Duality for location problems with unbounded unit balls

Given an optimization problem with a composite of a convex and componentwise increasing function with a convex vector function as objective function, by means of the conjugacy approach based on the perturbation theory, we determine a dual to it. Necessary and sufficient optimality conditions are derived using strong duality. Furthermore, as special case of this problem, we consider a location problem, where the “distances” are measured by gauges of closed convex sets. We prove that the geometric characterization of the set of optimal solutions for this location problem given by Hinojosa and Puerto in a recently published paper can be obtained via the presented dual problem. Finally, the Weber and the minmax location problems with gauges are given as applications.     

Temperature dependence of the density of calamitic and discotic nematic lyotropic liquid crystals containing sodium lauryl sulphate/decanol/water

Experimental results for the temperature dependence of density at normal pressure for two compositions of sodium lauryl sulphate/decanol/water solutions, exhibiting either a calamitic or a discotic lyotropic nematic phase at room temperature, are presented. Within the limits of experimental precision (±1 ×10^-5 g cm^-3), the systems show no jump in density at the nematic to isotropic phase transition. Over the studied temperature range, the mean thermal expansion coefficients were also evaluated.     

Comparison between different duals in multiobjective fractional programming

The present paper is a continuation of [2] where we deal with the duality for a multiobjective fractional optimization problem. The basic idea in [2] consists in attaching an intermediate multiobjective convex optimization problem to the primal fractional problem, using an approach due to Dinkelbach ([6]), for which we construct then a dual problem expressed in terms of the conjugates of the functions involved. The weak, strong and converse duality statements for the intermediate problems allow us to give dual characterizations for the efficient solutions of the initial fractional problem. The aim of this paper is to compare the intermediate dual problem with other similar dual problems known from the literature. We completely establish the inclusion relations between the image sets of the duals as well as between the sets of maximal elements of the image sets.      

High frequency parallel plate probe for the measurement of the complex viscosity of liquids

In this work an instrument is described which measures the complex shear viscosity of liquids in the kHz frequency range. The instrument is driven electromagnetically and operates in resonant mode. The measurement of the primary data, from which the rheological properties of the fluid sample are inferred, does not include any deflection amplitude measuring step and is purely digital. Models allowing the interpretation of the probe primary data in terms of fluid complex viscosity are presented. The theoretically predicted mechanical behaviour of the probe is compared with the measured one and the rheometric ability of the device is discussed.