled monolayers. The surface density of thiolate-Au bonds did not depend on film thickness provided sufficient PMPMS material was present. Differential capacitance measurements show that the effective dielectric barrier presented by PMPMS films under aqueous environments corresponds closely to their physical thickness, with even approximately 1 nm films remaining impermeable to electrolyte species. Modification of the films with an oligoethylene glycol compound was also examined, in anticipation of future applications in label-free, impedance-based biomolecular diagnostics.     

Lehmer pairs of zeros,the de Bruijn-Newman constant Λ, and the Riemann Hypothesis

We give here a rigorous formulation for a pair of consecutive simple positive zeros of the functionH ₀ (which is closely related to the Riemann -function) to be a Lehmer pair of zeros ofH ₀. With this formulation, we establish that each such pair of zeros gives a lower bound for the de Bruijn-Newman constant (where the Riemann Hypothesis is equivalent to the assertion that 0). We also numerically obtain the following new lower bound for :

Iodide-promoted uncatalyzed bromate oscillators

Iodide ions—in a rather narrow concentration range—induce some of the uncatalyzed bromate oscillators to a more pronounced oscillatory activity: the number of oscillations increases considerably and the overall rate of the chemical reaction drops about an order of magnitude. Preliminary suggestion is made on the mechanism of iodide-induced oscillatory reactions.

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Improved sample preparation method for environmental plutonium analysis by ICP-SFMS and alpha-spectrometry

A rapid and simple sample preparation method for plutonium determination in environmental samples by inductively coupled plasma sector field mass spectrometry (ICP-SFMS) and alpha-spectrometry is described. The developed procedure involves a selective CaF₂ co-precipitation for preconcentration followed by extraction chromatographic separation. The proposed method effectively eliminates the possible interferences in mass spectrometric analysis and also removes interfering radionuclides that may disturb alpha-spectrometric measurement. For ²³⁹Pu, ²⁴⁰Pu and ²⁴¹Pu limits of detection of 9.0 fg·g⁻¹ (0.021 mBq), 1.7 fg·g⁻¹ (0.014 mBq) and 3.1 fg·g⁻¹ (11.9 mBq) were achieved by ICP-SFMS, respectively, and 0.02 mBq by alpha-spectrometry. Results of certified reference materials agreed well with the recommended values.