Commutative ${\rm QF}-1$ artinian rings are ${\rm QF}$

Fundamentals Qf

. . l 'be&t imd~in i te~ard~en~th (FWL) state-space digital comp&satordesign~r~b lem is investigated. Instead of the usual sensitivity measure, it h argued that it may be desirable to mini&e a frequency weighted sensitivity measure over all similarity bmformations. The set of optimal realizations minimizing this weighted sensitivity b completely chaacterized, and an algorithm is proposed to fin...

Strongly Rational Comodules and Semiperfect Hopf Algebras over QF Rings

Let C be a coalgebra over a QF ring R. A left C-comodule is called strongly rational if its injective hull embeds in the dual of a right Ccomodule. Using this notion a number of characterizations of right semiperfect coalgebras over QF rings are given, e.g., C is right semiperfect if and only if C is strongly rational as left C-comodule. Applying these results we show that a Hopf algebra H over...

Qf Functors and (co)monads

One reason for the universal interest in Frobenius algebras is that their characterisation can be formulated in arbitrary categories: a functor K : A → B between categories is Frobenius if there exists a functor G : B → A which is at the same time a right and left adjoint of K; a monad F on A is a Frobenius monad provided the forgetful functor AF → A is a Frobenius functor, where AF denotes the...

Topological superconductor in quasi-one-dimensional ${\rm Tl}_{2-x}{\rm Mo}_6{\rm Se}_6$

Identifying an Honest ${\rm EXP}^{\rm NP}$ Oracle Among Many

We provide a general framework to remove short advice by formulating the following computational task for a function f : given two oracles at least one of which is honest (i.e. correctly computes f on all inputs) as well as an input, the task is to compute f on the input with the help of the oracles by a probabilistic polynomial-time machine, which we shall call a selector. We characterize the ...