Synergy of homomorphisms in relational systems

AbstractSuppose that a relational system R can be exhausted (in an obvious sense) by a family Rω, ω ϵ Ω, of subrelational systems, each of which can be mapped by a homomorphism onto a subrelational system Sω of a second relational system S. We show that, under suitable finiteness conditions, there is a homomorphism from R into S which finitely agrees with the homomorphisms mapping Rω onto Sω. A similar result holds for isomorphisms

Biogenic silica as an estimate of siliceous microfossil abundance in Great Lakes sediments

Biogenic silica concentration (BSi) in sediment cores from the Great Lakes is evaluated as an estimate of siliceous microfossil abundance. A significant linear relationship was found between measured BSi and diatom valve abundance for sediment cores from the Bay of Quinte, Lake Ontario, Lake Erie, Lake Michigan and Lake Superior and between measured BSi and diatom biovolume for Lake Erie, Lake Michigan, and Lake Superior but not for Lake Ontario. Diatom silica predicted from diatom species abundance and an estimated silica content per cell in the Lake Erie cores accounted for 117% and 103% of measured BSi, respectively. By contrast, predicted diatom silica could only account for 28% of measured BSi in the Lake Michigan core and only 25% in the Lake Superior core. A few large diatoms with a large silica content per cell comprised a major portion of predicted diatom silica in all cores. The discrepancy between chemically measured BSi and the silica predicted from diatoms in the Lake Michigan and Lake Superior cores was partially due to the inability of the regression model, used to estimate diatom silica content, to account for different degrees of silicification in the diatom asemblages from the more dissolved silica rich Lake Michigan and Lake Superior.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/42475/1/10533_2004_Article_BF02182994.pd