The aza-Pudovik reaction accelerated in external constant magnetic field

The aza-Pudovik reaction of N-benzyl aromatic and aliphatic aldimines with dimethyl H-phosphonate was found to be accelerated significantly when carried out in an external magnetic field. Its conversion rates were analyzed and compared with those obtained during the aza-Pudovik reaction carried out under standard conditions. Magnetic acceleration was found to have a similar degree as in that observed in the Kabachnik–Fields reaction. However, the formation of the starting imines was found not to be susceptible to constant magnetic field–no acceleration was observed.     

Equations of log del Pezzo surfaces of index ≤ 2

Del Pezzo surfaces over with log terminal singularities of index ≤ 2 were classified by Alekseev and Nikulin. In this paper, for each of these surfaces, we find an appropriate morphism to projective space. These morphisms enable us to describe equations of natural embeddings of log del Pezzo surfaces of index ≤ 2 in some weighted projective space. The results obtained give a completion of similar results of Du Val, Hidaka, and Watanabe, describing del Pezzo surfaces of index 1. The work was done during the authors’ stay at the University of Liverpool supported by the Marie Curie program in Autumn 2004.     

Regular atomic narrowing of Ni, Fe, and V nanowires resolved by two-dimensional correlation analysis

We present a novel statistical method for the study of stable atomic configurations in breaking nanowires based on the 2D cross-correlation analysis of conductance versus electrode separation traces. Applying this method, we can clearly resolve the typical evolutions of the conductance staircase in some transition metal nanojunctions (Ni, Fe, V) up to high conductance values. In these metals our analysis demonstrates a very well ordered atomic narrowing of the nanowire, indicating a very regular, stepwise decrease of the number of atoms in the minimal cross section of the junction, in contrast to the majority of the metals. All these features are hidden in traditional conductance histograms.     

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.     

Hitting Half-spaces by Bessel-Brownian Diffusions

The purpose of the paper is to find explicit formulas describing the joint distributions of the first hitting time and place for half-spaces of codimension one for a diffusion in ℝ ^n + 1, composed of one-dimensional Bessel process and independent n-dimensional Brownian motion. The most important argument is carried out for the two-dimensional situation. We show that this amounts to computation of distributions of various integral functionals with respect to a two-dimensional process with independent Bessel components. As a result, we provide a formula for the Poisson kernel of a half-space or of a strip for the operator (I − Δ) ^α/2, 0 < α < 2. In the case of a half-space, this result was recently found, by different methods, in Byczkowski et al. (Trans Am Math Soc 361:4871–4900, 2009). As an application of our method we also compute various formulas for first hitting places for the isotropic stable Lévy process.     

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.     

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.     

Progress in planar electrochromatography

Developments in planar electrochromatography in open (PEC) and closed (PPEC) systems are reviewed. The discussion focuses on progress in chamber construction for planar electrochromatography, separating system performance, equilibration of the PPEC process, separation time and selectivity, and the general advantages, disadvantages and prospects of this separation mode. Presented at the 11th International Conference on Chemistry and the Environment, 9–12 September 2007, Torum, Poland.