A molecular fluorophore in citric acid/ethylenediamine carbon dots identified and quantified by multinuclear solid-state nuclear magnetic resonance

The composition of fluorescent polymer nanoparticles, commonly referred to as carbon dots, synthesized by microwave-assisted reaction of citric acid and ethylenediamine was investigated by ¹³C, ¹³C{¹H}, ¹H─¹³C, ¹³C{¹⁴N}, and ¹⁵N solid-state nuclear magnetic resonance (NMR) experiments. ¹³C NMR with spectral editing provided no evidence for significant condensed aromatic or diamondoid carbon phases. ¹⁵N NMR showed that the nanoparticle matrix has been polymerized by amide and some imide formation. Five small, resolved ¹³C NMR peaks, including an unusual ═CH signal at 84 ppm (¹H chemical shift of 5.8 ppm) and ═CN₂ at 155 ppm, and two distinctive ¹⁵N NMR resonances near 80 and 160 ppm proved the presence of 5-oxo-1,2,3,5-tetrahydroimidazo[1,2-a]pyridine-7-carboxylic acid (IPCA) or its derivatives. This molecular fluorophore with conjugated double bonds, formed by a double cyclization reaction of citric acid and ethylenediamine as first shown by Y. Song, B. Yang, and coworkers in 2015, accounts for the fluorescence of the carbon dots. Cross-peaks in a ¹H─¹³C HETCOR spectrum with brief ¹H spin diffusion proved that IPCA is finely dispersed in the polyamide matrix. From quantitative ¹³C and ¹⁵N NMR spectra, a high concentration (18 ± 2 wt%) of IPCA in the carbon dots was determined. A pronounced gradient in ¹³C chemical-shift perturbations and peak widths, with the broadest lines near the COO group of IPCA, indicated at least partial transformation of the carboxylic acid of IPCA by amide or ester formation.     

Reactions of quinones with some amino alcohols,thiols and a UV-Vis study

Abstract

In the present study, the reactions of 2,3-dichloro-1,4-naphthoquinone (DCNQ) with amino-1,2-propanediol and some thiols were investigated. Novel N-, N,S-, and S,O- substituted derivatives were obtained and the structures of all compounds were characterized by spectroscopic methods (FT-IR, ¹H NMR, ¹³ Baker, R. A.; Tatum, J. H.; Nemec, S. Antimicrobial Activity of Naphthoquinones from Fusaria. Mycopathologia 1990, 111, 9–15. DOI: 10.1007/BF02277294.[Crossref], [PubMed], [Web of Science ®] , [Google Scholar]C NMR, Mass spectroscopy) and microanalysis. The absorption behaviors of novel compounds were also investigated with UV-Vis spectroscopy in different solvents, such as ethanol, tetrahydrofuran and chloroform.     

The projective dimension of three cubics is at most 5

Let R be a polynomial ring over a field and I an ideal generated by three forms of degree three. Motivated by Stillman's question, Engheta proved that the projective dimension $\mathrm{pd}(R/I)$ of $R/I$ is at most 36, although the example with largest projective dimension he constructed has $\mathrm{pd}(R/I)=5$. Based on computational evidence, it had been conjectured that $\mathrm{pd}(R/I)\le 5$. In the present paper we prove this conjectured sharp bound.     

Gaps in the number of generators of monomial Togliatti systems

Let $I_{d,n}?k[x_0,?,x_n]$ be a minimal monomial Togliatti system of forms of degree d. In [4], Mezzetti and Miró-Roig proved that the minimal number of generators $\mu (I_{d,n})$ of $I_{d,n}$ lies in the interval $[2n+1,\left(\begin{array}{c}n+d?1\\ n?1\end{array}\right)]$. In this paper, we prove that for $n\ge 4$ and $d\ge 3$, the integer values in $[2n+3,3n?1]$ cannot be realized as the number of minimal generators of a minimal monomial Togliatti system. We classify minimal monomial Togliatti systems $I_{d,n}?k[x_0,?,x_n]$ of forms of degree d with $\mu (I_{d,n})=2n+2$ or 3n (i.e. with the minimal number of generators reaching the border of the non-existence interval). Finally, we prove that for $n=4$, $d\ge 3$ and $\mu \in [9,\left(\begin{array}{c}d+3\\ 3\end{array}\right)]?\{11\}$ there exists a minimal monomial Togliatti system $I_{d,n}?k[x_0,?,x_n]$ of forms of degree d with $\mu (I_{n,d})=\mu$.     

Some results about zero‐cycles on abelian and semi‐abelian varieties

In this short note we extend some results obtained in [7]. First, we prove that for an abelian variety A with good ordinary reduction over a finite extension of with p an odd prime, the Albanese kernel of A is the direct sum of its maximal divisible subgroup and a torsion group. Second, for a semi‐abelian variety G over a perfect field k, we construct a decreasing integral filtration of Suslin's singular homology group, , such that the successive quotients are isomorphic to a certain Somekawa K‐group.     

Automorphisms of Hilbert schemes of points on a generic projective K3 surface

We study automorphisms of the Hilbert scheme of n points on a generic projective K3 surface S, for any . We show that is either trivial or generated by a non‐symplectic involution and we determine numerical and divisorial conditions which allow us to distinguish between the two cases. As an application of these results we prove that, for any , there exist infinitely many admissible degrees for the polarization of the K3 surface S such that admits a non‐natural involution. This provides a generalization of the results of [7] for .     

On the variety of triangles for a hyper-Kähler fourfold constructed by Debarre and Voisin

We study the similarities between the Fano varieties of lines on a cubic fourfold, a hyper-Kähler fourfold studied by Beauville and Donagi, and the hyper-Kähler fourfold constructed by Debarre and Voisin in [3]. We exhibit an analog of the notion of “triangle” for these varieties and prove that the 6-dimensional variety of “triangles” is a Lagrangian subvariety in the cube of the constructed hyper-Kähler fourfold.     

K3 surfaces with an order 50 automorphism

In any characteristic p different from 2 and 5, Kondō gave an example of a K3 surface with a purely non-symplectic automorphism of order 50. The surface was explicitly given as a double plane branched along a smooth sextic curve. In this note we show that, in any characteristic $p\ne 2,5$, a K3 surface with a cyclic action of order 50 is isomorphic to the example of Kondō.