Weak Liouville-Arnol′d Theorems and Their Implications

This paper studies the existence of invariant smooth Lagrangian graphs for Tonelli Hamiltonian systems with symmetries. In particular, we consider Tonelli Hamiltonians with n independent but not necessarily involutive constants of motion and obtain two theorems reminiscent of the Liouville-Arnol′d theorem. Moreover, we also obtain results on the structure of the configuration spaces of such systems that are reminiscent of results on the configuration space of completely integrable Tonelli Hamiltonians.     

Existence of Non-degenerate Continua of Singular Radial Solutions for Several Classes of Semilinear Elliptic Problems

We establish the existence of countably many branches of uncountably many solutions to elliptic boundary value problems with subcritical, and subsuper critical growth. We also prove the existence of two branches of uncountably many solutions to a problem with jumping nonlinearities. This case is remarkable since, generically, this problem has only finitely many regular solutions.     

Temperature dependence of the properties of ternary systems ethanol + water + an aliphatic alkane (C6-C9)

The measures and calculation of different properties such as refractive index, density, speed of sound, excess molar volume, and isentropic compressibility of the ternary heterogeneous compounds by ethanol + water + (n-hexane, n-heptane, n-octane, n-nonane) have been performed in the range 288.15–323.15 K and atmospheric pressure. Attending to the accurate results of these models, the equation of state enclosing mixing rules is indicated as a simple estimation of the procedures of these properties for this kind of multicomponent systems.     

pH‐Dependent Chloride Transport by Pseudopeptidic Cages for the Selective Killing of Cancer Cells in Acidic Microenvironments

Acidic microenvironments in solid tumors are a hallmark of cancer. Inspired by that, we designed a family of pseudopeptidic cage‐like anionophores displaying pH‐dependent activity. When protonated, they efficiently bind chloride anions. They also transport chloride through lipid bilayers, with their anionophoric properties improving at acidic pH, suggesting an H⁺/Cl^? symport mechanism. NMR studies in DPC micelles demonstrate that the cages bind chloride within the lipid phase. The chloride affinity and the chloride‐exchange rate with the aqueous bulk solution are improved when the pH is lowered. This increases cytotoxicity towards lung adenocarcinoma cells at the pH of the microenvironment of a solid tumor. These properties depend on the nature of the amino‐acid side chains of the cages, which modulate their lipophilicity and interactions with the cell membrane. This paves the way towards using pH as a parameter to control the selectivity of cytotoxic ionophores as anticancer drugs.     

Janus Gold Nanostars–Mesoporous Silica Nanoparticles for NIR-Light-Triggered Drug Delivery

Janus gold nanostar–mesoporous silica nanoparticle ( AuNSt–MSNP ) nanodevices able to release an entrapped payload upon irradiation with near infrared (NIR) light were prepared and characterized. The AuNSt surface was functionalized with a thiolated photolabile molecule ( 5 ), whereas the mesoporous silica face was loaded with a model drug (doxorubicin) and capped with proton-responsive benzimidazole-β-cyclodextrin supramolecular gatekeepers ( N 1 ). Upon irradiation with NIR-light, the photolabile compound 5 photodissociated, resulting in the formation of succinic acid, which induced the opening of the gatekeeper and cargo delivery. In the overall mechanism, the gold surface acts as a photochemical transducer capable of transforming the NIR-light input into a chemical messenger (succinic acid) that opens the supramolecular nanovalve. The prepared hybrid nanoparticles were non-cytotoxic to HeLa cells, until they were irradiated with a NIR laser, which led to intracellular doxorubicin release and hyperthermia. This induced a remarkable reduction in HeLa cells viability.     

Cytotoxic and NF-κB inhibitory sesquiterpene lactones from Piptocoma rufescens

Six new (1-6) and eight known germacranolide-type sesquiterpene lactones, along with several known phenylpropanol coumarates and methylated flavonoids, were isolated from the leaves of Piptocoma rufescens, collected in the Dominican Republic. The new compounds were identified by analysis of their spectroscopic data, with the molecular structure of 3 being established by single-crystal X-ray diffraction. The absolute configurations of the sesquiterpene lactones isolated were determined from their CD and NOESY NMR spectra, together with the analysis of Mosher ester reactions. Bioassay screening results showed the majority of the sesquiterpene lactones isolated (1-13) to be highly cytotoxic toward the HT-29 human colon cancer cell line, with the most potent compound being 15-deoxygoyazensolide (10, IC(50), 0.26 μM). In addition, several of the sesquiterpene lactones exhibited NF-κB (p65) inhibitory activity.