A review of robust clustering methods

Deviations from theoretical assumptions together with the presence of certain amount of outlying observations are common in many practical statistical applications. This is also the case when applying Cluster Analysis methods, where those troubles could lead to unsatisfactory clustering results. Robust Clustering methods are aimed at avoiding these unsatisfactory results. Moreover, there exist certain connections between robust procedures and Cluster Analysis that make Robust Clustering an appealing unifying framework. A review of different robust clustering approaches in the literature is presented. Special attention is paid to methods based on trimming which try to discard most outlying data when carrying out the clustering process.     

A semi-empirical approach to determine gamma activities in environmental cylindrical samples

A semi-empirical method to determine radionuclide concentrations in large environmental samples without the use of reference material and avoiding the typical complexity of Monte-Carlo codes is proposed. The calculation of full-energy peak efficiencies was carried out from a relative efficiency curve (obtained from the gamma spectra data), and the geometric (simulated by Monte-Carlo), absorption, sample and intrinsic efficiencies for energies between 130 and 3000 keV. The absorption and sample efficiencies were determined from the mass absorption coefficients, whereas the intrinsic efficiency was approximated by an empirical function. The deviations between calculated and experimental efficiencies for a reference material in most cases are less than 10%. Radionuclide activities in marine sediment samples calculated by the proposed method and by the experimental comparative method were not significantly different. This new method can be used for routine environmental monitoring when uncertainties up to 10% are acceptable.     

Chromium complexes of an isomeric N-donor ligand, 2-[(N-arylamino)phenylazo]pyridine: amination reactions,X-ray structure,and redox properties

The chromium chemistry of two positional isomers of the ligand 2-[(N-arylamino)phenylazo]pyridine (HL(1)and HL(2)) are described. While the ligand HL(1) coordinates as a bischelating tridentate N,N,N-donor, [L(1)](-), with deprotonation of the amine nitrogen, its isomer HL(2) coordinates as a neutral bidentate N,N-donor. The amine nitrogen in this case remains protonated. Thus the reaction of CrCl(3).nH(2)O with HL(1) produced the brown cationic complex, [Cr(L(1))(2)](+), [1](+). The representative X-ray structure of [1a](ClO(4)) is reported. The two azo nitrogens of the anioinc tridentate ligand approach the metal center closest with Cr(1)-N(azo) av 1.862(6) A. There is a significant degree of ligand backbone conjugation in the coordinated ligands, which resulted in shortening of the C-N distances and also in lengthening of the diazo (N=N) distances. Two synthetic approaches for the synthesis of chromium complexes of HL(2) are investigated. The first approach is based on the substitution reaction, wherein all the coordinated CO ligands of Cr(CO)(6) were completely substituted by the three bidentate HL(2) ligands to produce a violet complex [Cr(HL(2))(3)]. The second approach is based on para-amination reaction of coordinated 2-(phenylazo)pyridine (pap). Thus the reaction of an inert complex, [CrCl(2)(pap)(2)], with ArNH(2) yields a mixed ligand complex, [CrCl(2)(pap)(HL(2))], 3. In this reaction one of the two coordinated pap ligands in [CrCl(2)(pap)(2)] undergoes amination at the para carbon (with respect to the diazo function) to yield HL(2) in situ. This metal-promoted transformation is authenticated by the X-ray structure determination of a representative complex, [CrCl(2)(pap)(HL(2a))], 3a. Notable differences in bond distances along the ligand backbones of the two coordinated ligands in 3a indicate different levels of metal-ligand overlap in this complex. All the chromium complexes of HL(2) are characterized by their intense blue-violet color. The frequencies of the visible range transitions in these complexes linearly correlate with the Hammett's substitution constant. Intraligand charge-transfer transitions in the visible region are believed to be responsible for the intense color. Redox properties of all these complexes are reported.     

Influence of metal ions on antioxidant behaviour in polypropylene

The effect of Cr(III), Fe(III) and Cu(II) ions, at trace levels, on the effectiveness of four commercial antioxidant systems, viz. Topanol, Santowhite, Hostanox 03 and Irganox 1425, in polypropylene (PP) films is examined using infra-red and second-order derivative uv spectroscopy. The results show that at these levels the metal ions have a minor effect on the unstabilised polymer. However, the ions can have a beneficial or adverse effect on antioxidant activity, particularly under oven ageing conditions. The observed effect depends on the metal/antioxidant system, and is attributed to an indirect interaction between the components which can delay or accelerate antioxidant decomposition in the polymer. An exception to this behaviour is the metal complex Irganox 1425, which interacts strongly with copper ions in the polymer matrix. The antioxidant is partially transformed by copper ions during the compression moulding stage. The beneficial effect present in some cases is in direct contrast with what has generally been observed in studies using unstabilised polymers.     

Nucleophilic addition of the thiocyanate ion to ferrocenyl-stabilised carbocations

The reaction of ferrocenylmethylcarbocations with the ambident thiocyanate ion produces only the isothiocyanate isomer.     

The Volterra Operator is not Supercyclic

It is shown that the classical Volterra operator, which is cyclic, is not supercyclic on any of the spaces L^p[0, 1], 1 p < . This solves a question posed by Héctor Salas. This contrasts with the fact that the derivative operator, the left inverse of the Volterra operator, although unbounded, is hypercyclic on L^p[0, 1].     

The twistor structure of the biquaternionic projective point

Souček [1, 2] discovered an intriguing connection between the standard twistor correspondence and the biquaternionic projective line The biquaternionic projective point, also has twistor structure corresponding to the collection of α- or β-planes passing through the origin in spacetime. The duality between α- or β-planes is shown to correspond to the choice of left vs. right scalar action. Moreover, we find that is homeomorphic to the scheme      

New proof of the Calabi-Bernstein theorem

By means of a local integral formula on a maximal surface, which involves the hyperbolic angle between the unit normal vector field and a fixed timelike direction, we give a new proof of the parametric Calabi-Bernstein theorem. A suitable modification of the integral formula gives an independent proof to the non-parametric case of this result.