On the second smallest distance between finitely many points on the sphere

In the following note we investigate the second smallest distance between finitely many points on the sphere. Actually we look for the smallest upper bound for the second smallest distance between n points on the unit sphere. We solve this problem for n=9 and also we give a general, non-trivial upper bound for the second smallest distance of n points with n9.Supported by the Hungarian National Foundation for Scientific Research, Number 1238.     

On the Role of Mixed Strategies in Elementary Decision Analysis and Related Decision-Support-System Treatments

We first demonstrate that mixed strategies are relevant in decision analysis for a maximin decision-maker quite apart from any game-theory considerations. This rectifies the apparent misconception that results from MS/OR textbooks which discuss mixed strategies only in the game-theory setting. Next we show an example of an implementable mixed strategy, by which we mean a mixed decision strategy which does not require randomization for its implementation. This application is to portfolio construction.     

Optimal Discrete Approximations for Continuous Outcomes with Applications in Decision and Risk Analysis

In decision and risk analysis, it is common to use discrete probability distributions to approximate uncertain events with continuous outcomes. This paper discusses how these approximations may be selected. A class of approximations based on a modification to Taguchi's work on tolerance analysis is shown to be optimal under assumptions of independent uncertainties with normally distributed outcomes. The approximation procedure is shown to be robust in many other situations and is extremely easy to use in practice. We also show how the approximation may be integrated into the process of subjective probability estimation by a ‘subject-matter expert’.     

Optimal Inventory Policies with Service-Level Constraints

In a practical situation it is often difficult to determine the value of the shortage costs for use in in ventory-control systems. However, in cost-minimization problems including service-level constraints, shortage costs are implicitly prevailing. With the purpose of exploring these relations, a continuous review (Q, r) stock-control system is considered, where the order points and lot sizes are computed simultaneously. Instead of explicitly expressing the shortage cost in the objective function, it is taken into consideration through a service-level constraint. The shadow price of this constraint can in some sense be interpreted as the shortage cost corresponding to the requested service level. By changing the value of the service level, interesting relations between shortage costs and service levels can be viewed for different sets of other inventory parameters. In order to investigate the sensitivity for probabilistic variations in the input data, two different probability distributions are used to describe the lead-time demand.     

Interpolatory properties of best rationalL 1-approximations

In this paper the distribution of the zeros of the error function for bestL ₁-approximation by rational functions fromR _n,m is considered. It is shown that the maximal distance between such zeros isO(1/(n–m)), ifn > m.Communicated by Edward B. Saff.