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Thirdly, based on the relationship properties between the normalizing signal and all the signals in the closed-loop system and on some important mathematical tools on discrete-time systems, as in the continuous-time case, a systematic stability and convergence analysis approach to the discrete indirect MRAC scheme is developed rigorously.
We reprove the discrete-time conclusions on the p and 2δ relationship properties between the input and the output, and the discrete-time swapping Lemmas 1 and 2. We also establish the properties of discrete-time adaptive law, define the normalizing signal, and relate the signal with all the signals in the closed-loop system.
The fluctuating nature of the generated light meant that for individual Q measurements we used a control sample with a known, flat reflectance that was used as our normalizing signal for the fibre.
The normalizing signal in SDS-extracts was α-tubulin while Na+/K+ ATPase was used in microsomal fractions.
A correction for the size bias was applied by normalizing signal to that found with wildtype (untreated) cells.
Future work may benefit from T1 mapping of the brain [31] since this will be sensitive to a broader range of tissue manganese concentrations while being unaffected by receive-coil artifacts – the primary motive for normalizing signal intensities in the present study.
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Densitometry analyses were conducted in ImageJ, and lipoylation and biotinylation levels were determined by normalizing signals for these cofactors to anti-HSP70 signal.
Comparison of the timing of different signaling events relied on normalizing signals to their peak intensities during macropinosome formation.
Data were analyzed by first subtracting background and then normalizing signals using a LOWESS filter (Locally-weighted Regression).
Accordingly, we accounted for changes to myocardial blood flow throughout DCM development by dynamically imaging the infused hyperpolarized [C]pyruvate bolus, and normalizing metabolite signals to the LV signal from infused [C]pyruvate.
Vehicle controls were used for normalizing biomarker signal for the treated samples.
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