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As follows from the above calculations, this means that SMS waves decay fast (γs ~ ω).
Therefore, when we consider our problem in L 2 ( R ), the exact data function g ˆ must decay fast.
With increasing solvent size, the radius of gyration and the diffusion coefficient of the polymer decay fast until a critical solvent size is reached.
In contrast with the classical situation, the oscillations involve approximation of the identities or semigroups whose kernels decay fast enough and the resulting estimates take into account their lack of localization.
On the other hand, the trapezoidal tau method which estimates the asymptotic variance exactly for linear systems suffers from the fact that the transients of the method do not decay fast enough in the context of very stiff systems.
Note that the functions A and B are continuous and have also continuous first derivatives, while their second derivatives with respect to φ and φ' have only logarithmic singularities and hence belong to L 2. Therefore on the curve C their Fourier coefficients in φ decay fast enough with larger indices and hence can be efficiently computed by the Fast Fourier Transform algorithm.
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If foliage rots under water, the flowers decay faster, and even the best smelling aromatic foliage produces a rank odor.
But also because wet newspapers will decay faster, and roots from young plants will be able to grow right through to the soil below.
The improvement in tone quality was enormous, because the ear normally expects nuances such as higher partials that decay faster than lower ones.
We would expect box-office on a sequel to be more front-loaded, so it's likely that Ultron will decay faster than Avengers did, probably falling short of its mighty £51.8m final tally.
We, therefore, hypothesized that the DH curve would decay faster than the NDH curve.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com