Area orthogonality in normed linear spaces

A new concept of orthogonality in real normed linear spaces is introduced. Typical properties of orthogonality (homogeneity, symmetry, additivity, ...) and relations between this orthogonality and other known orthogonalities (Birkhoff, Boussouis, Unitary-Boussouis and Diminnie) are studied. In particular, some characterizations of inner product spaces are obtained.     

Relative morsification theory

In this paper we develop a Morsification Theory for holomorphic functions defining a singularity of finite codimension with respect to an ideal, which recovers most previously known morsification results for non-isolated singularities and generalise them to a much wider context. We also show that deforming functions of finite codimension with respect to an ideal within the same ideal respects the Milnor fibration. Furthermore we present some applications of the theory: we introduce new numerical invariants for non-isolated singularities, which explain various aspects of the deformation of functions within an ideal; we define generalisations of the bifurcation variety in the versal unfolding of isolated singularities; applications of the theory to the topological study of the Milnor fibration of non-isolated singularities are presented. Using intersection theory in a generalised jet-space we show how to interpret the newly defined invariants as certain intersection multiplicities; finally, we characterise which invariants can be interpreted as intersection multiplicities in the above mentioned generalised jet space.     

Influence of the loading path on the strength of fiber-reinforced composites subjected to transverse compression and shear

The influence of the loading path on the failure locus of a composite lamina subjected to transverse compression and out-of-plane shear is analyzed through computational micromechanics. This is carried out using the finite element simulation of a representative volume element of the microstructure, which takes into account explicitly fiber and matrix spatial distribution within the lamina. In addition, the actual failure mechanisms (plastic deformation of the matrix and interface decohesion) are included in the simulations through the corresponding constitutive models. Two different interface strength values were chosen to explore the limiting cases of composites with strong or weak interfaces. It was found that failure locus was independent of the loading path for the three cases analyzed (pseudo-radial, compression followed by shear and shear followed by compression) in the composites with strong and weak interfaces. This result was attributed to the fact that the dominant failure mechanism in each material was the same in transverse compression and in shear. Failure is also controlled by the same mechanisms under a combination of both stresses and the failure locus depended mainly on the magnitude of the stresses that trigger fracture rather than in the loading path to reach the critical condition.     

Estimation of the aggregation number and core radius of microemulsions

Summary A simple working method for the estimation of the aggregation numbers and core radii from weight measurements of sodium bis-2-ethylhexylsulphosuccinate (aerosol-OT orAOT)/decane/water microemulsions of several compositions is proposed.Starting out from the hypotheses that (i) the density of the water inside the droplets is the same as that of free water, (ii) all the surfactant is localized as interface, and (iii) the penetration of the organic phase into the interface is negligible, values for the aggregation number and core radii comparable to those determined using more sophisticated methods were obtained.The results/methodological simplicity ratio may be of great advantage in kinetic work on reaction mechanisms in microemulsions.

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Abschätzung von Aggregationszahl und Radius von Mikroemulsionen

Zusammenfassung Es wird eine einfache Methode zur Abschätzung von Aggregationszahl und Core-Radius von Mikroemulsionen aus Gewichtsmessungen von Natriumbis-2-ethylhexylsulphosuccinat (aerosol-OT oderAOT)/Decan/Wasser-Mikroemulsionen verschiedener Zusammensetzung vorgeschlagen. Unter den Annahmen, daß (i) die Dichte von Wasser innerhalb der Aggregationen die gleiche als bei freiem Wasser ist, (ii) das ganze Emulsionsmittel in der Grenzfläche vorliegt und (iii) das Eindringen der organischen Phase in die Grenzfläche vernachlässigbar ist, können Werte für Aggregationszahlen und Core-Radien erhalten werden, die durchaus mit entsprechenden Werten aus aufwendigeren Methoden vergleichbar sind. Das Leistungsverhältnis (Ergebnisse/geringer Aufwand) ist sehr vorteilhaft und macht die Methode für kinetische Arbeiten zur Bestimmung von Reaktionsmechanismen in Mikroemulsionen interessant.

     

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.