Estimating the order of mean-square derivatives with quadratic variations

We consider a real Gaussian process X with unknown smoothness r ₀ where r ₀ is a none negative integer and the mean-square derivative X^(r₀){X^{(r_{\rm 0})}} is supposed to be locally stationary. From n + 1 equidistant observations, we propose and study an estimator of r ₀ based on results for quadratic variations of the underlying process. We derive an exponential inequality for IP ([^(r)]_n 1 r₀){{\rm I}\kern-2.1pt{\rm P} (\widehat{r}_n \neq {r_{\rm 0}})} implying the strong consistency of [^(r)]_n{\widehat{r}_n} . An application to interpolation of processes of unknown regularity is also provided.     

Parameter identification in multistage population dynamics model

We present a numerical analysis to solve a parameter identification problem. We identify the demographical parameters of a multistage population dynamics model (Ainseba et al., 2011 [12]). Our nonlinear optimization problem with constraints is solved by a Quasi-Newton method. The convergence proof of this numerical method is performed here. Some numerical applications of it are also given at the end of the paper.     

Polyethylenimine-modified metal oxides for fabrication of packed capillary columns for capillary electrochromatography and capillary liquid chromatography

The need for novel packing materials in both capillary electrochromatography (CEC) and capillary liquid chromatography (CLC) is apparent and the development towards more selective, application-oriented chromatographic phases is under progress world-wide. In this study we have synthesized new polyethyleneimine (PEI) functionalized Mn(2)O(3), SiO(2), SnO(2), and ZrO(2) particles for the fabrication of packed capillary columns for CEC and CLC. The nanocasting approach was successful for the preparation of functionalized metal oxide materials with a controlled porosity and morphology. PEI functionalization was done using ethyleneimine monomers to create particles which are positively charged in aqueous solution below pH 9. This functionalization allowed the possibility to have both hydrophobic (due to its alkyl chain) and ionic interactions (due to positively charged amino groups) with selected compounds. For comparison aminopropyl-functionalized silica was also synthesized and tested. Both slurry pressure and electrokinetic packing procedures used gave similar results, but fast sedimentation of the material caused some problems during the packing. The high stability and wide pH range of PEI-functionalized SiO(2) material, with potential for hydrophobic and electrostatic interactions, proved to be useful for the CEC and CLC separation of some model acidic and neutral compounds.     

Kerr black holes are not unique to general relativity

Considerable attention has recently focused on gravity theories obtained by extending general relativity with additional scalar, vector, or tensor degrees of freedom. In this Letter, we show that the black-hole solutions of these theories are essentially indistinguishable from those of general relativity. Thus, we conclude that a potential observational verification of the Kerr metric around an astrophysical black hole cannot, in and of itself, be used to distinguish between these theories. On the other hand, it remains true that detection of deviations from the Kerr metric will signify the need for a major change in our understanding of gravitational physics.     

Raman microscopic identification of gunshot residues

Raman microscopy was used to identify unambiguously the anions of lead and barium in gunshot residues (ca. 5 μm in size) deposited on cellulosic substrates. It was found that most of the particles consist of mixtures of oxides, sulphate and carbonate (along with carbon). In particular, there is strong evidence for the formation of mixed oxides of iron but only relatively little evidence for oxides of antimony. The Raman technique has been shown to be able to identify individual or mixed components and to confirm the presence of microcrystalline particles with a particular crystal structure (e.g. orthorhombic lead oxide). © 1998 John Wiley & Sons, Ltd.