On the Hong–Krahn–Szego inequality for the p-Laplace operator

Given an open set Ω, we consider the problem of providing sharp lower bounds for λ ₂(Ω), i.e. its second Dirichlet eigenvalue of the p-Laplace operator. After presenting the nonlinear analogue of the Hong–Krahn–Szego inequality, asserting that the disjoint unions of two equal balls minimize λ ₂ among open sets of given measure, we improve this spectral inequality by means of a quantitative stability estimate. The extremal cases p = 1 and p = ∞ are considered as well.     

Marine Sediments and Snow from Ross Sea Region (Antarctica) Dating by 210Pb Method

Abstract

²¹⁰Pb is widely used to determine accumulation rates in order to obtain a time scale in environmental samples. The most accurate method uses the determination of ²¹⁰Pb via its grand-daughter ²¹⁰Po by alpha spectrometry. Unfortunately this method requires a complex wet-chemistry procedure to achieve the separation of ²¹⁰Po from its matrix. In this work a simplified procedure for the chemical separation of ²¹⁰Po is proposed and applied to three marine sediment cores and a 10 m snow core collected in Antarctica. The calculated sedimentation rates for marine sediments range from 0.053 to 0.071 cm y^?1. The mean annual accumulation rate for the snow is 16.6 cm y^?1 w.e. A comparison with literature data in the same region is given.     

Modifying LnHPDO3A Chelates for Improved T1 and CEST MRI Applications

The new ligand HPDO3MA [(R,R,R,R)-10-(2-hydroxypropyl)-α,α′,α′′-trimethyl-1,4,7,10-tetraazacyclododecane-1,4,7-triacetic acid] was designed to combine and optimize the chemical properties of the macrocyclic ligands HPDO3A and DOTMA. The presence of the methyl groups on the acetic pendant arms of HPDO3A is expected to rigidify the structure of the ligand and favor an increase of the kinetic inertness of the Ln complexes. ¹H NMR spectra of Eu(HPDO3MA) displayed the presence of two pairs of diastereoisomers: SAP (square antiprismatic) and TSAP (twisted square antiprismatic) isomers (56 and 44 %, respectively). In addition, ¹H and ¹⁷O relaxometric NMR studies of Gd(HPDO3MA) showed approximately a 10 % increase in relaxivity and a faster water exchange rate with respect to Gd(HPDO3A). Moreover, a detailed chemical exchange saturation transfer (CEST) characterization of Yb(HPDO3MA) displayed a sensitivity about two times larger than that of Yb(HPDO3A) both in phantom and in cell labeling experiments. Finally, the kinetic inertness of Yb(HPDO3MA) was measured to be twice as high as that of Yb(HPDO3A), with a dissociation half-life at physiological pH of about 2500 years.     

Pseudopeptide‐Based Hydrogels Trapping Methylene Blue and Eosin Y

We present herein the preparation of four different hydrogels based on the pseudopeptide gelator Fmoc‐l ‐Phe‐d ‐Oxd‐OH (Fmoc=fluorenylmethyloxycarbonyl), either by changing the gelator concentration or adding graphene oxide (GO) to the water solution. The hydrogels have been analysed by rheological studies that demonstrated that pure hydrogels are slightly stronger compared to GO‐loaded hydrogels. Then the hydrogels efficiency to trap the cationic methylene blue (MB) and anionic eosin Y (EY) dyes has been analyzed. MB is efficiently trapped by both the pure hydrogel and the GO‐loaded hydrogel through π–π interactions and electrostatic interactions. In contrast, the removal of the anionic EY is achieved in less satisfactory yields, due to the unfavourable electrostatic interactions between the dye, the gelator and GO.     

A Journey from Thermally Tunable Synthesis to Spectroscopy of Phenylmethanimine in Gas Phase and Solution

Phenylmethanimine is an aromatic imine with a twofold relevance in chemistry: organic synthesis and astrochemistry. To tackle both aspects, a multidisciplinary strategy has been exploited and a new, easily accessible synthetic approach to generate stable imine-intermediates in the gas phase and in solution has been introduced. The combination of this formation pathway, based on the thermal decomposition of hydrobenzamide, with a state-of-the-art computational characterization of phenylmethanimine laid the foundation for its first laboratory observation by means of rotational electric resonance spectroscopy. Both E and Z isomers have been accurately characterized, thus providing a reliable basis to guide future astronomical observations. A further characterization has been carried out by nuclear magnetic resonance spectroscopy, showing the feasibility of this synthetic approach in solution. The temperature dependence as well as possible mechanisms of the thermolysis process have been examined.     

Relaxation Dynamics and Magnetic Anisotropy in a Low‐Symmetry DyIII Complex

The magnetic behaviour of a Dy(LH)₃ complex (LH^? is the anion of 2‐hydroxy‐N′‐[(E)‐(2‐hydroxy‐3‐methoxyphenyl)methylidene]benzhydrazide) was analysed in depth from both theoretical and experimental points of view. Cantilever torque magnetometry indicated that the complex has Ising‐type anisotropy, and provided two possible directions for the easy axis of anisotropy due to the presence of two magnetically non‐equivalent molecules in the crystal. Ab initio calculations confirmed the strong Ising‐type anisotropy and disentangled the two possible orientations. The computed results obtained by using ab initio calculations were then used to rationalise the composite dynamic behaviour observed for both pure Dy^III phase and Y^III diluted phase, which showed two different relaxation channels in zero and non‐zero static magnetic fields. In particular, we showed that the relaxation behaviour at the higher temperature range can be correctly reproduced by using a master matrix approach, which suggests that Orbach relaxation is occurring through a second excited doublet.