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The geodesic distance between points in real hyperbolic space is a hypermetric, and hence is a kernel negative type. The proof given here uses an integral formula for geodesic distance, in terms of a measure on the space of hyperplanes. An analogous integral formula, involving the space of horospheres, is given for complex hyperbolic space. By contrast… (More)

- L Wasungu, J-M Escoffre, A Valette, J Teissie, M-P Rols
- International journal of pharmaceutics
- 2009

Electropermeabilization is a physical method to deliver molecules into cells and tissues. Clinical applications have been successfully developed for antitumoral drug delivery and clinical trials for gene electrotransfer are currently underway. However, little is known about the mechanisms involved in this transfer. The main difficulties stem from the lack… (More)

- Chun-Gil Park, A. Valette
- 2005

It is shown that every almost linear mapping h:A → B of a unital Lie JC∗ -algebra A to a unital Lie JC∗ -algebra B is a Lie JC∗ algebra homomorphism when h(2nu ◦ y) = h(2nu) ◦ h(y) , h(3nu ◦ y) = h(3nu)◦h(y) or h(qnu◦y) = h(qnu)◦h(y) for all y ∈ A , all unitary elements u ∈ A and n = 0, 1, 2, · · · , and that every almost linear almost multiplicative… (More)

- Beata Kocel-Cynk, Anna Valette, ANNA VALETTE
- 2012

The aim of this note is to give yet another proof of the following theorem: given an arbitrary o-minimal structure on the ordered field of real numbers R and any definable family A of definable nonempty compact subsets of R n , then the closure of A in the sense of the Hausdorff metric (or, equivalently, in the Vietoris topology) is a definable family. In… (More)

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