Constructions of economic functions and calculations of marginal rates in DEA using parametric optimization methods

The aim of the paper is to present and substantiate a technique to visualize DEA modelling results without any loss of mathematical rigour. The proposed family of parametric optimization methods allows one to construct an intersection of the multidimensional frontier with a two-dimensional plane determined by any pair of given directions. This approach reduces the efficiency analysis of production units to the investigation of well-known functions in economics. We also propose constructive methods to calculate marginal rates of substitution, marginal rates of transformation and so on.     

Universal spaces for asymptotic dimension

We construct a universal space for the class of proper metric spaces of bounded geometry and of given asymptotic dimension. As a consequence of this result, we establish coincidence of asymptotic dimension with asymptotic inductive dimension.     

Allocating electricity transmission costs through tracing: a game-theoretic rationale

Tracing is a method of assigning flows in an electricity network to particular generators and loads, assuming perfect mixing at each node. It can be used to assign costs to transmission users. We show that the resulting allocation is equal to the Shapley value of an equivalent co-operative game.     

A branch and bound algorithm for the robust shortest path problem with interval data

Many real problems can be modelled as robust shortest path problems on interval digraphs, where intervals represent uncertainty about real costs and a robust path is not too far from the shortest path for each possible configuration of the arc costs.A branch and bound algorithm for this problem is presented.     

On the Essential Self-Adjointness of Wick Powers of Relativistic Fields and of Fields Unitary Equivalent to Random Fields

The essential self-adjointness on a natural domain of the sharp-time Wick powers of the relativistic free field in two space-time dimension is proven. Other results on Wick powers are reviewed and discussed.     

Timelike Minimal Surfaces via Loop Groups

This work consists of two parts. In Part I, we shall give a systematic study of Lorentz conformal structure from structural viewpoints. We study manifolds with split-complex structure. We apply general results on split-complex structure for the study of Lorentz surfaces.In Part II, we study the conformal realization of Lorentz surfaces in the Minkowski 3-space via conformal minimal immersions. We apply loop group theoretic Weierstrass-type representation of timelike constant mean curvature for timelike minimal surfaces. Classical integral representation formula for timelike minimal surfaces will be recovered from loop group theoretic viewpoint.     

Isomorphisms of Certain Locally Nilpotent Finitary Groups and Associated Rings

For any chain Γ the ring NT(Γ,K) of all finitary Γ-matrices ‖a _ij ‖ _i,jεΓ over an associative ring K with zeros on and above the main diagonal is locally nilpotent and hence radical. If R′=NT(Γ′,K′),R=NT(Γ,K) and either |Γ|<∞ or K is a ring with no zero-divisors, then isomorphisms between rings R and R′, their adjoint groups and associated Lie rings are described.