Reallocation of an infinetely divisible good

We consider the problem of reallocating the total initial endowments of an infinitely divisible commodity among agents with single-peaked preferences. With the uniform reallocation rule we propose a solution which satisfies many appealing properties, describing the effect of population and endowment variations on the outcome. The central properties which are studied in this context are population monotonicity, bilateral consistency, (endowment) monotonicity and (endowment) strategy-proofness. Furthermore, the uniform reallocation rule is Pareto optimal and satisfies several equity conditions, e.g., equal-treatment and envy-freeness. We study the trade-off between properties concerning variation and properties concerning equity. Furthermore, we provide several characterizations of the uniform reallocation rule based on these properties.mathematical economics and econometrics ;

Strategy-proof division with single-peaked preferences and initial endowments

We consider the problem of (re)allocating the total endowment of an infinitely divisible commodity among agents with single-peaked preferences and initial endowments. We propose an extension of the so-called uniform rule and show that it is the unique rule satisfying strategy-proofness, Pareto optimality, and an equal-treatment condition. This last condition is implied by the combination of anonymity and translation invariance, which fact is used to obtain a second characterization. The resulting rule turns out to be peaks-only and individually rational: the allocation assigned by the rule depends only on the peaks of the preferences, and no agent is worse off than at his initial endowment.mathematical economics and econometrics ;

Working at Higher Magnifications in Scanning Electron Microscopy with Secondary and Backscattered Electrons on Metal Coated Biological Specimens and Imaging Macromolecular Cell Membrane Structures

Membrane structures of macromolecular dimensions were imaged with high resolution secondary electron type I (SE-I) signal contrasts on metal coated biological specimens. The quality of the surface information was strongly dependent on the signal used for microscopy and on the properties of metal films, i.e., thickness, continuity, structure and decoration effects. Films of 10 nm thickness produced so much type II electrons that identical images were obtained with the conventional SE-II and BSE-II signals. In such images, the type I SE signal was so low that only very weak contrasts were recognizable. If the films - continuous or discontinuous - were composed of large metal aggregates (gold and platinum) a strong micro-roughness contrast was produced by the type II signal. At high magnifications (100,000 x) this background signal greatly reduced the S/N ratio of the SE-I signal. A similar effect was previously shown to be produced by the type III background signal. The type II background signal minimized when continuous films of small aggregates (tantalum and chromium) were applied. SE-I contrast dominated in the image if the film thickness was limited to 1 nm. Additionally, it was found that gold and platinum decorated membrane surface structures, \u3c 20 nm in size, and did not reveal all the topographic information available (size, shape, orientation spacing of small surface features) but merely displayed center-to-center distances. These decoration effects were avoided and extensive topographic information was obtained through surface coating with Ta or Cr