We analyse the role of new weak and strong commensurability conditions on efficiency measures especially productivity measurement. If fails, then a index (indicator) may exhibit homogeneity bias yielding inconsistent contradictory results. In particular, we show that Luenberger indicator is sensitive to proportional changes in input-output quantities, while Malmquist not affected by such change...

An optical device for measuring high particle concentrations is presented. The sensor consists of two optical fibers used for the emission and reception of the light scattered by particles in suspension. To describe the light path in this medium, we developed a Monte Carlo calculation including a mean free path, a phase function for particle scattering, and an absorption rate. A similarity law ...

This is a review of various problems and results on the illumination of convex bodies in the spirit of combinatorial geometry. The topics under review are: history of the Gohberg–Markus–Hadwiger problem on the minimum number of exterior sources illuminating a convex body, including the discussion of its equivalent forms like the minimum number of homothetic copies covering the body; generalizat...

Conformal Killing vectors (CKVs) preserve the spacetime metric up to a factor. Homothetic vectors and Killing vectors are special cases of CKVs. Classification of some classes of spacetimes on the basis of CKVs give interesting results showing how homothetic and Killing vectors which form subsets of the set of CKVs can be recovered as a result of the above classification. ∗On leave from: Centre...

We represent interval ordered homothetic preferences with a quantitative homothetic utility function and a multiplicative bias. When preferences are weakly ordered (i.e. when indifference is transitive), such a bias equals 1. When indifference is intransitive, the biasing factor is a positive function smaller than 1 and measures a threshold of indifference. We show that the bias is constant if ...

• Input homotheticity is equivalent with output under the α -returns to scale technology. Hicks neutrality neutral technical change α-returns The Malmquist and Hicks-Moorsteen productivity indexes can coincide if technology either input homothetic or homothetic. neutral. We analyze two popular notions in production theory: notion of Both these are characterized by radial expansions contractions...