A class of finite-dimensional Hopf algebras which generalise the notion Taft is studied. We give necessary and sufficient conditions for these to omit a pair in involution, that is, not have group-like character implementing square antipode. As consequence we prove existence an infinite set examples without such pairs. This has implications theory anti-Yetter-Drinfeld modules as well biduality ...

Heterocyclic nitrogen compounds are extensively used as intermediates in the manufacture of pesticides and herbicides, while their toxicity has been little reported (Chen et al, 1997). In this paper, we report the toxicity of 14 heterocyclic nitrogen compounds to Photobacterium phosphoreum measured by Microtox® test which has been proposed as a cost-effective prescreening procedure to eliminate...

background: radioactive substances are water chemical contaminants. in this study, the concentration of radon was measured in drinking water supplies of taft villages (part of dehshir-baft fault located in central part of iran) and also shirkooh area with granite rocks (containing uranium). materials and methods: this cross sectional research was conducted in fall 2013 and winter 2014 on the so...

We study actions of pointed Hopf algebras in the Z-graded setting. Our main result classifies inner-faithful generalized Taft on quantum Weyl which respect Z-grading. also show that generically invariant rings are commutative rings.