A note on integer polynomials with small integrals. II

The smart method of Gelfond–Shnirelman–Nair allows one to obtain a lower bound for the prime counting function \({\pi(x)}\) in an elementary way in terms of integrals of suitable integer polynomials. In this paper we carry on the study of the sets of integer polynomials relevant for the method.     

Enhanced resolution of Mentha piperita volatile fraction using a novel medium‐polarity ionic liquid gas chromatography stationary phase

The evaluation of a novel medium‐polarity ionic‐liquid‐based gas chromatography column, SLB‐IL60, towards the analysis of a complex essential oil, namely, a peppermint essential oil sample, is reported. The SLB‐IL60 30 m column was subjected to bleeding measurements, by means of conventional gas chromatography with mass spectrometry. The SLB‐IL60 column was then evaluated in the analysis of pure standard compounds, chosen as typical constituents of peppermint essential oil. Resolution and peak symmetry (expressed as tailing factors at 10% of peak height) were measured and the results were compared to those obtained on the most widely used columns in such an application, namely a medium‐polarity [100% poly(ethyleneglycol)] stationary phase, and an apolar 5% diphenyl/95% dimethyl siloxane. The final part of the evaluation was dedicated to the gas chromatography with mass spectrometry analysis of a peppermint essential oil sample and again the data were compared to those obtained on the 100% poly(ethyleneglycol) and the 5% diphenyl/95% dimethyl siloxane phase. Linear retention indices were determined for all the identified components on the ionic liquid capillary.     

On finite groups with automorphisms whose fixed points are Engel

The main result of the paper is the following theorem. Let q be a prime, n a positive integer, and A an elementary abelian group of order q². Suppose that A acts coprimely on a finite group G and assume that for each \({a \in A^{\#}}\) every element of C_G(a) is n-Engel in G. Then the group G is k-Engel for some \({\{n,q\}}\)-bounded number k.     

A 10-A spectroscopic ruler applied to short polyprolines

Fluorescence resonance energy transfer (FRET) from the amino acid tryptophan (Trp) as donor and a 2,3-diazabicyclo[2.2.2]oct-2-ene-labeled asparagine (Dbo) as acceptor in peptides of the general structure Trp-(Pro)n-Dbo-NH2 (n = 1-6) was investigated by steady-state and time-resolved fluorescence, CD, and NMR spectroscopy as well as by molecular dynamics (MD) simulations (GROMOS96 force field). The Trp/Dbo FRET pair is characterized by a very short F?rster radius (R0 ca. 9 A), which allowed distance determinations in such short peptides. Water and propylene glycol were investigated as solvents. The peptides were designed to show an early nucleation of the poly(Pro)II (PPII) secondary helix structure for n > or = 2, which was confirmed by their CD spectra. The shortest peptide (n = 1) adopts preferentially the trans conformation about the Trp-Pro bond, as confirmed by NMR spectra. The FRET efficiencies ranged 2-72% and were found to depend sensitively on the peptide length, i.e., the number of intervening proline residues. The analysis of the FRET data at different levels of theory (assuming either a fixed distance or distance distributions according to a wormlike chain or Gaussian model) afforded donor-acceptor distances between ca. 8 A (n = 1) and ca. 16 A (n = 6) in water, which were found to be similar or slightly higher in propylene glycol. The distances afforded by the Trp/Dbo FRET pair were found to be reasonable in comparison to literature data, expectations from the PPII helix structure, and the results from MD simulations. The persistence lengths for the longer peptides were found to lie at 30-70 A in water and 220 +/- 40 A in propylene glycol, suggesting a more rigid PPII helical structure in propylene glycol. A detailed comparison with literature data on FRET in polyprolines demonstrates that the donor-acceptor distances extracted by FRET are correlated with the F?rster radii of the employed FRET pairs. This demonstrates the limitations of using FRET as a spectroscopic ruler for short polyprolines, which is presumably due to the breakdown of the point dipole approximation in F?rster theory, when the size of the chromophores becomes comparable or larger than the distances under investigation.     

Analysis of Roman wall paintings found in Verona

The present paper deals with the analysis of roman wall paintings fragments recovered from twelve buildings of Verona, Italy. The analytical techniques used were Optical Microscopy, Scanning Electron Microscopy (SEM) equipped with an EDS microanalysis detector, Xray powder diffraction (XRD) Fourier Transform infrared spectroscopy (FTIR) and Raman Spectroscopy. The wall preparation generally consisted of three layer: the pictorial layer, an intonachino layer of hydrated lime and a plaster one made of slaked lime and sand. The pigments found in the studied domus are different reflecting the taste and culture of Xa Regio of Italy but also the economical possibilities of the dominus and the building period.     

Chiodo formulas for the <Emphasis Type="Italic">r</Emphasis>-th roots and topological recursion

We analyze Chiodo’s formulas for the Chern classes related to the r-th roots of the suitably twisted integer powers of the canonical class on the moduli space of curves. The intersection numbers of these classes with \(\psi \)-classes are reproduced via the Chekhov–Eynard–Orantin topological recursion. As an application, we prove that the Johnson-Pandharipande-Tseng formula for the orbifold Hurwitz numbers is equivalent to the topological recursion for the orbifold Hurwitz numbers. In particular, this gives a new proof of the topological recursion for the orbifold Hurwitz numbers.