The Neumann problem for the Hénon equation,trace inequalities and Steklov eigenvalues

We consider the Neumann problem for the Hénon equation. We obtain existence results and we analyze the symmetry properties of the ground state solutions. We prove that some symmetry and variational properties can be expressed in terms of eigenvalues of a Steklov problem. Applications are also given to extremals of certain trace inequalities.     

Contact Ion Pairs on a Protonated Azamacrocycle: the Role of the Anion Basicity

A potassium-containing hexaazamacrocyclic dication, [M?H?K]²⁺, is able to add in the gas phase mono- and dicarboxylate anions as well as inorganic anions by forming the corresponding monocharged adducts, the structure of which markedly depends on the basicity of the anion. With anions, such as acetate or fluoride, the neutral hexaazamacrocycle M acts as an acceptor of monosolvated K⁺ ion. With less basic anions, such as trifluoroacetate or chloride, the protonated hexaazamacrocycle [M?H]⁺ performs the unusual functions of an acceptor of contact K⁺/anion pairs.

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Encapsulation of Trimethine Cyanine in Cucurbit[8]uril: Solution versus Solid-State Inclusion Behavior

Inclusion of polymethine cyanine dyes in the cavity of macrocyclic receptors is an effective strategy to alter their absorption and emission behavior in aqueous solution. In this paper, the effect of the host-guest interaction between cucurbit[8]uril (CB[8]) and a model trimethine indocyanine (Cy3) on dye spectral properties and aggregation in water is investigated. Solution studies, performed by a combination of spectroscopic and calorimetric techniques, indicate that the addition of CB[8] disrupts Cy3 aggregates, leading to the formation of a 1 : 1 host-guest complex with an association constant of 1.5×10⁶ M⁻¹. At concentrations suitable for NMR experiments, the slow formation of a supramolecular polymer was observed, followed by precipitation. Single crystals X-ray structure elucidation confirmed the formation of a polymer with 1 : 1 stoichiometry in the solid state.     

Selective and Reversible Solvent Uptake in Tetra-4-(4-pyridyl)phenylmethane-based Supramolecular Organic Frameworks

The dynamic behavior of supramolecular organic frameworks (SOFs) based on the rigid tetra-4-(4-pyridyl)phenylmethane ( TPPM) organic tecton has been elucidated through 3D electron diffraction, X-ray powder diffraction and differential scanning calorimetry (DSC) analysis. The SOF undergoes a reversible single-crystal-to-single-crystal transformation when exposed to vapours of selected organic solvents, moving from a closed structure with isolated small voids to an expanded structure with solvated channels along the b axis. The observed selectivity is dictated by the fitting of the guest in the expanded SOF, following the degree of packing coefficient. The effect of solvent uptake on TPPM solid-state fluorescence was investigated, evidencing a significant variation in the emission profile only in the presence of chloroform.     

Near Infared Circularly Polarized Luminescence From Water Stable Organic Nanoparticles Containing a Chiral Yb(III) Complex

We report the first example of very efficient NIR Circularly Polarized Luminescence (CPL) (around 970 nm) in water, obtained thanks to the combined use of a chiral Yb complex and of poly lactic-co-glycolic acid (PLGA) nanoparticles. [Yb L (tta)₂]CH₃COO ( L =N, N’-bis(2-pyridylmethylidene)-1,2-(R,R+S,S) cyclohexanediamine and tta=2-thenoyltrifluoroacetonate) shows good CPL in organic solvents, because the tta ligands efficiently sensitize Yb NIR luminescence and the readily prepared chiral ligand L endows the complex with the necessary dissymmetry. PLGA nanoparticles incorporate the complex and protect the metal ion from the intrusion of solvent molecules, while ensuring biocompatibility, water solubility and stability to the complex. Hydrophilic NIR-CPL optical probes can find applications in the field of NIR-CPL bio-assays.     

Asymptotic Resonance, Interaction of Modes and Subharmonic Bifurcation

We study the existence of small amplitude oscillations near elliptic equilibria of autonomous systems, which mix different normal modes. The reference problem is the Fermi-Pasta-Ulam β-model: a chain of nonlinear oscillators with nearest-neighborhood interaction. We develop a new bifurcation approach that locates secondary bifurcations from the unimodal primary branches. Two sufficient conditions for bifurcation are given: one involves only the arithmetic properties of the eigenvalues of the linearized system (asymptotic resonance), while the other takes into account the nonlinear character of the interaction between normal modes (nonlinear coupling). Both conditions are checked for the Fermi-Pasta-Ulam problem.     

Water‐Splitting Electrocatalysis in Acid Conditions Using Ruthenate‐Iridate Pyrochlores

The pyrochlore solid solution (Na_0.33Ce_0.67)₂(Ir_1?xRu_x)₂O₇ (0≤x≤1), containing B‐site Ru^IV and Ir^IV is prepared by hydrothermal synthesis and used as a catalyst layer for electrochemical oxygen evolution from water at pH<7. The materials have atomically mixed Ru and Ir and their nanocrystalline form allows effective fabrication of electrode coatings with improved charge densities over a typical (Ru,Ir)O₂ catalyst. An in situ study of the catalyst layers using XANES spectroscopy at the Ir L_III and Ru K edges shows that both Ru and Ir participate in redox chemistry at oxygen evolution conditions and that Ru is more active than Ir, being oxidized by almost one oxidation state at maximum applied potential, with no evidence for ruthenate or iridate in +6 or higher oxidation states.