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Stability for nonlinear impulsive differential equations with "supremum"is studied. Special type of stability, combining two different measures and scalar product, is defined. The definition is generalization of several known in the literature types of stabiUty. Method of Razumikhin, perturbing Lyapunov functions and comparison method for scalar impulsive ordinary differential equations have been employed.Keywords: (po-stability in terms of two measures, piecewise continuous Lyapunov functions, impidsive differential equations with "supremum".

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Low resolution electromagnetic tomography (LORETA) is a well-known method for the solution of the l2-based minimization problem for EEG/MEG source reconstruction. LORETA with a volume-based source space is widely used and much effort has been invested in the theory and the application of the method in an experimental context. However, it is especially interesting to use anatomical prior knowledge and constrain the LORETA's solution to the cortical surface. This strongly reduces the number of unknowns in the inverse approach. Unlike the Laplace operator in the volume case with a rectangular and regular grid, the mesh is triangulated and highly irregular in the surface case. Thus, it is not trivial to choose or construct a Laplace operator (termed Laplace-Beltrami operator when applied to surfaces) that has the desired properties and takes into account the geometry of the mesh. In this paper, the basic methodology behind cortical LORETA is discussed and the method is applied for source reconstruction of simulated data using different Laplace-Beltrami operators in the smoothing term. The results achieved with the different operators are compared with respect to their accuracy using various measures. Conclusions about the choice of an appropriate operator are deduced from the results.

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