Anti-PROC monoclonal antibody, clone BIQD-5072

Let X be a strictly convex Banach space, whose predual space is Y(X=Y '), having the weak star sequentially compact unit ball for the topology sigma (X,Y) and the weak star Kadec-Klee property. Furthermore, we suppose that the unit ball of the dual space X ' is weak star sequentially compact for the topology sigma (X ' ,X). Let C be a nonempty convex bounded closed subset of X; then every nonexpansive mapping T:C -> C has a fixed point. As consequences of this result, we generalize the Browder (Proc Natl Acad Sci USA 54:1041-1044, 1965) and Gohde (Math Nachr 301:251-258, 1965) theorems, where X is a uniformly convex Banach space and the Lin's theorem by Lin (Nonlinear Anal 68:2303-2308, 2008) and Lin (J Math Anal Appl 362:534-541, 2010), where X=l1.

The number of virus particles on Earth is frequently reported in the scientific literature and in general-interest publications as being on the order of 10(31), with some confusion about whether this is a high or low estimate. This number is often given without a source, although it should be attributed to a paper by Hendrix et al. published in 1999 (R. W. Hendrix, M. C. Smith, R. N. Burns, M. E. Ford, and G. F. Hatfull, Proc Natl Acad Sci U S A 96:2192-2197, 1999, https://doi.org/10.1073/pnas.96.5.2192). As with any oft-repeated statistic, it is informative to know how it has been derived and whether it should be revised in the light of new evidence. I review the history of the 10(31) estimate and use more recent assessments of the number of bacterial and viral particles in various habitats to conclude that the best estimate of the number of virus particles on Earth ("the Hendrix product") remains close to 10(31) and is unlikely to be either much less or much more than that.