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Admissibility for quasiregular representations of exponential solvable Lie groups

Vignon Oussa — 2013

Colloquium Mathematicae

Let N be a simply connected, connected non-commutative nilpotent Lie group with Lie algebra of dimension n. Let H be a subgroup of the automorphism group of N. Assume that H is a commutative, simply connected, connected Lie group with Lie algebra . Furthermore, assume that the linear adjoint action of on is diagonalizable with non-purely imaginary eigenvalues. Let τ = I n d H N H 1 . We obtain an explicit direct integral decomposition for τ, including a description of the spectrum as a submanifold of (+)*, and a...

Optimal solutions for a model of tumor anti-angiogenesis with a penalty on the cost of treatment

Urszula LedzewiczVignon OussaHeinz Schättler — 2009

Applicationes Mathematicae

The scheduling of angiogenic inhibitors to control a vascularized tumor is analyzed as an optimal control problem for a mathematical model that was developed and biologically validated by Hahnfeldt et al. [Cancer Res. 59 (1999)]. Two formulations of the problem are considered. In the first one the primary tumor volume is minimized for a given amount of angiogenic inhibitors to be administered, while a balance between tumor reduction and the total amount of angiogenic inhibitors given is minimized...

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