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For the case ℓ = ∞ the sharpness follows by just making a limit procedure with the result above in mind.
The proof of Theorem 2.1 is essentially based on a careful examination of a priori estimates and a limit procedure.
We propose a generalized ((n,N-n -fold Darboux tran,N-n -foldfor this system by usin,N-n -foldrDarbouxboux matransformationxpansion, and a limit procedure.
The n-fold DT is given by a gauge transformation, then a generalized DT is proposed through the Taylor expansion and a limit procedure.
Remark 1 This result is not the same as Theorem 4.4 in [4], where the traces that appear are defined by a limit procedure, not in the way stated here.
Thus, the model (3.2) can be understood as resulting from (1.6) after a limit procedure taking l ( k ) → ∞ has been applied and the firing rate functions are connected via the formal limit lim l ( k ) → ∞ l ( k ) f ¯ k = f ˜ k.
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Given the calculated gain values, a limiting procedure is applied.
A limiting procedure is carefully designed to suppress numerical oscillations.
Then, a limiting procedure is performed to obtain admissible decoding results.
To remove the non-physical oscillations, a limiting procedure is required.
As a limiting procedure, the case of resilient Kalman filter is derived.
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