let $x$ be a sufficiently nice scheme. we survey some recent progress on dualizing complexes. it turns out that a complex in $kinj x$ is dualizing if and only if tensor product with it induces an equivalence of categories from murfet's new category $kmpr x$ to the category $kinj x$. in these terms, it becomes interesting to wonder how to glue such equivalences.

The concept of complex fuzzy sets is a generalization of ordinary fuzzy sets. In this paper, we introduce the concept of complex fuzzy subhypergroups ($H_{v}$-subgroups) as well as the concept of complex anti-fuzzy subhypergroups ($H_{v}$-subgroups). We investigate their properties and their relations with the traditional fuzzy (anti-fuzzy) subhypergroups ($H_{v}$-subgroups), and we prove some ...

Due to the extremely high stability of perfluorooctane sulfonate (PFOS), effective defluorination is difficult. Previous studies indicated that PFOS can be decomposed under catalysis vitamin B12 (VB12) with strong artificial reductants such as Ti(III)-citrate and nZn0. In this study, we explored if naturally occurring reductant like sulfide (S2−) could initiate reaction. S2−/VB12 system, branch...

A combined computational and experimental investigation of three different Cp*CoIII systems used in combination with a base as catalysts “borrowing hydrogen” alkylations by secondary alcohols (ROH), resulting C–N or C–C bond formation, reveal the existence new pathway for alcohol activation, differing from existing paradigms oxidative ionic activations. The metal-coordinated alkoxide (OR) gener...