FORECASTING MINERAL SUPPLY FROM MINERAL RENT DATA

An optimal control model of exhaustible resources is used to clarify the long run relationship between mineral rent and depletion cost at the industry level. A standard first order condition of the time rate of change of rents is reformulated to reveal that rent data may be used to help forecast the rise in extraction costs resulting from resource depletion. This application of the theory of exhaustible resources is illustrated using historical mineral industry rent and extraction cost data. A forecast of U.S. coal extraction costs, following the method proposed in this paper, suggests that future rates of extraction cost increases will be similar to rates experienced in the past.     

C 1 Quintic Splines on Type-4 Tetrahedral Partitions

Starting with a partition of a rectangular box into subboxes, it is shown how to construct a natural tetrahedral (type-4) partition and associated trivariate C ¹ quintic polynomial spline spaces with a variety of useful properties, including stable local bases and full approximation power. It is also shown how the spaces can be used to solve certain Hermite and Lagrange interpolation problems.     

Approximating weak Chebyshev subspaces by Chebyshev subspaces

We examine to what extent finite-dimensional spaces defined on locally compact subsets of the line and possessing various weak Chebyshev properties (involving sign changes, zeros, alternation of best approximations, and peak points) can be uniformly approximated by a sequence of spaces having related properties.     

An Electroacoustic Investigation of Concentrated Aqueous Suspensions of Calcium Pyrophosphate

The zeta potential of concentrated suspensions of calcium pyrophosphate were investigated using electroacoustics. The particles were negatively charged over the entire pH range studied. It proved impossible to reduce the pH of the suspension below 1.8, but the iso electric point could be estimated to occur at approximately pH 1. Two commercially available dispersants (one cationic and one anionic) were then added in small increments to the suspension in order to follow the change in zeta potential as the dispersants adsorbed onto the particles. From the shape of the curve it was possible to estimate the optimum adsorbed amount of dispersant required to fully coat the particles. The cationic dispersant adsorbed strongly and the optimum dosage was estimated at 2.5 ml of active polymer/kg of powder. Anionic dispersants are known to adsorb onto negatively charged ceramic oxide particles, but the anionic dispersant used in this study did not adsorb onto the negatively charged calcium pyrophosphate particles.     

On the evolution of islands

Letn cells be arranged in a ring, or alternatively, in a row. Initially, all cells are unmarked. Sequentially, one of the unmarked cells is chosen at random and marked until, aftern steps, each cell is marked. After thekth cell has been marked the configuration of marked cells defines some number of islands: maximal sets of adjacent marked cells. Let ξ _k denote the random number of islands afterk cells have been marked. We give explicit expressions for moments of products of ξ _k ’s and for moments of products of 1/ξ _k ’s. These are used in a companion paper to prove that if a random graph on the natural number is made by drawing an edge betweeni≧1 andj>i with probabilityλ/j, then the graph is almost surely connected ifλ>1/4 and almost surely disconnected ifλ≦1/4.     

A comparative study of the silent discharge treatment of saturated and unsaturated hydrocarbon polymers

Dielectric barrier air discharge treatment of polyethylene, polypropylene, polyisobutylene, polystyrene, and polyisoprene substrates has been characterized by x-ray photoelectron spectroscopy (XPS). The relative reactivities of these polymers towards silent discharge oxidation are rationalized in terms of ozone molecules interacting with an excited surface. © 1994 John Wiley & Sons, Inc.     

Information and asymptotic efficiency of the case-cohort sampling design in Cox's regression model

Efficiencies of the maximum pseudolikelihood estimator and a number of related estimators for the case-cohort sampling design in the proportional hazards regression model are studied. The asymptotic information and lower bound for estimating the parametric regression parameter are calculated based on the effective score, which is obtained by determining the component of the parametric score orthogonal to the space generated by the infinite-dimensional nuisance parameter. The asymptotic distributions of the maximum pseudolikelihood and related estimators in an i.i.d. setting show that these estimators do not achieve the computed asymptotic lower bound. Simple guidelines are provided to determine in which instances such estimators are close enough to efficient for practical purposes.