193 research outputs found

    Grid diagrams and Khovanov homology

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    We explain how to compute the Jones polynomial of a link from one of its grid diagrams and we observe a connection between Bigelow's homological definition of the Jones polynomial and Kauffman's definition of the Jones polynomial. Consequently, we prove that the Maslov grading on the Seidel-Smith symplectic link invariant coincides with the difference between the homological grading on Khovanov homology and the Jones grading on Khovanov homology. We give some evidence for the truth of the Seidel-Smith conjecture

    Fluorescent dissolved organic matter components as surrogates for disinfection byproduct formation in drinking water: a critical review

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    Disinfection byproduct (DBP) formation, prediction, and minimization are critical challenges facing the drinking water treatment industry worldwide where chemical disinfection is required to inactivate pathogenic microorganisms. Fluorescence excitation–emission matrices-parallel factor analysis (EEM-PARAFAC) is used to characterize and quantify fluorescent dissolved organic matter (FDOM) components in aquatic systems and may offer considerable promise as a low-cost optical surrogate for DBP formation in treated drinking waters. However, the global utility of this approach for quantification and prediction of specific DBP classes or species has not been widely explored to date. Hence, this critical review aims to elucidate recurring empirical relationships between common environmental fluorophores (identified by PARAFAC) and DBP concentrations produced during water disinfection. From 45 selected peer-reviewed articles, 218 statistically significant linear relationships (R2 ≥ 0.5) with one or more DBP classes or species were established. Trihalomethanes (THMs) and haloacetic acids (HAAs), as key regulated classes, were extensively investigated and exhibited strong, recurrent relationships with ubiquitous humic/fulvic-like FDOM components, highlighting their potential as surrogates for carbonaceous DBP formation. Conversely, observed relationships between nitrogenous DBP classes, such as haloacetonitriles (HANs), halonitromethanes (HNMs), and N-nitrosamines (NAs), and PARAFAC fluorophores were more ambiguous, but preferential relationships with protein-like components in the case of algal/microbial FDOM sources were noted. This review highlights the challenges of transposing site-specific or FDOM source-specific empirical relationships between PARAFAC component and DBP formation potential to a global model
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