The Shock Location for a Class of Sensitive Boundary Value Problems

Bohé, Adriana

doi:10.1006/jmaa.1999.6399

Cited by 8 publications

(3 citation statements)

References 13 publications

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“…Now y ∈ V j−1 by the induction hypothesis. Applying (4), and the fact that N j ⊆ N i for all i with 1 ≤ i < j we obtain…”

Section: Proofmentioning

confidence: 99%

“…Neutrices and external numbers have occurred in various settings (the terminology not being explicit in all papers): singular perturbation theory (in particular as thicknesses of boundary layers [1,11,12,[2][3][4]) asymptotic approximations (domains of validity of asymptotic behavior and reasoning [23]), probability theory (mass and queue of probability distributions [24]) and mathematical psychology (imperfect knowledge of maximal utility [25]). Special mention has to be made of the work of Bosgiraud, who applies the external numbers to problems of modeling and calculation of insecure statistical events in a series of papers [5][6][7][8][9].…”

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confidence: 99%

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A decomposition theorem for neutrices

Berg¹

2010

Annals of Pure and Applied Logic

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a b s t r a c tNeutrices are convex additive subgroups of the nonstandard space R k , most of them are external sets. Because of the convexity and the invariance under some translations and multiplications, external neutrices are models for orders of magnitude. One dimensional neutrices have been applied to asymptotics, singular perturbations, and statistics. This paper shows that in R k , with standard k, every neutrix is the direct sum of k neutrices of R. These components may be chosen to be orthogonal.

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“…Now y ∈ V j−1 by the induction hypothesis. Applying (4), and the fact that N j ⊆ N i for all i with 1 ≤ i < j we obtain…”

Section: Proofmentioning

confidence: 99%