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The paper translated here, "De Fractionibus Continuis Dissertatio", represents Euler's first published work on the theory of continued fractions, a subject to which he often returned during his long career. The emphasis is on basic identities and analytic theory, culminating in the development of the continued fraction expansion for e. A discussion of the periodic continued fractions associated with quadratic irrationalities is also included, but applications to number theory come in later publications. Readers interested in mathematical system theory will be concerned primarily with Euler's treatment of the Riccati equation, Sections 28-33. This aspect of the paper sewed as the chief motivation for the translation project. We are...
Gough, Christopher M.; Vogel, Christoph; Schmid, Hans Peter; Curtis, Peter S.
The temperate forests of North America may play an important role in future carbon (C) sequestration strategies. New multi-year ecosystem-scale C cycling studies are providing a process-level understanding of the factors controlling annual forest C storage. Using a combination of ecological and meteorological methods, we quantified the response of annual C storage to historically widespread disturbances, forest succession, and climate variation in a common forest type of the upper Great Lakes region. At our study site in Michigan, repeated clear-cut harvesting and fire disturbance resulted in a lasting decrease in annual forest C storage. However, climate variation exerts a strong...