Division and the Giambelli Identity

Given two polynomials f(x) and g(x), we extend the formula expressing the remainder in terms of the roots of these two polynomials to the case where f(x) is a Laurent polynomial. This allows us to give new expressions of a Schur function, which generalize the Giambelli identity.Comment: 9 pages, 1 figur

ECONOMIES OF SIZE AMONG MUNICIPAL WATER AUTHORITIES IN PENNSYLVANIA

Resource /Energy Economics and Policy,

Distribution of Fish Within Headwater Riffles of the Illinois River System, Washington County, Arkansas

Quantitative sampling of fish was performed in five headwater riffles of the Illinois River System, Washington County, Arkansas during low flow conditions. This study revealed differing fish species composition, biomass and feeding guild segregation between head and tail riffle reaches in 1st through 3rd order. Thirty species representing 10 families were identified. Of this number, darters (Percidae), sculpins (Cottidae), madtoms (Ictaluridae), and central stonerollers (Campostoma anomalum) (Cyprinidae) comprised 67 to 98 percent of riffle head populations. Fish biomass was greater for riffle head areas (0.58-6.6/0.28-2.0 g/m2 ) within sectivores and herbivores dominating. Total fish numbers decreased from riffleheads to tails, while number of species increased. Dominant fish groups in tail areas were minnows (Cyprinidae), darters (Percidae), and sunfishes (Centrarchidae). Feeding guild fish groups in tail areas were predominately insectivore and insectivore-piscivore. Stomach analysis of Cottus carolinae, the dominant headwater riffle predator, indicated selective feeding of macrobenthic invertebrates and fish based on size class. Abundance of herbivore and insectivore fishes in riffles, particularly head reaches, suggests a correlation with positive rheotaxic behavior, microhabitat preference or abundance of macrobenthic invertebrate populations

Dynamics of Multidimensional Secession

We explore a generalized Seceder Model with variable size selection groups and higher dimensional genotypes, uncovering its well-defined mean-field limiting behavior. Mapping to a discrete, deterministic version, we pin down the upper critical size of the multiplet selection group, characterize all relevant dynamically stable fixed points, and provide a complete analytical description of its self-similar hierarchy of multiple branch solutions.Comment: 4 pages, 4 figures, PR

Recent changes in U. S. family finances: results from the 1998 Survey of Consumer Finances

Using data from the Federal Reserve Board's two most recent Surveys of Consumer Finances, this article provides a detailed picture of changes in the financial condition of U.S. families between 1995 and 1998. The financial situation of families changed notably in the three-year period. While income continued a moderate upward trend, net worth grew strongly, and the increase in net worth was broadly shared by different demographic groups. A booming stock market accounts for a substantial part of the rise in net worth, but the data also suggest that improvements in financial circumstances extended to many families that did not own stocks. The indebtedness of families grew, but less rapidly than their assets. Nonetheless, compared with 1995, debt repayments in 1998 accounted for a larger share of the income of the typical family with debt, and the proportion of debtors who were late with their payments by sixty days or more in the year preceding the survey was also higher.Income ; Consumer behavior ; Saving and investment