Recovering plane curves of low degree from their inflection lines and inflection points

In this paper we consider the following problem: is it possible to recover a smooth plane curve of degree d ≥ 3 from its inflection lines? We answer the posed question positively for a general smooth plane quartic curve, making the additional assumption that also one inflection point is given, and for any smooth plane cubic curve.     

Tautological Classes of the Stack of Rational Nodal Curves

This is the second in a series of three papers in which we investigate the rational Chow ring of the stack 𝔐₀ consisting of nodal curves of genus 0. Here we define the basic classes: the classes of strata and the Mumford classes.     

Sustainable Access to Acridin-9-(10H)ones with an Embedded m-Terphenyl Moiety Based on a Three-Component Reaction

A Ce(IV)-catalyzed three-component reaction between chalcones, anilines and β-ketoesters followed by a microwave-assisted thermal cyclization afforded 1,3-diaryl-1,2-dihydroacridin-9(10H)-ones. Their microwave irradiation in nitrobenzene, acting both as solvent and oxidant, afforded fully unsaturated 1,3-diarylacridin-9(10H)-ones, which combine acridin-9-(10H)one and m-terphenyl moieties. Overall, the route generates three C-C and one C-N bond and has the advantage of requiring a single chromatographic separation.     

The Effects of Ring Strain on Cyclic Tetraaryl[5]cumulenes

Cyclic tetraaryl[5]cumulenes ( 1 a–f ) have been synthesized and studied as a function of increasing ring strain. The magnitude of ring strain is approximated by the extent of bending of the cumulenic core as assessed by a combination of X-ray crystallographic analysis and DFT calculations. Trends are observed in ¹³C NMR, UV-vis, and Raman spectra associated with ring strain, but the effects are small. In particular, the experimental HOMO-LUMO gap is not appreciably affected by bending of the [5]cumulene framework from ca. 174° (λ_max=504 nm) in 1 a to ca. 178° (λ_max=494 nm) in 1 f .     

Synthesis of Triply Fused Porphyrin‐Nanographene Conjugates

Two unprecedented porphyrin fused nanographene molecules, 1 and 2 , have been synthesized by the Scholl reaction from tailor‐made precursors based on benzo[m]tetraphene‐substituted porphyrins. The chemical structures were validated by a combination of high‐resolution matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry (HR MALDI‐TOF MS), IR and Raman spectroscopy, and scanning tunnelling microscopy (STM). The UV‐vis‐near infrared absorption spectroscopy of 1 and 2 demonstrated broad and largely red‐shifted absorption spectra extending up to 1000 and 1400 nm, respectively, marking the significant extension of the π‐conjugated systems.     

Fano varieties in index one Fano complete intersections

Let be a smooth complex complete intersection such that . Let f : S → X be a generically finite morphism from a smooth projective variety to X. Under some positivity assumption on the anticanonical divisor of S, if 2 ≤ dim S ≤ dim X − 2 we prove that the deformations of f are contained in a subvariety of codimension at least 2.     

Bottom-up Solution Synthesis of Graphene Nanoribbons with Precisely Engineered Nanopores

The incorporation of nanopores into graphene nanostructures has been demonstrated as an efficient tool in tuning their band gaps and electronic structures. However, precisely embedding the uniform nanopores into graphene nanoribbons (GNRs) at the atomic level remains underdeveloped especially for in-solution synthesis due to the lack of efficient synthetic strategies. Herein we report the first case of solution-synthesized porous GNR ( pGNR ) with a fully conjugated backbone via the efficient Scholl reaction of tailor-made polyphenylene precursor ( P1 ) bearing pre-installed hexagonal nanopores. The resultant pGNR features periodic subnanometer pores with a uniform diameter of 0.6 nm and an adjacent-pores-distance of 1.7 nm. To solidify our design strategy, two porous model compounds ( 1 a , 1 b ) containing the same pore size as the shortcuts of pGNR , are successfully synthesized. The chemical structure and photophysical properties of pGNR are investigated by various spectroscopic analyses. Notably, the embedded periodic nanopores largely reduce the π-conjugation degree and alleviate the inter-ribbon π–π interactions, compared to the nonporous GNRs with similar widths, affording pGNR with a notably enlarged band gap and enhanced liquid-phase processability.     

Carbynes phonons: a tight binding force field

Modeling the vibrational structure of linear carbon chains has proved to be a difficult task with present first-principles calculations. This limits their applicability for the interpretation of experimental data, such as Raman scattering experiments on linear carbon chains within nanotubes. These limitations can be overcome by means of a simple tight binding scheme for pi-electrons. In this work a force field for the calculation of longitudinal phonon dispersion branches is built on the basis of bond-bond polarizabilities and just three parameters. The so obtained phonon dispersion branches are in very good agreement with the experimental data on carbynes in different environments and polyynes of any length. The model is discussed in relation to the importance of long range vibrational interactions in carbynes. The physical phenomena affecting their vibrational properties (i.e., Kohn anomaly, electron-phonon coupling) can be accurately and analytically described by the present approach.     

Syzygies of Multi-Variable Higher Spin Dirac Operators on $$\mathbb{R}^{3}$$

This paper is a short report on the generalization of some results of our previous paper [12] to the case of spin j/2 Dirac operators in real dimension three for arbitrary odd integer j. We use an explicit formula for the local expression of such operators to study their algebraic properties, construct the compatibility conditions of the overdetermined system associated to the operator in several spatial variables, and we prove that its associated algebraic complex, dual do the BGG sequence coming from representation theory, has substantially the same pattern as the Cauchy-Fueter complex. The author is a member of the Eduard Čech Center and his research is supported by the relative grants.     

An investigation on the nature of the peptide at m/z 904, overexpressed in plasma of patients with colorectal cancer and familial adenomatous polyposis

In an investigation devoted to the search for plasma markers for colorectal cancer (CRC), carried out by matrix-assisted laser desorption/ionization (MALDI) mass spectrometry, a series of overexpressed peptides were identified in the plasma of patients. Among them the peptide with molecular weight 903 Da was the most abundant one, with a mean +/- (SD) relative abundance of 37 +/- 17% and a frequency over 60%. Interestingly, also in plasma samples of ten subjects affected by familial adenomatous polyposis (FAP), the peptide with molecular weight 903 was overexpressed. In this investigation, MALDI/MS/MS experiments were carried out on the ion at m/z 904 detected in the MALDI mass spectra of CRC and FAP patients. The data analysis by SwissProt.2007.01.09 indicates that this peptide is due to the sequence RPPGFSPF, found in the kininogen-1 precursor, which is an alpha-2-thiol proteinase inhibitor. In the case of subjects affected by a particular FAP syndrome, the MALDI/MS/MS spectra were quite different from those obtained from CRC and FAP patients. In fact, two sequences have been evidenced: RPPGFSPF belonging to kininogen-1 precursor, and PRKSSSSR belonging to Forkhead box protein 01A.