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This paper deals with the interpolation of given real boundary values into a bounded domain in Euclidean n-space, under a prescribed gradient bound. It is well known that there exist an upper solution (an inf-convolution) and a lower solution (a sup-convolution) to this problem, provided that a certain compatibility condition is satisfied. If the upper and lower solutions coincide somewhere in the domain, then several interesting consequences follow. They are considered here. Basically, the upper and lower solutions must be regular wherever they coincide.
This paper investigates the association between opportunities to take part in work-environment dialogue and peripheral labour market position, which was operationalised in terms of short-term employment. A stratified representative sample from Statistics Sweden's Labour Market Survey – with 50 per cent of persons on short-term, and 50 per cent on a long-term contracts – is analysed (n=1,564). More contingent workers than permanent employees report a lack of work environment knowledge. They perceive themselves to be disfavoured with regard to the education/training required to do their job. Further, they regard their form of employment as making it more difficult to raise criticism and to get their viewpoints heard. Women show a greater risk of not being involved in work environment issues. The findings are discussed in relation to legislation and further research.
This work treats the injection of certain thermoplastics into a planar mould cavity. The problem is to determine the filling pattern. It is assumed that the thermoplastic can be modelled as a non-Newtonian fluid of power-law type whose power-law exponent is relatively small (the pseudo-plastic case). The dependence of the viscosity on thermal variations is neglected. The mathematical description leads to a moving boundary problem, for which an asymptotic solution is found. According to this solution, the expansion of the polymer melt follows the level sets of an interior distance function, which is determined by the geometry of the mould, and the position of the injection point. The solution is easily computed and results of numerical experiments are given.
This paper reviews the governing equations for a plane Hele–Shaw flow of a power-law fluid. We find two closely related partial differential equations, one for the pressure and one for the stream function. Some mathematical results for these equations are presented, in particular some exact solutions and a representation theorem. The results are applied to Hele–Shaw flow. It is then possible to determine the flow near an arbitrary corner for any power-law fluid. Other examples are also given.
This paper gives sufficient conditions ensuring that a non-linear control system of the form
is controllable by means of control functions u(t), such that each ui(t) only takes two values, with a finite number of switches. It is assumed that the ‘unperturbed’ system ẋ = A(t)x + B(t)u is controllable in the usual sense, i.e. by measurable and bounded controls.
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