A maximal domain of preferences for tops-only rules in the division problem

The division problem consists of allocating an amount M of a perfectly divisible good among a group of n agents. Sprumont (1991) showed that if agents have single-peaked preferences over their shares, the uniform rule is the unique strategy-proof, efficient, and anonymous rule. Ching and Serizawa (1998) extended this result by showing that the set of single-plateaued preferences is the largest domain, for all possible values of M, admitting a rule (the extended uniform rule) satisfying strategy-proofness, efficiency and symmetry. We identify, for each M and n, a maximal domain of preferences under which the extended uniform rule also satisfies the properties of strategy-proofness, efficiency, continuity, and "tops-onlyness". These domains (called weakly single-plateaued) are strictly larger than the set of single-plateaued preferences. However, their intersection, when M varies from zero to infinity, coincides with the set of single-plateaued preferences.

Solvable dynamics in a system of interacting random tops

A new solvable model of synchronization dynamics is introduced. It consists of a system of long range interacting tops or magnetic moments with random precession frequencies. The model allows for an explicit study of orientational effects in synchronization phenomena as well as nonlinear processes in resonance phenomena in strongly coupled magnetic systems. A stability analysis of the incoherent solution is performed for different types of orientational disorder. A system with orientational disorder always synchronizes in the absence of noise.

Evaluation of Concrete Sealers for Use on Bridge Pier Tops and Abutments, R-242, 1971

Many reports have been written concerning investigations of concrete sealants. The primary concern of most investigators is the protection of bridge decks from de-icing chemicals which cause surface scaling and, when allowed to permeate to reinforcing steel, result in deep spalling and general concrete deterioration. The problem of protecting abutments and pier tops from salt solutions entails a significantly different approach than the problem of protecting bridge decks. The epoxy resins become eligible as a protective material since one need not be concerned with slipperiness or its abrasive characteristics. Protection with linseed oil at regular intervals would prove bothersome because of the inaccessibility of pier tops after the deck is placed. The primary purpose of this investigation was to evaluate various commercial products in terms of their ability to prevent concrete scaling of bridge abutments and pier tops which are subject to salt water deterioration.

Coriolis interactions about x-y axes in symmetric tops

Selection rules and matrix elements are derived for Coriolis interactions between vibrational levels due to rotation about (x, y) axes in symmetric top molecules. The theory is developed in detail for the case of interaction between an A1 and an E species vibrational level in a C3v molecule; perturbations to both the positions and the intensities of the rovibration transitions in the spectrum are considered. A computer program has been written which calculates exactly the perturbed spectrum of two interacting rovibration bands according to this model, the results being presented directly by a graph plotter connected to the computer. This has been used to interpret perturbations observed in two pairs of interacting fundamentals in the spectrum of CH3F (ν2 - ν5 and ν3 - ν6) and one pair in CD3Cl (ν2 - ν5). The resulting analysis of the observed spectrum leads to new values for some vibration-rotation interaction constants and also leads to a unique determination of the sign relationship between the dipole moment derivatives in each pair of interacting normal vibrations. These sign relations are summarized in Figs. 8, 12, and 15.

Calcium isotopes in planktonic foraminifera - core tops and sediment trap samples

For paleoceanographic studies, it is important to understand the processes that influence the calcium (Ca) isotopic composition of foraminiferal calcite tests preserved in the sediment record. Seven species of planktonic foraminifera from coretop sediments collectively exhibited a Ca temperature dependent fractionation of 0.013 per mil per °C. This is in agreement with previously published estimates for most species of planktonic foraminifera as well as biogenic and inorganic calcite and aragonite. Four species of planktonic foraminifera collected from a sediment trap showed a considerable amount of scatter and no consistent temperature dependent fractionation. Analyzed size fractions of coretop samples show no significant relationship with d44/40Ca. However, preliminary results suggest that the symbiotic and spinose foraminifera G. sacculifer might exhibit a relationship between test size and d44/40Ca. A one-box model in which Ca isotopes are allowed to fractionate by Rayleigh distillation from a biomineralization reservoir (internal pool) was used to constrain the isotopic composition of the original biomineralization Ca reservoir, assuming around 85% of the Ca reservoir is precipitated and the fractionation factor during precipitation is 0.9985 + 0.00002(T ºC). To explain the foraminiferal Ca isotope data, this model indicates that the Ca isotopic composition of the biomineralization reservoir is offset from seawater (approximately -0.8per mil).