Exempel på asymptotic

• The study focuses on the asymptotic properties of equilibrium paths.

• The asymptotic solution (5.3) also be used to obtain expressions from (3.14)for can the fluctuating viscous stresses a t the wall.

• Moreover, in many cases, the rejection rates based on finite-sample critical values increase substantially, reflecting the convergence of asymptotic and finite-sample critical values.

• For the other sum in the variance the more precise asymptotic estimates (5.1) and (5.2) are required.

• Also, an interface appears for the minimal solutions, whose asymptotic velocity is c*.

• However, when (6.43) applies, additional regions are required, the asymptotic structure being as described in the previous subsection.

• Note that the statistical theory developed in this paper depends crucially on the assumption that spectral density estimates have an asymptotic normal distribution.

• The numerical integration is started at the singular point r = 0 by using asymptotic expression of the solutions.

• Our computations show that the asymptotic drop shape consists of a compact, nearly spherical drop that encloses a spike of entrained ambient fluid.

• We now review some of the elementary notions of the method of matched asymptotic expansions in the context of expansions of mean velocity.

• Again far downstream from the leading edge, we expect an asymptotic behaviour independent of streamwise distance.

• The concepts of asymptotic and local invariances suggest that the flow structure sufficiently downstream from the origin should be universal.

• For streaming below a certain threshold we determined matched asymptotic expansions for the electric potential, ion number density and ion velocity.

• A homogenization algorithm is implemented, and asymptotic formulae are derived for the effective elastic moduli of the periodic structures.

• The empirical laws have not been interpreted as asymptotic laws although some small systematic departures have been noted.