Convergence global uniform

Theorem 5.1 If the rate constants are bounded as in (2.32) and (2.33), then, there exists a set of observer gains such that the state estimation error x is globally uniformly convergent lo 0 as / -> oc and the parameter estimation error 90 is bounded for every t. 

Hence, V0 is negative semi-definite this guarantees the boundedness of and 90. By invoking Barbalat s lemma [3], it can be recognized that V0 -> 0, which implies the global uniform convergence to 0 of as t -> oo, while 9a is only guaranteed to be uniformly bounded. ... 

In contrast to the upper water column, deep water has rather uniform and small Cd isotopic fractionation despite the fact that Cd concentrations increase along the global deep-water pathway from the Atlantic to the Pacific Ocean [31-34]. The Cd in deep water that is remineralized from exported organic matter, must thus have a small Cd isotopic fractionation [32]. To the extent that the bulk of the surface Cd is taken up by phytoplankton, this result is not inconsistent with isotopic fractionation by phytoplankton the isotopic composition of any nutrient in the biomass must converge to that of the source (upwelled) water when the fraction of nutrient taken up increases, as observed, for example, for nitrogen [35]. More studies on Cd isotopic fractionation by different phytoplankton taxa under various conditions are warranted to help understand the isotopic composition of Cd in the oceans. 

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