The subject of this talk concerns to the classical inverse spectral problem. This inverse problem can be formulated as follows: do the Dirichlet eigenvalues and the derivatives (which order?) of the normalized eigenfunctions at the boundary determine uniquely the coefficients of the corresponding differential operator? For operators of order two this type of theorem is called Borg-Levinson theo...

1.1. Review of topology. Definition 1.1. A topological space is a pair (X, T) consisting of a set X and a collection T = {U α } of subsets of X, satisfying the following: (1) ∅, X ∈ T , (2) if U α , U β ∈ T , then U α ∩ U β ∈ T , (3) if U α ∈ T for all α ∈ I, then ∪ α∈I U α ∈ T. (Here I is an indexing set, and is not necessarily finite.) T is called a topology for X and U α ∈ T is called an ope...

Using standard analysis only, we present an extension •R of the real field containing nilpotent infinitesimals. On the one hand we want to present a very simple setting to formalize infinitesimal methods in Differential Geometry, Analysis and Physics. On the other hand we want to show that these infinitesimals may be also useful in infinite dimensional Differential Geometry, e.g. to study space...

My main research goal is to develop robust, predictive, and multi-purpose computation tools by leveraging differential geometric concepts and foundations. In particular, I wish to contribute a number of practical applications in computer graphics and related areas, such as medical imaging, biometrics, medical simulation, and visualization, by focusing on the geometrical foundations common to co...