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- Asymptotic Expansions (1)
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Articles 1 - 3 of 3
Full-Text Articles in Physical Sciences and Mathematics
Inverse Limits On [0,1] Using Logistic Bonding Maps, Marcy Barge, William Thomas Ingram
Inverse Limits On [0,1] Using Logistic Bonding Maps, Marcy Barge, William Thomas Ingram
Mathematics and Statistics Faculty Research & Creative Works
In this paper we investigate inverse limits on [0,1] using a single bonding map chosen from the logistic family, fλ (x) = 4λx(1-x) for 0 ≤ λ ≤ 1. Many interesting continua occur as such inverse limits from arcs to indecomposable continua. Among other things we observe that up through the Feigenbaum limit the inverse limit is a point or is hereditarily decomposable and otherwise the inverse limit contains an indecomposable continuum. © 1996 Elsevier Science B.V. All rights reserved.
Applications Of The Upside-Down Normal Loss Function, David Drain, A. M. Gough
Applications Of The Upside-Down Normal Loss Function, David Drain, A. M. Gough
Mathematics and Statistics Faculty Research & Creative Works
The upside-down normal loss function (UDNLF) is a weighted loss function that has accurately modeled losses in a product engineering context. The function''s scale parameter can be adjusted to account for the actual percentage of material failing to work at specification limits. Use of the function along with process history allows the prediction of expected loss-the average loss one would expect over a long period of stable process operation. Theory has been developed for the multivariate loss function (MUDNLF), which can be applied to optimize a process with many parameters-a situation in which engineering intuition is often ineffective. Computational formulae …
Asymptotic Analysis Of Oseen Equations For Small Viscosity, R. Temam, X. Wang
Asymptotic Analysis Of Oseen Equations For Small Viscosity, R. Temam, X. Wang
Mathematics and Statistics Faculty Research & Creative Works
In this article, we derive explicit asymptotic formulas for the solutions of Oseen's equations in space dimension two in a channel at large Reynolds number (small viscosity ε). These formulas exhibit typical boundary layers behaviors. Suitable correctors are defined to resolve the boundary obstacle and obtain convergence results valid up to the boundary. We study also the behavior of the boundary layer when simultaneously time and the Reynolds number tend to infinity in which case the boundary layer tends to pervade the whole domain.