29 research outputs found
Karhunen-Lo\`eve expansion for a generalization of Wiener bridge
We derive a Karhunen-Lo\`eve expansion of the Gauss process , , where is a
standard Wiener process and is a twice continuously
differentiable function with and . This
process is an important limit process in the theory of goodness-of-fit tests.
We formulate two special cases with the function
, , and , ,
respectively. The latter one corresponds to the Wiener bridge over from
to .Comment: 25 pages, 1 figure. The appendix is extende
Transformation Products and Human Metabolites of Triclocarban and Triclosan in Sewage Sludge Across the United States
Removal
of triclocarban (TCC) and triclosan (TCS) from wastewater
is a function of adsorption, abiotic degradation, and microbial mineralization
or transformation, reactions that are not currently controlled or
optimized in the pollution control infrastructure of standard wastewater
treatment. Here, we report on the levels of eight transformation products,
human metabolites, and manufacturing byproducts of TCC and TCS in
raw and treated sewage sludge. Two sample sets were studied: samples
collected once from 14 wastewater treatment plants (WWTPs) representing
nine states, and multiple samples collected from one WWTP monitored
for 12 months. Time-course analysis of significant mass fluxes (α
= 0.01) indicate that transformation of TCC (dechlorination) and TCS
(methylation) occurred during sewage conveyance and treatment. Strong
linear correlations were found between TCC and the human metabolite
2′-hydroxy-TCC (<i>r</i> = 0.84), and between the
TCC-dechlorination products dichlorocarbanilide (DCC) and monochlorocarbanilide
(<i>r</i> = 0.99). Mass ratios of DCC-to-TCC and of methyl-triclosan
(MeTCS)-to-TCS, serving as indicators of transformation activity,
revealed that transformation was widespread under different treatment
regimes across the WWTPs sampled, though the degree of transformation
varied significantly among study sites (α = 0.01). The analysis
of sludge sampled before and after different unit operation steps
(i.e., anaerobic digestion, sludge heat treatment, and sludge drying)
yielded insights into the extent and location of TCC and TCS transformation.
Results showed anaerobic digestion to be important for MeTCS transformation
(37–74%), whereas its contribution to partial TCC dechlorination
was limited (0.4–2.1%). This longitudinal and nationwide survey
is the first to report the occurrence of transformation products,
human metabolites, and manufacturing byproducts of TCC and TCS in
sewage sludge