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.     

Stability results for Mountain Pass and Linking type solutions of semilinear problems involving Dirichlet forms

Some stability results for Mountain Pass and Linking type solutions of semilinear problems involving a very general class of Dirichlet forms are stated. The non linear terms are supposed to have a suitable superlinear growth and the family of Dirichlet forms is required to be dominated from below and from above by a fixed diffusion type form. Some concrete examples are also given.     

Semigroups Generated by Ordinary Differential Operators in L 1(I)*

In this paper we give necessary and sufficient conditions for the existence of a C> ₀-semigroup in L ¹(I) (I real interval) generated by a second-order differential operator when suitable boundary conditions at the endpoints are imposed.     

Stable determination of an inhomogeneous inclusion by local boundary measurements

We deal with the problem of determining an inclusion within an electrostatic conductor from boundary measurements. Under mild a priori assumptions we establish optimal stability estimates. Measurements are performed on a portion of the boundary of the conductor.     

Packing into the smallest square: Worst-case analysis of lower bounds

We address the problem of packing a given set of rectangles into the minimum size square. We consider three versions of the problem, arising when the rectangles (i) are squares; (ii) have a fixed orientation; (iii) can be rotated by 90. For each case we study lower bounds, and analyze their worst-case performance ratio. In addition, we evaluate through computational experiments their average performance on instances from the literature.     

A remark on Serrin’s Theorem

An approximation theorem for families of weakly coercive convex functions by means of countably many smooth families of convex functions is proved. As a consequence, the classical “three-fold” lower semicontinuity theorem for integral functionals of the Calculus of Variations by James Serrin is unified in one single statement.     

Ab initio path-integral molecular dynamics

A path-integral molecular dynamics technique for strongly interacting atoms using ab initio potentials derived from density functional theory is implemented. This allows the efficient inclusion of nuclear quantum dispersion in ab initio simulations at finite temperatures. We present an application to the quantum cluster H ₅ ⁺ .     

General theorems and fundamental solutions in the dynamical theory of mixtures

This paper is concerned with the dynamic theory of a binary mixture consisting of a gas and an elastic solid. First, we derive general theorems (reciprocal theorem, uniqueness theorem, minimum principle). The, we establish a Galerkin representation and the fundamental solutions in the case of steady vibrations.Work performed under the auspices of G.N.F.M. of the Italian Research Council (C.N.R.), with the grant 60% M.U.R.S.T. (ITALY).