Affine representations of Fibonacci groups and flat manifolds

We construct examples of affine representations for a family of Fibonacci groups. As an application, we prove that all Hantzsche–Wendt groups of the same dimension are epimorphic images of the same Fibonacci group.     

Rearrangement of conditionally convergent series on a small set

We consider ideals I of subsets of the set of natural numbers such that for every conditionally convergent series _∑n∈ωan and every there is a permutation such that _∑n∈ωaπr(n)=r and

     

On truncated variation,upward truncated variation and downward truncated variation for diffusions

The truncated variation, TV^c${\text{TV}}^c$, is a fairly new concept introduced in ?ochowski (2008) [5]. Roughly speaking, given a càdlàg function f$f$, its truncated variation is “the total variation which does not pay attention to small changes of f$f$, below some threshold c>0$c>0$”. The very basic consequence of such approach is that contrary to the total variation, TV^c${\text{TV}}^c$ is always finite. This is appealing to the stochastic analysis where so-far large classes of processes, like semimartingales or diffusions, could not be studied with the total variation. Recently in ?ochowski (2011) [6], another characterization of TV^c${\text{TV}}^c$ has been found. Namely TV^c${\text{TV}}^c$ is the smallest possible total variation of a function which approximates f$f$ uniformly with accuracy c/2$c/2$. Due to these properties we envisage that TV^c${\text{TV}}^c$ might be a useful concept both in the theory and applications of stochastic processes.     

On the transposition anti-involution in real Clifford algebras I: the transposition map

A particular orthogonal map on a finite-dimensional real quadratic vector space (V,?Q) with a non-degenerate quadratic form Q of any signature (p,?q) is considered. It can be viewed as a correlation of the vector space that leads to a dual Clifford algebra C?(V*,?Q) of linear functionals (multiforms) acting on the universal Clifford algebra C?(V,?Q). The map results in a unique involutive automorphism and a unique involutive anti-automorphism of C?(V,?Q). The anti-involution reduces to reversion (resp. conjugation) for any Euclidean (resp. anti-Euclidean) signature. When applied to a general element of the algebra, it results in transposition of the element matrix in the left regular representation of C?(V,?Q). We also give an example for real spinor spaces. The general setting for spinor representations will be treated in part II of this work [R. Ab?amowicz and B. Fauser, On the transposition anti-involution in real Clifford algebras II: Stabilizer groups of primitive idempotents, Linear Multilinear Algebra, to appear].     

Monitoring the changes of 5-caffeoylquinic acid during its reaction with ABTS cation radicals by LC-MS

Abstract

Reactive oxygen species including free radicals are responsible for noxious changes in living organisms which can be associated with many diseases for e.g. cardiovascular, neurodegenerative, and inflammatory diseases or cancer. In the struggle against free radicals the organism is supported by antioxidants. As they are often provided by nature, they can be considered safe. 5-Caffeoylquinic acid is one of main chlorogenic acids found in vegetables and fruits. The main objective of the presented article was monitoring the changes of 5-caffeoylquinic acid during the reaction with colorful radicals. The experiments were conducted at different molar ratios of radicals to antioxidant using liquid chromatography–mass spectrometry. Irrespective of the applied molar ratios, the obtained results proved that the antioxidant takes part in the reaction for three days. Additionally, during the radical neutralization the formation of semiquinones and/or quinones, methoxy adduct of caffeoylquinic acid, and quinones adduct with methanol was observed.