On the regularity near the boundary of viscosity solutions of eikonal equations

Abstract We consider a non-characteristic boundary value problem for equations of eikonal type and we show that, near the boundary, the viscosity solution inherits the regularity of the data. As a consequence, we slightly improve the results in [1] on the structure of the cut-locus of a class of distance functions. Keywords: Viscosity solutions, Eikonal equation, Cut-locus, Analytic regularity     

Solvent effects on the tautomerism of apigeninidin

Solvent effects are found to be responsible for the predominance in water solution of a highly unstable tautomer of apigeninidin in vacuo. We present free energy perturbation in molecular dynamics simulations and self-consistent reaction field calculations of the relative solvation of the anionic tautomers of apigeninidin.     

Non-equilibrium thermodynamics of interfaces including electromagnetic effects

The application of non-equilibrium thermodynamics to a system consisting of two bulk phases and their interface is extended to include electromagnetic effects. The interface is assumed to carry singular mass, energy, and entropy densities as well as singular electric charge, electric current, polarization and magnetization. Electric and magnetic fields are allowed to be discontinuous across the interface, but not singular.Maxwell's equations are used to derive relationships among electromagnetic quantities on the surface and boundary conditions for the bulk phases. An expression for the surface entropy production including electromagnetic effects is obtained, and the resulting linear laws relating thermodynamic forces and fluxes are investigated.     

Models of the work function changes upon adsorbate clustering; application to experimental data

Two models are developed in order to explain the work function changes upon island formation of adsorbed metal atoms. The first model is based on a modified Helmholtz equation and the images method. It shows that the strong depolarization effect between the atoms belonging to the same cluster causes the work function to depend markedly on the average cluster size $\text{(}\text{N}{}_{\mathrm{<mtext>c</mtext>}}\text{)}$ for $\text{1 <}\text{N}{}_{\mathrm{<mtext>c</mtext>}}\text{? 6.}$ The second method has been developed using Monte-Carlo Simulation Processes in order to understand the mechanisms of cluster growth and their dependence on coverage and temperature. In spite of the different procedures employed to describe the experimental data the conclusions extracted from both models are in full agreement.     

Metal-Organic Layer Delivers 5-Aminolevulinic Acid and Porphyrin for Dual-Organelle-Targeted Photodynamic Therapy

The efficacy of photodynamic therapy (PDT) depends on the subcellular localization of photosensitizers. Herein, we report a dual-organelle-targeted nanoparticle platform for enhanced PDT of cancer. By grafting 5-aminolevulinic acid (ALA) to a Hf₁₂-based nanoscale metal-organic layer (Hf-MOL) via carboxylate coordination, ALA/Hf-MOL enhanced ALA delivery and protoporphyrin IX (PpIX) synthesis in mitochondria, and trapped the Hf-MOL comprising 5,15-di-p-benzoatoporphyrin (DBP) photosensitizers in lysosomes. Light irradiation at 630 nm simultaneously excited PpIX and DBP to generate singlet oxygen and rapidly damage both mitochondria and lysosomes, leading to synergistic enhancement of the PDT efficacy. The dual-organelle-targeted ALA/Hf-MOL outperformed Hf-MOL in preclinical PDT studies, with a 2.7-fold lower half maximal inhibitory concentration in cytotoxicity assays in vitro and a 3-fold higher cure rate in a colon cancer model in vivo.     

Asymmetric synthesis of 8-aminoindolizidine from chiral 2-pyrroleimines

1-Allyl-2-pyrroleimines obtained from (S)-valinol and (S)-phenylglycinol underwent highly diastereoselective addition of allylmagnesium chloride, used in excess amounts, to give the corresponding secondary amines with concomitant allyl to (Z)-1-propenyl isomerization of the 1-pyrrole substituent. Transformation of the 2-amino alcohol moiety to an oxazolidinone, or its cleavage and subsequent N-protection, followed by ring-closing metathesis of the two alkene groups gave the unsaturated bicyclic compound. Full hydrogenation of the alkene function and the aromatic rings afforded the indolizidine derivative as a mixture of two or three diastereomers with a ratio which was dependent on the nature of both the N-substituent and the catalyst. The two prevalent diastereomers were isolated, and their configuration was determined by X-ray crystallographic analysis.     

On the Experimental Determination of 4f–4f Intensity Parameters from the Emission Spectra of Europium (III) Compounds

Optics and Spectroscopy - Eu3+ complexes and specially β-diketonate compounds are well known and studied in several areas due to their luminescence properties, such as sensors and lightning...     

Singular gradient flow of the distance function and homotopy equivalence

Let $M$ be a Riemannian manifold and let $\varOmega $ be a bounded open subset of $M$ . It is well known that significant information about the geometry of $\varOmega $ is encoded into the properties of the distance, $d_{\partial \varOmega }$ , from the boundary of $\varOmega $ . Here, we show that the generalized gradient flow associated with the distance preserves singularities, that is, if $x_0$ is a singular point of $d_{\partial \varOmega }$ then the generalized characteristic starting at $x_0$ stays singular for all times. As an application, we deduce that the singular set of $d_{\partial \varOmega }$ has the same homotopy type as $\varOmega $ .