Further results of existence of positive solutions of elliptic Kirchhoff equation with general nonlinearity of source terms

The paper deals with some existence results for elliptic Kirchhoff equations with respect to general nonlinear source terms and changing sign data, where we have used three different methods: direct variational method, Galerkin approach, and subsolution–supersolution method.     

Ratiometric pH Sensing in Living Cells Using Carbon Dots

The ability to precisely sense physiological pH changes in the cellular environment is exceedingly difficult. Novel technologies are thus required to address this challenge. Fluorescent nanomaterials can be exploited to this effect because their optical properties can exhibit strong pH dependence. Herein, an intracellular pH-sensing probe is developed via a facile microwave-reaction synthesis method for the preparation of carbon dots (CDs) using glutathione and formamide. The CDs possess unique optical properties allowing for concomitant fluorescence in the blue and red regions of the spectrum. These dots are investigated as pH-sensors using the red fluorescence signatures at 650 and 680 nm. The two fluorescence bands respond differently following pH changes in their environment and could thus be used for ratiometric measurements. Cytotoxicity studies of the CDs in glioblastoma cells show no decrease in cell viability up to 100 μg mL⁻¹ (24 h). Fluorescence imaging reveals that the dots localize in lysosomal compartments. Moreover, they can sense changes in lysosomal pH in response to serum and amino acid starvation, as well as administration of diclofenac and metformin, drugs currently in clinical trials for combination treatments of cancer. These CDs offer a new self-referencing approach for live intracellular pH sensing in 2D- and 3D-cell models.     

Blue Highly Fluorescent Boranil Derived From Anil Ligand: Synthesis,Characterization, Experimental and Theoretical Evaluation of Solvent Effect on Structures and Photophysical Properties

In this study, we report the design and the synthesis of a Schiff base; Anil and its corresponding Boron Difluoride complexe; Boranil. The synthesis procedure was carried out adopting new, optimized reaction conditions. The Boranil dye presents the advantage to be emissive in solution. 1H and 19F NMR along with FTIR confirmed both compound's structure. To gain a better understanding of the solvatochromic behavior of Anil and Boranil, the dependence of the absorption spectra on the solvent's polarity was studied in depth. Thus, UV–Vis spectroscopy was performed in five selected solvents. In addition to the solvent's polarity effect, the influence of BF2 moiety introduction on the molecule's photophysical properties was also evaluated. When examining different absorption spectra, we found that the title fluorescent dye exhibited weak solvatochromic (11 nm in THF) as well as a slight redshift broader and relatively more structured absorption spectra after complexation. Besides, we investigate the obtained key structure–property relationships through DFT and TD-DFT calculations using a 6–311++ G (d, p) basis set. Quantum chemical calculations allowed confirming proposed structures and understanding their electronic structure in larger details. Theoretical results also showed good agreement with the experimental findings. Finally, the frontier molecular orbitals were investigated to illustrate the pi-conjugation and charge transfer effect.     

An electron spin resonance investigation into dark and light-induced paramagnetism in metal-free phthalocyanines

The origin of the g = 2.003 ESR signal observed in diamagnetic metal-free phthalocyanines (H₂Pc) is discussed. A model is proposed which suggests that holes and electrons delocalized over one or more phthalocyanine molecules gives rise to the signal. Results on the variation of polymorphic state, chemical purity, oxygen content and surface area of phthalocyanine samples give support to these conclusions. Visible light absorbed by H₂Pc was found to increase this signal which reversibly returns to the dark level upon blocking the light. These results suggest that structural defects and chemical impurities can act as deep and shallow traps for holes and electrons and that ESR is therefore an exceptional method for probing trap densities.     

Anomalously soft dynamics of water in a nanotube: a revelation of nanoscale confinement

Quasi-one-dimensional water encapsulated inside single-walled carbon nanotubes, here referred to as nanotube water, was studied by neutron scattering. The results reveal an anomalously soft dynamics characterized by pliable hydrogen bonds, anharmonic intermolecular potentials, and large-amplitude motions in nanotube water. Molecular dynamics simulations consistently describe the observed phenomena and propose the structure of nanotube water, which comprises a square-ice sheet wrapped into a cylinder inside the carbon nanotube and interior molecules in a chainlike configuration.     

BLOCH modes dressed by evanescent waves and the generalized Goos-Hänchen effect in photonic crystals

It is common knowledge that in an infinite periodic medium, for instance, an infinite photonic crystal, the direction of propagation of a monochromatic wave packet is given by the normal to the isofrequency diagram. We show that this is no longer true in a finite size medium, due to the existence of evanescent waves near the interfaces of the photonic crystal. We derive a renormalized isofrequency diagram giving the correct direction. We give a physical interpretation, showing that this phenomenon can be considered as a generalized Goos-H?nchen effect.     

Transcendence of Thue–Morse p-Adic Continued Fractions

It has been proved that real numbers defined as a limit of continued fractions with a Thue–Morse sequence as the sequence of positive integer partial quotients are transcendental. The same holds for more general sequences of partial quotients. Moreover, transcendence results have been proved for p-adic numbers defined by Hensel development. Here, we tackle the transcendence question in case of p-adic numbers defined as a limit of continued fractions by proving a similar result as the first one.