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Then we can construct a limit pseudo orbit ξ as follows.
Our goal is to construct a limit weight function β (the same for each equation) using the approach of BV diffusion coefficients by piecewise-constant coefficients.
Then we can construct a limit pseudo orbit { ( x i, t i ) : t i ≥ 1, i ∈ Z } as follows: for all i ∈ Z, (i) X i ( x ) = x i, t i = 1, i > 0 and (ii) X i ( y ) = x i, t i = 1, i ≤ 0. By the limit shadowing property, there are z ∈ M and an increasing homeomorphism h : R → R with h ( 0 ) = 0 such that for i ∈ Z, d ( X h ( t ) ( z ), X t − S i ( x i ) ) → 0 as i → ± ∞.
To construct a limit cycle representation of the cyclic force variation, we define an effective centre-of-mass for the flagellum, x (t ) = ∑ i N (| f i | x i (t ) ) / ∑ i N (| f i | ), averaging over all N discretised force vectors f i applied at points x i along the flagellum.
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In Le Rousseau's paper, the author constructed a limit weight function as he approached BV coefficient by piecewise-constant coefficient.
While making the latest instalment of Canadian Cannabis, which focused on edibles, I came up with the idea of constructing a limit-testing sundae featuring a range of the amazing edible products available on the market.
We make no attempt to construct a lower limit, because the physical constraints upon such a limit are not obvious.
A method to construct a forming limit corresponding to local necking is sought for aluminum alloy sheet metal.
Thus you can construct a magnitude limited sample by calculating the absolute magnitudes of the galaxies in the survey using the equation above and then creating a new sample, centered on the GA, but cut to be brighter (more negative) than -22.0.
Thus you can construct a magnitude limited sample by calculating the absolute magnitudes of the galaxies in the survey using the equation above and then creating a new sample, centered on Virgo, but cut to be brighter (more negative) than -22.0.
Then we construct a δ-limit pseudo orbit ξ = { x i } i ∈ Z ⊂ R ( f ) as follows.
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