Synoptic water sampling at a fixed site monitoring station provides only limited ‘snap-shots’ of the complex water quality dynamics within a surface water system. However, water quality often changes rapidly in both spatial and temporal dimensions, especially in highly polluted urban rivers. In this study, we designed and applied a continuous longitudinal sampling technique to monitor the fine-...

We show that the set of bounded linear operators from X to X admits a Bishop–Phelps–Bollobás type theorem for numerical radius whenever X is `1(C) or c0(C). As an essential tool we provide two constructive versions of the classical Bishop–Phelps– Bollobás theorem for `1(C).

The Lactobacillus casei response to folate is normally estimated by measuring the culture turbidity after 16 to 20 hours' incubation. Streeter and O'Neill (1969) found that cultures containing serum grew more rapidly than similar cultures containing folic acid (PteGlu) unless grown into the stationary phase (44 hours). Others, however, have reported comparable results from 20and 44-hour assays ...

We study the celebrated Phelps-Koopmans theorem in environments with nonconvex production technologies. We argue that a robust failure of the theorem occurs in such environments. Specifically, we prove that the Phelps-Koopmans theorem must fail whenever the net output of the aggregate production function f (x), given by f (x) − x, is increasing in any region between the golden rule and the maxi...

The Phelps–Koopmans theorem states that if every limit point of a path of capital stocks exceeds the “golden rule,” then that path is inefficient: there is another feasible path from the same initial stock that provides at least as much consumption at every date and strictly more consumption at some date. I show that in a model with nonconvex technologies and preferences, the theorem is false i...