How to build a new athletic track to break records

We introduce a new optimal control model which encompasses pace optimization and motor control effort for a runner on a fixed distance. The system couples mechanics, energetics, neural drive to an economic decision theory of cost and benefit. We find how effort is minimized to produce the best running strategy, in particular, in the bend. This allows us to discriminate between different types of tracks and estimate the discrepancy between lanes. Relating this model to the optimal path problem called the Dubins path, we are able to determine the geometry of the optimal track and estimate record times.

Optimal Inspection Methodology for Offshore Structures Based on an Economic Decision Theory

About 200 marine platforms are installed in the Mexican sector of the Gulf of Mexico so that maintenance and inspection schedules play an important role to avoid excessive structural deterioration of the oil facilities and at the same time to keep the facilities within acceptable safety margins. Large costs associated with inspection and repair actions moved managers towards the application of an optimal strategy in order to minimize inspection expenses. For these purposes, it is necessary to consider deterioration process such as fatigue crack growth under the influence of uncertain wave loading which is the dominant force while effort is focused on maintaining structural integrity and safe production. This paper presents an optimal inspection methodology for offshore structures based on an economic decision theory, bearing in mind that large costs are associated with structural failure and extensive inspection and repairs. A system failure analysis of a given sub set of the critical structural components is included as well as a mathematical framework for the assessment of failure and repair cost associated.

Premium Calculation by Transforming the Layer Premium Density

This paper examines a class of premium functionals which are (i) comonotonic additive and (ii) stochastic dominance preservative. The representation for this class is a transformation of the decumulative distribution function. It has close connections with the recent developments in economic decision theory and non-additive measure theory. Among a few elementary members of this class, the proportional hazard transform seems to stand out as being most plausible for actuaries.

Use of Response Surface Methodology to Select a Cutting Tool to Maximize Profit

A technique is presented which uses Response Surface Methodology to select a cutting tool in order to maximize profit. Different tools are analyzed to determine what combinations of cutting speed, feed, and depth of cut will give maximum profit for each kind of tool. Only then may different tools be compared. There is a possibility that the tool which is capable of yielding maximum profit may be most economical at operating conditions which are somewhat anomolous. With conventional tests a suboptimal tool may be selected, or the best tool may be used at suboptimal operating conditions. The contribution of this article is the expression of profit as a function of the direct physical decision variables and the subsequent optimization. The use of these techniques with economic decision theory is unique.