Cuomo, G. J., Rudstrom, M. V., Johnson, D. G., Anderson, J. E., Singh, A., Peterson, P. R., and Sheaffer, C. C., "
Nitrogen Fertilization Impacts on Stand and Forage Mass of Cool-Season Grass-Legume Pastures," in
Forage and Grazinglands, pp: doi:10.1094/FG-2005-0831-01-RS, 2005
Combining the benefits of legume N2 fixation and N fertilization may increase the productivity and profitability of pasture systems. Our objectives were to study the effects of N fertilization on productivity and persistence of legumes in mixtures with cool-season grasses under rotational stocking with short grazing periods. Twelve N fertilization regimes ranging from 0 to 336 kg of N per ha were applied annually to smooth bromegrass and reed canarygrass in monoculture and mixture with alfalfa, birdsfoot trefoil, and kura clover. Alfalfa was the dominant legume in mixtures with cool season grasses in 1999. As kura clover developed, it became the dominant legume species and by the trials end stands averaged over 70% in mixtures with both smooth bromegrass and reed canarygrass and across N treatments. Nitrogen fertilization did not affect alfalfa stands, but reduced kura clover stands by 17%. Smooth bromegrass-legume mixtures with no N fertilization produced more forage (10.5 ! Mg DM/ha) than any smooth bromegrass monoculture with N treatment (336 kg of N per ha produced 8.0 Mg DM/ha). Cost of forage mass in smooth bromegrass-legume mixtures was less than 50% of smooth brome monocultures. While N fertilization did not increase forage production in treatments with legumes, legumes were able to maintain vigorous stands with up to 336 kg of N per ha. Link: Click Here
Engin Sungur, Peh Ng, " A Decomposition of Copulas and Its Use." In Communications in Statistics--Theory and Methods: Regression Analysis, Volume 34, No. 12 pp. 2269-2282: Taylor and Francis, Inc., 2005
ABSTRACT: In this article, we create a decomposition that represents and describes the dependence structure between two variables. Since copulas provide a deep understanding of the dependence structure by eliminating the effects of the marginals, they play a key role in this study. We define a discretized copula density matrix and we decompose it into a set of permutation matrices by using the Birkhoff - von Neumann Theorem. This decomposition provides a way to effectively apply the concepts of copulas to solve problems in multivariate statistical data analysis.
KEY WORDS: Birkhoff - von Neumann theorem, Copulas, Discretized copulas, Gini's measure, Permutation matrix, Doubly stochastic matrix, Prior probability.
Peh H. Ng, "Designing Efficient Snow Plow Routes: A Service-Learning Project," In Mathematics in Service to the Community: Concepts and Models for Service-Lerning in the Mathematical Sciences, MAA Notes #66, pp. 69-80, The Mathematical Association of America, 2005
ABSTRACT: We descibe our experience incorporating service-learning into a combinatorics and graph theory course. In particular, we present a discrete mathematical model which we used to design efficient snow plow routes for Morris, Minnesota. We also discuss several issues of service-learning within the course as well as beyond the classroom.