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For nonlinear systems filtering can be approximated in a systematic way by particle filters.
Of course this cannot ever be literally true, but it can be approximated in a sort of artificial way, so that life can be experienced as if it were true within a given community.
Moreover, he applied this result to prove that every analytic function can be approximated in a neighborhood of by the Legendre function with an error bound expressed by (see [13 16]).
As in compartmental models, this allows the full morphology of the dendritic tree to be approximated, in a trade-off between high speed (large Δx) and accuracy (small Δx).
To resolve the computational difficulty at the wave crest where the first-order derivative may diverge and the shockpeakon solution may form, the first-order spatial derivative term in the two-step equations will be approximated in a conservative form.
This is nonintuitive and highlights the fact that theoretical boundary conditions are only prescribed for continuous partial differential equations (PDEs), while they must be approximated in a consistent way (even though they could be exactly valued) when the PDEs are discretized.
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Really more of a stew than a soup, packed with potatoes and flavored with white wine, it could only be approximated in an American kitchen, because it contained distinctly Mediterranean seafood -- the small, ridged clams called vongole verace, scampi or langoustines and red mullet.
First, numerical lower and upper bound estimates for the macroscopic strength criterion of the stone column reinforced soil are approximated in a rigorous way with convex ellipsoidal sets, which makes the approximated criteria much easier to handle than the initial ones.
By means of a Linear Matrix Inequality (LMI) problem based on first order Pade approximation for time delay this performance guaranteed time delay bound is approximated in a systematic way.
Trumpets are approximated in a simple, chordal fanfare, and the guitar (no surprise here) is imitated in a pizzicato section.
For the sake of tractability, the observation model is approximated in a similar manner as in the VTS approach.
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