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In this thesis we are interested in the following problem : given two differential k–forms g and f, most of the time they will be assumed closed, on what conditions can we pullback g to f by a map φ ? In other words we ask when it is possible to solve the ...
The identification of kinetic models is an important step for the monitoring, control and optimization of industrial processes. This is particularly the case for highly competitive business sectors such as chemical and pharmaceutical industries, where the ...
Instances of control systems are presented for which dynamical feedback linearizability can be assessed from differential forms of highest relative degree after some “contact” transformation has been applied. This bypasses the need to find a polynomial dif ...
The fractional Laplacian (-Delta)(gamma/2) commutes with the primary coordination transformations in the Euclidean space Rd: dilation, translation and rotation, and has tight link to splines, fractals and stable Levy processes. For 0 < gamma < d, its inver ...
We investigate the axial phase evolution of light emerging from microstructures. The high-resolution interference microscope (HRIM) allows to record three-dimensional (3D) phase distributions in differential and propagation modes along the longitudinal dir ...
In Control System Theory, the study of continuous-time, finite dimensional, underdetermined systems of ordinary differential equations is an important topic. Classification of systems in different categories is a natural initial step to the analysis of a g ...
The hash function Skein is the submission of Ferguson et al. to the NIST Hash Competition, and is arguably a serious candidate for selection as SHA-3. This paper presents the first third-party analysis of Skein, with an extensive study of its main componen ...
We analyze the internal permutations of Keccak, one of the NIST SHA-3 competition finalists, in regard to differential properties. By carefully studying the elements composing those permutations, we are able to derive most of the best known differential pa ...
We consider second-order quasilinear elliptic systems on un-bounded domains in the setting of Sobolev spaces. We complete our earlier work on the Fredholm and properness properties of the associated differential operators by giving verifiable conditions fo ...
In this paper we present a new statistical cryptanalytic technique that we call improbable differential cryptanalysis which uses a differential that is less probable when the correct key is used. We provide data complexity estimates for this kind of attack ...
