A Statistic for Testing the Null Hypothesis of Elliptical Symmetry

We present and study a procedure for testing the null hypothesis of multivariate elliptical symmetry. The procedure is based on the averages of some spherical harmonics over the projections of the scaled residual (1978, N. J. H. Small, Biometrika65, 657–658) of the d-dimensional data on the unit sphere of ^d. We find, under mild hypothesis, the limiting null distribution of the statistic presented, showing that, for an appropriate choice of the spherical harmonics included in the statistic, this distribution does not depend on the parameters that characterize the underlying elliptically symmetric law. We describe a bivariate simulation study that shows that the finite sample quantiles of our statistic converge fairly rapidly, with sample size, to the theoretical limiting quantiles and that our procedure enjoys good power against several alternatives.     

On the consistency properties of linear and quadratic discriminant analyses

The limit behavior of the conditional probability of error of linear and quadratic discriminant analyses is studied under wide assumptions on the class conditional distributions. Results obtained may help to explain analytically the behavior in applications of linear and quadratic discrimination techniques.     

Solid‐state 13C and 129Xe NMR study of poly(vinyl alcohol) and poly(vinyl alcohol)/lactosilated chitosan gels

Dry and hydrated poly(vinyl alcohol) (PVA) gels with 55% (a‐PVA) and 61% (s‐PVA) syndiotacticity and related PVA/lactyl chitosan (LC) blends have been investigated with ¹²⁹Xe and cross‐polarization/magic‐angle‐spinning ¹³C NMR techniques. Although the dry gels exhibit two broad ¹²⁹Xe resonances in the slow‐to‐intermediate exchange limit, both hydrated gels show three resonances. The corresponding dry blends exhibit two signals, the chemical shifts and line widths of which change with respect to those of pure PVA, whereas one (a‐PVA/LC) or two (s‐PVA/LC) signals appear in the spectra of the hydrated blends. A comparative analysis of the data demonstrates that LC rearranges the domains of the polymeric matrix in both the dry and hydrated blends according to the syndiotacticity of the PVA chains. Information on the molecular motions of the amorphous and swollen polymeric domains in the kilohertz range has been obtained from an analysis of the spin‐lattice relaxation times. These data indicate that the dynamics and arrangement of the PVA chains in the gels are strongly affected by their tacticity and the addition of the copolymer LC. © 2003 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 3123–3131, 2003     

Optical hole burning and matrix effects in a phthalocyanine complex of ruthenium(II)

A doubling of the origin is observed in the low-temperature electronic absorption spectrum of the complex carbonyl(pyridine)-phthalocyaninatoruthenium(II) in glassy matrices. The effect is studied by optical hole burning and results suggest a non-degenerate singlet ground state of near C_2v symmetry to be invoked.     

Ueber F?ulnissalkaloide

Ohne Zusammenfassung     

Sui connettivi tra eventi e l’impostazione assiomatica del calcolo delle probabilità

Riassunto Ammesso il connettivoaut sull’insieme degli eventi, si mostra come risultano definiti i connettivivel edet. Si deducono quindi i teoremi delle probabilità totali e delle probabilità composte.

---

Résumé Admis le connectifaut sur l’ensemble des événements, on montre comme résultent définis les connectifvel etet. On déduit de là les théorèmes des probabilités totales et des probabilités composées.

     

Nuclear magnetic resonance of benzobisheterocyclic compounds

The nuclear magnetic resonance spectra of forty-nine benzobisheterocyclic compounds, containing various heterocycles, were determined. The observed spectral data made possible the elucidation of the structure and also clarified the influences of the heterocyclic substituents and of heterocyclic rings on chemical shift values of the aromatic protons.     

Design and validation of a single sphere multi-detector neutron spectrometer based on LiF: Mg,Cu,P thermoluminescent dosemeters

This communication describes a new neutron spectrometer consisting of pairs of ⁷Li and ⁶Li based thermoluminescent dosemeters (MCP-6, MCP-7) located at selected positions within a single moderating polyethylene sphere. The spatial arrangement of the dosemeters has been designed using the MCNPX Monte Carlo code to calculate the response matrix in order to obtain a nearly isotropic response for neutrons in the energy range up to 20 MeV. A partial validation of the calculated response matrix has been performed with the calibrated ²⁴¹Am–Be neutron source at the INFN–LNF Laboratory, using the shadow cone technique.     

Chemical sensing based on the plasmonic response of nanoparticle aggregation: anion sensing in nanoparticles stabilized by amino-functional ionic liquid

We report the synthesis, characterization and modellization of optical anion sensors based on gold nanoparticles (Au NPs) stabilized by amino-functional imidazolium ionic liquids (AFIL). The addition of different salts results in anion exchange of the imidazolium ionic liquid stabilizer leading to a change in the optical response of the original nanoparticle aqueous solution. In all cases except with dodecylbenzenesulfonic acid sodium salt, a sufficient amount of salt concentration (5 times larger than equimolar) leads to the appearance of an absorption band between 600 and 700 nm in the ultravioletvisible (UV-vis) spectrum. The presence of the salt produces aggregation of the particles that localise the optical response and produce a large spectral red shift. Transmission electron microscopy images demonstrated that this optical change was due to the aggregation of the nanoparticles. We simulate the optical response of both situations, before and after salt addition, and interpret the experimental observations in terms of the different response of metallic single nanoparticles and nanoparticle aggregates. Theoretical calculations for single nanoparticle and single nanoparticle dimers demonstrate that the colour change is not due to the enlargement or structural changes of the Au NPs, but due to the formation of NP aggregation. These results show the potential of nanoparticle plasmonics to perform effective chemical sensing.