Four fundamental physical parameters of series of benzene derivatives were studied to ascertain correlations with biological activity. These included octanol/water coefficient, vapor pressure, infrared absorption (out-of-plane C-H vibration), and the pi values. Each physicochemical constant exhibited a partial correlation with biological activity suggesting that each played a role. It was presu...

We prove that any multi-variate Hasse-Schmidt derivation can be decomposed in terms of substitution maps and uni-variate derivations. As a consequence we the bracket two $m$-integrable derivations is also $m$-integrable, for $m$ positive integer or infinity.

Given a Laurent polynomial over flat $$\mathbf {Z}$$ -algebra, Vlasenko defines formal group law. We identify this law with coordinate system of functor. When the “Hasse–Witt matrix” is invertible, matrix by taking certain $$p$$ -adic limit. show that Frobenius Dieudonné module modulo .