Résumé: © 2018, SBMAC – Sociedade Brasileira de Matemática Aplicada e Computacional. Our goal is to propose an efficient approach to characterize the eigenvalues and eigenfunctions of the Helmholtz equation with mixed (Dirichlet and Neumann) boundary conditions. Our approach is based on layer potentials. We extend the eigenvalue characterization known for Neumann boundary conditions to the case of mixed boundary conditions. The problem is motivated by the need of such methods for real-time wave-field shaping by electronically tunable surfaces.

Résumé: © 2018 American Chemical Society. Amphiphilic triblock (Atri) copolymers made of perfluorinated alkyl chain linked to hydrocarbon chain and methoxy-poly(ethylene glycol) of three different molecular weights were synthesized. In vitro evaluation demonstrated that these new compounds were noncytotoxic. Characterization and interaction of each triblock copolymer with a branched polyamine myristoyl lipid (2-{3[bis-(3-amino-propyl)-amino]-propylamino}-N-ditetradecyl carbamoyl methyl-acetamide, DMAPAP) were studied by the Langmuir film method and thermal analysis. The triblock copolymer/cationic lipids (1:10, w/w) were mixed with perfluorobutane gas to form microbubbles (MBs). The latter were characterized by optical microscopy to get the microbubble size and concentration by densimetry to determine the amount of encapsulated gas and by ultrasound to assess oscillation properties. Atri with the lowest and intermediate weights were shown to interact with the cationic lipid DMAPAP and stabilize the Langmuir film. In that case, monodisperse microbubbles ranging from 2.3 ± 0.1 to 2.8 ± 0.1 μm were obtained. The proportion of encapsulated gas within the MB shell increased up to 3 times after the incorporation of the copolymer with the lowest and intermediate weights. Moreover, the acoustic response of the microbubbles was maintained in the presence of the copolymers.