A note on a paper by Massa and Pagani

Massa and Pagani [1] have given a neat refutal to the conjecture [2] that the Riemann tensor is derivable from a tensor potential. Their method consists of assuming such a relationship does exist and examining the resulting integrability conditions; they show that the existence of such a potential will impose nontrivial restrictions on the Riemann tensor and so conclude that, in general, such a potential cannot exist. Although Massa and Pagani posed the problem and interpreted the conclusion in ordinary tensor notation the actual derivation of the crucial constraint equation was carried out in the language of tensor-valued differential forms, and is quite involved. In this note it is shown that the crucial equation can be obtained quite naturally and easily in ordinary tensor notation.     

Singlewall carbon nanotubes covered with polystyrene nanoparticles by in‐situ miniemulsion polymerization

This work is to make carbon nanotubes dispersible in both water and organic solvents without oxidation and cutting nanotube threads. Polystyrene‐singlewall carbon nanotube (PS‐SWNT) composites were prepared with three different methods: miniemulsion polymerization, conventional emulsion polymerization, and mixing SWNT with PS latex. The two factors, crosslinking and surface coverage of PS are important factors for the mechanical and electrical properties, including dispersion states of SWNT in various solvents. The PS‐SWNT composite prepared via a conventional emulsion polymerization showed SWNT bundles entirely covered with PS, whereas the PS‐SWNT composite prepared via a miniemulsion polymerization showed SWNT partially covered with crosslinked PS nanoparticles. The method of mixing SWNTs with PS latex did not show the well dispersed state of carbon nanotubes because PS was not crosslinked and was dissolved in a solvent, and nanotubes separated from PS precipitated. So the PS nanoparticle‐SWNT composite had lower electrical resistance, and higher mechanical strength than the other composites made by the latter two methods. As the amount of SWNT increases, the bare surface area of SWNT increases and the electrical conductivity increases in the composite made by the miniemulsion polymerization. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 573–584, 2006     

Gold ultra-microelectrode arrays: application to the steady-state voltammetry of hydroxide ion in aqueous solution.

Gold ultra-microelectrode arrays are used to explore the electrochemical oxidation of hydroxide ions and are shown to be analytical useful. Two types of ultra-microelectrode arrays are used; the first consist of 256 individual electrodes of 5 microm in radius, 170 of which are electrochemically active in a cubic arrangement which are separated from their nearest neighbour by a distance of 100 microm. The second array compromises 2597 electrodes of 2.5 microm in radius and of which 1550 of which are electrochemically active in a hexagonal arrangement separated by the nearest neighbour by 55 microm. Well defined voltammetric waves are found with peak currents proportional to the concentration of hydroxide ions in the range 50 microM to 1 mM. Detection limits of 20 microM using the 170 ultra-microelectrode and 10 microM with the 1550 ultra-microelectrode array are shown to be possible but with a higher sensitivity of 4 mA M(-1) observed using the 1550 ultra-microelectrode array compared to 1.2 mA M(-1) with the 170 ultra-microelectrode array.     

Mössbauer, X-ray diffraction and magnetization studies of Fe–Mn–Al–Nb alloys prepared by high energy ball milling

Fe₆₀Mn₁₀Al₂₀Nb₁₀, (Fe₆₀Mn₁₀Al₃₀)₉₅Nb₅ and (Fe₆₀Mn₁₀Al₃₀)₉₀Nb₁₀ ball milled powdered alloys were investigated using X-ray diffraction, Mössbauer spectrometry, thermomagnetic (TGM) and magnetization measurements. We studied the influence of Nb content and of different milling times on the structural and magnetic properties. Two main features can be concluded: (1) the FeAlMn induces a BCC phase whatever the Nb content is, and (2) as both increasing Nb content and milling time give rise to an highly disordered state in conjunction with a decrease of the ferromagnetic behavior.     

A simple model for magnetic after-effects in magnetite at room temperature

Magnetic after-effects in vacancy-doped magnetite at room temperature are considered on the basis of a statistical thermodynamic treatment. In this paper we study the kinetics of a very small vacancy concentration distributed on the four non-equivalent octahedral sites of the inverse spinel structure. It is to be noted that satisfactory agreement is found between recent experimental results and the theoretical model.     

On conservative approximation by linear polynomial operators an extension of the Bernstein's operator

In this work we study linear polynomial operators preserving some consecutive i-convexities and leaving invariant the polynomials up to a certain degree. First, we study the existence of an incom patibility between the conservation of certain i-convexities and the invariance of a space of polynomials. Interpolation properties are obtained and a theorem by Berens and DeVore about the Bernstein's operator is extended. Finally, from these results a generalized Bernstein's operator is obtained. This work was supported by Junta de Andalucia. Grupo de investigación: Matemática Aplicada. Código: 1107     

KWTA networks and their applications

Winner-Take-All (WTA) or K-Winner-Take-All (KWTA) networks have been frequently used as the basic building blocks of complex neural networks. This paper introduces a new selection rule for network connections that implements stable KWTA networks. To widen the applications of WTA networks, a new class of WTA networks is proposed, and their efficient design methods are presented. We demonstrate the properties of the generalized class of WTA networks, through three application examples.     

Isomorphisms of integral alternative loop rings

This paper first settles the “isomorphism problem” for alternative loop rings; namely, it is shown that a Moufang loop whose integral loop ring is alternative is determined up to isomorphism by that loop ring. Secondly, it is shown that every normalized automorphism of an alternative loop ringZ L is the product of an inner automorphism ofQ L and an authomorphism ofL.     

New extraction method for the analysis of linear alkylbenzene sulfonates in marine organisms. Pressurized liquid extraction versus Soxhlet extraction

A new method has been developed for the determination of linear alkylbenzene sulfonates (LAS) from various marine organisms, and compared with Soxhlet extraction. The technique applied includes the use of pressurized liquid extraction (PLE) for the extraction stage, preconcentration of the samples, purification by solid-phase extraction (SPE) and analysis by liquid chromatography with fluorescence detection. The spiked concentrations were added to the samples (wet mass of the organisms: Solea senegalensis and Ruditapes semidecussatus), which were homogenized and agitated continuously for 25 h. The samples were extracted by pressurized hot solvent extraction using two different extraction temperatures (100 and 150 degrees C) and by traditional Soxhlet extraction. The best recoveries were obtained employing pressurized hot solvent extraction at 100 degrees C and varied in the range from 66.1 to 101.3% with a standard deviation of between 2 and 13. Detection limit was between 5 and 15 microg kg(-1) wet mass using HPLC-fluorescence detection. The analytical method developed in this paper has been applied for LAS determination in samples from a Flow-through exposure system with the objective of measuring the bioconcentration of this surfactant.