Interpreting a conformally flat pure radiation space-time

A physical interpretation is presented of the general class of conformally flat pure radiation metrics that has recently been identified by Edgar and Ludwig. It is shown that, at least in the weak field limit, successive wave surfaces can be represented as null (half) hyperplanes rolled around a two-dimensional null cone. In the impulsive limit, the solution reduces to a pp-wave whose direction of propagation depends on retarded time. In the general case, there is a coordinate singularity which corresponds to an envelope of the wave surfaces. The global structure is discussed and a possible vacuum extension through the envelope is proposed.Comment: 9 pages, Plain TeX, 2 figures. To appear in Class. Quantum Grav. Reference adde

A local potential for the Weyl tensor in all dimensions

In all dimensions and arbitrary signature, we demonstrate the existence of a new local potential -- a double (2,3)-form -- for the Weyl curvature tensor, and more generally for all tensors with the symmetry properties of the Weyl curvature tensor. The classical four-dimensional Lanczos potential for a Weyl tensor -- a double (2,1)-form -- is proven to be a particular case of the new potential: its double dual.Comment: 7 pages; Late

Dimensionally Dependent Tensor Identities by Double Antisymmetrisation

Some years ago, Lovelock showed that a number of apparently unrelated familiar tensor identities had a common structure, and could all be considered consequences in n-dimensional space of a pair of fundamental identities involving trace-free (p,p)-forms where 2p >= n$. We generalise Lovelock's results, and by using the fact that associated with any tensor in n-dimensional space there is associated a fundamental tensor identity obtained by antisymmetrising over n+1 indices, we establish a very general 'master' identity for all trace-free (k,l)-forms. We then show how various other special identities are direct and simple consequences of this master identity; in particular we give direct application to Maxwell, Lanczos, Ricci, Bel and Bel-Robinson tensors, and also demonstrate how relationships between scalar invariants of the Riemann tensor can be investigated in a systematic manner.Comment: 17 pages, 2 figure

USING BOTH SOCIOLOGICAL AND ECONOMIC INCENTIVES TO REDUCE MORAL HAZARD

Economists tend to focus on monetary incentives. In the model developed here, both sociological and economic incentives are used to diminish the apparent moral hazard problem existing in commodity grading. Training that promotes graders' response to sociological incentives is shown to increase expected benefits. The model suggests that this training be increased up to the point where the marginal benefit due to training equals its marginal cost. It may be more economical to influence the grader's behavior by creating cognitive dissonance through training and rules rather than by using economic incentives alone.Marketing,

Using Both Sociological and Economic Incentives to Reduce Moral Hazard

Economists tend to focus on monetary incentives. In the model developed here, both sociological and economic incentives are used to diminish the apparent moral hazard problem existing in commodity grading. Training that promotes graders' response to sociological incentives is shown to increase expected benefits. The model suggests this training be increased up to the point where the marginal benefit due to training equals its marginal cost. It may be more economical to influence the grader's behavior by creating cognitive dissonance through training and rules rather than by using economic incentives alone.grading, incentives, moral hazard, norms, social sanctions, Institutional and Behavioral Economics,

THE EFFECT OF ROUNDING ON THE PROBABILITY DISTRIBUTION OF REGRADING IN THE U.S. PEANUT INDUSTRY

This article determines the effect of rounding (pointing-off) of grade percentages to the nearest whole number on the probability distribution of regrading in the peanut industry. Results show that rounding causes graders to have to regrade an extra 4% of samples even when they follow all directions and make no mistakes. When rounding was not used, the sample weight had little effect on the probability of regrading. With rounding, the probability of regrading was reduced by beginning with a larger than 500-gram sample. Thus, rounding provides an incentive to take overweight samples in order to avoid regrading. Overweight samples can overestimate the value of peanuts. A low-cost way to improve peanut grading accuracy would be to round to tenths rather than whole numbers.grading, normal-jump distribution, peanuts, regrading, rounding, Crop Production/Industries,