Embeddings of ultradistributions and periodic hyperfunctions in Colombeau type algebras through sequence spaces

In a recent paper, we gave a topological description of Colombeau type algebras introducing algebras of sequences with exponential weights. Embeddings of Schwartz' spaces into the Colombeau algebra G are well known, but for ultradistribution and periodic hyperfunction type spaces we give new constructions. We show that the multiplication of regular enough functions (smooth, ultradifferentiable or quasianalytic), embedded into corresponding algebras, is the ordinary multiplication

Encapsulation de proteins thérapeutiques dans des microspheres de CaCO3 élaborées en milieu CO2 supercritique

National audienc

Microencapsulation of proteins within CaCO3 microspheres using supercritical CO2 media

International audienc

Synthesis of hollow vaterite CaCO(3) microspheres in supercritical carbon dioxide medium

We here describe a rapid method for synthesizing hollow core, porous crystalline calcium carbonate microspheres composed of vaterite using supercritical carbon dioxide in aqueous media, without surfactants. We show that the reaction in alkaline media rapidly conducts to the formation of microspheres with an average diameter of 5 mu m. SEM, TEM and AFM observations reveal that the microspheres have a hollow core of around 0.7 mu m width and are composed of nanograins with an average diameter of 40 nm. These nanograins are responsible for the high specific surface area of 16 m(2) g(-1) deduced from nitrogen absorption/desorption isotherms, which moreover confers an important porosity to the microspheres. We believe this work may pave the way for the elaboration of a biomaterial with a large potential for therapeutic as well as diagnostic applications

Generalized Fourier Integral Operators on spaces of Colombeau type

Generalized Fourier integral operators (FIOs) acting on Colombeau algebras are defined. This is based on a theory of generalized oscillatory integrals (OIs) whose phase functions as well as amplitudes may be generalized functions of Colombeau type. The mapping properties of these FIOs are studied as the composition with a generalized pseudodifferential operator. Finally, the microlocal Colombeau regularity for OIs and the influence of the FIO action on generalized wave front sets are investigated. This theory of generalized FIOs is motivated by the need of a general framework for partial differential operators with non-smooth coefficients and distributional data