Consider a cubic extension K := Q(α), when the minimal polynomial f(x) of α does not totally split in K. The normal closure L := (K) is a sextic extension of Q, with Gal(L/Q) = S3. Now we fix notation and pick one embedding of K as K1, say K1 is fixed by (2, 3) ∈ S3. Here (2, 3) has the explicit description that if I choose one root u1 of f(x), (2, 3) permute the other two conjugate roots of u1...

Let p be prime. Let L/K be a finite, totally ramified, purely inseparable extension of local fields, [L : K] = p, n ≥ 2. It is known that L/K is Hopf Galois for numerous Hopf algebras H, each of which can act on the extension in numerous ways. For a certain collection of such H we construct “Hopf Galois scaffolds” which allow us to obtain a Hopf analogue to the Normal Basis Theorem for L/K. The...

Activation energies ∆G act for the nucleation of nitric acid dihydrate (NAD) in super-cooled binary HNO 3 /H 2 O solution droplets were calculated from volume-based nucle-ation rate measurements using the AIDA (Aerosol Interactions and Dynamics in the Atmosphere) aerosol chamber of Forschungszentrum Karlsruhe. The experimental 5 conditions covered temperatures T between 192 K and 197 K, NAD sat...

The selectivity filter of K(+) channels is conserved throughout all kingdoms of life. Carbonyl groups of highly conserved amino acids point toward the lumen to act as surrogates for the water molecules of K(+) hydration. Ion conductivity is abrogated if some of these carbonyl groups flip out of the lumen, which happens (i) in the process of C-type inactivation or (ii) during filter collapse in ...

Resistance arteries exist in a maintained contracted state from which they can dilate or constrict depending on need. In many cases, these arteries constrict to membrane depolarization and dilate to membrane hyperpolarization and Ca-channel blockers. We discuss recent information on the regulation of arterial smooth muscle voltage-dependent Ca channels by membrane potential and vasoconstrictors...

lthough fuzzy set theory and  sheaf theory have been developed and studied independently,  ulrich hohle shows that a large part of fuzzy set  theory  is in fact a subfield of sheaf theory. many authors have studied mathematical structures, in particular, algebraic structures, in both  categories of these generalized (multi)sets. using hohle's idea, we show that for a (universal) algebra $a$, th...