Integral HOMFLY-PT and sl(n)-link homology

Using the diagrammatic calculus for Soergel bimodules, developed by B. Elias and M. Khovanov, as well as Rasmussen's spectral sequence, we construct an integral version of HOMFLY-PT and sl(n)-link homology.Comment: 26 pages, many figure

SgpDec : Cascade (de)compositions of finite transformation semigroups and permutation groups

We describe how the SgpDec computer algebra package can be used for composing and decomposing permutation groups and transformation semigroups hierarchically by directly constructing substructures of wreath products, the so called cascade products.Final Accepted Versio

Local differents of algebraic and finite extensions of valued fields

AbstractThe properties of discriminants and differents were studied first by Dedekind and Hilbert in finite algebraic extensions of fields of algebraic numbers. From a local point of view, that is equivalent to a study of the p-adic case, where the results of Dedekind and Hilbert can be formulated as follows. Dedekind's theorem: The g.c.d. Δ(Kk) of differents of integral bases of a finite algebraic extension Kk (which I call an algebraic different if Kk and the g.c.d δ(Kk) of differents of integral elements of Kk (which I call an arithmetic different of Kk) coincide; Hilbert's theorem (which is the basis of Herbrand's ramification theory of intermediate extensions): If K ⊃ L ⊃ k, δ(Kk) = δ(KL) δ(Lk). These results are easily generalizable to the “classical case” of henselian valued basic fields, i.e., the case when the valuation is discrete and the residual extension Kk of Kk is separable. But, in the general case of extensions Kk of valued fields (where k may be assumed to be henselian), Dedekind's and Hilbert's theorems are not always true: the algebraic different Δ(Kk) divides the arithmetic different δ(Kk), but generally δ(Kk) ≠ Δ(Kk), and Hilbert's theorem holds only for the algebraic different. When the valuation is discrete, I call an extension Kk dedekindian when δ(Kk) = Δ(Kk) and hilbertian if, for every intermediate field L of Kk (i.e., K ⊇ L ⊇ k), Hilbert's theorem δ(Kk) = δ(KL) δ(Lk) for arithmetic differents holds. When the valuation is dense, the situation is more complicated, because of the existence of two kinds of ideals (principal and other), and it is convenient to define dedekindian and hilbertian extensions in a slightly different manner and to introduce somewhat wider classes of extensions called quasi-dedekindian and quasi-hilbertian. I study the relations between Δ(Kk) and δ(Kk), and, in particular, I give a complete characterization of dedekindian extensions for both discrete and dense valuations; I also give examples of non-dedekindian and non-hilbertian extensions. In Section 4, some connections with the ramification theory (both for normal and non-normal extensions) are studied and a weak analog of Hilbert's theorem [δ(Kk) δ(Lk) divides δ(Kk)] is proved

A Divided Media: Filtered Rhetoric and the Rise of Donald Trump

This thesis explores the how the media filtered the rhetoric of candidate Donald Trump, specifically concerning how both right wing and left wing media reported his campaign announcement speech in June of 2015

Contribution of the antibiotic chloramphenicol and its analogues as precursors of dichloroacetamide and other disinfection byproducts in drinking water

Dichloroacetamide (DCAcAm), a disinfection byproduct, has been detected in drinking water. Previous research showed that amino acids may be DCAcAm precursors. However, other precursors may be present. This study explored the contribution of the antibiotic chloramphenicol (CAP) and two of its analogues (thiamphenicol, TAP; florfenicol, FF) (referred to collectively as CAPs), which occur in wastewater-impacted source waters, to the formation of DCAcAm. Their formation yields were compared to free and combined amino acids, and they were investigated in filtered waters from drinking-water-treatment plants, heavily wastewater-impacted natural waters, and secondary effluents from wastewater treatment plants. CAPs had greater DCAcAm formation potential than two representative amino acid precursors. However, in drinking waters with ng/L levels of CAPs, they will not contribute as much to DCAcAm formation as the μg/L levels of amino acids. Also, the effect of advanced oxidation processes (AOPs) on DCAcAm formation from CAPs in real water samples during subsequent chlorination was evaluated. Preoxidation of CAPs with AOPs reduced the formation of DCAcAm during postchlorination. The results of this study suggest that CAPs should be considered as possible precursors of DCAcAm, especially in heavily wastewater-impacted waters