Vector potential theory on nonsmooth domains in R<Superscript>3</Superscript> and applications to electromagnetic scattering

We study boundary value problems for the time-harmonic form of the Maxwell equations, as well as for other related systems of equations, on arbitrary Lipschitz domains in the three-dimensional Euclidean space. The main goal is to develop the corresponding theory for L^p-integrable bounday data for optimal values of p's. We also discuss a number of relevant applications in electromagnetic scattering.     

Strain of an anisotropic monolith during the excavation of minerals

We solve the problem of the normal and transverse shear in an anisotropic monolith during the excavation of a stratum of solid mineral. It is shown that the stress perturbation field in the rock is due to the whole extent of the excavated portion of the stratum. We study way in which the friction that arises between the interacting rock of the roof and the floor influences the strain and stress fields as the front of the excavation evolves, and also the influence of the extent of the excavated portion of the rock stratum on the magnitude of the accumulated tangential displacements. Three figures. Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 25, 1995, pp. 62–69.     

Developing models of decision making

Studies that focus on the decision making process can be classified in (at least) two ways: by psychological content and by contextual content. The first describes the degree to which the analysis focuses on the mental processes associated with decision making and the second deals with the degree to which the analysis is dependent upon the study's context. Several studies are examined in terms of where they fall in this two-dimensional taxonomy. Two analyses of maritime command and control conducted by the authors are examined more fully within this taxonomy. Both are context full, but are at opposite ends of the psychological content spectrum. These categorizations are useful in focusing future research aimed at developing models of decision making.     

Photodiffraction in InGaAs/InGaAsP multiple quantum wells enclosed in a microcavity

We report new results on the diffraction properties of photoinduced gratings in InGaAs/InGaAsP MQW structures. The original feature of this device is that the QWs are enclosed in an asymmetric Fabry–Perot microcavity in order to increase the diffraction efficiency. We observe oscillations in the diffraction efficiency due to resonant effects in the microcavity. The experimental spectra are compared with theory. Diffraction efficiency at 1.55 μm attains a maximum value of 2.7% at a write beam fluence of 260 μ J cm⁻², and then decreases at higher fluences. We explain this phenomenon by an absorption saturation at high excitation.     

Free Groups from Fields

In the nineteenth century, field theory brilliantly resolveda number of questions that had taxed mathematicians for centuries;for example, ‘The circle cannot be squared’ by straightedge and compass, and solving polynomial equations by radicalsis not always possible. These successes have continued to beheld up as superb examples of the power of mathematical thought,and are demonstrated at an undergraduate level. The purposeof this article is to provide another such natural example whichleads to a concrete realisation of the free group on 2 generators.