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Get Complete Project Material File(s) Now! » Summary and future perspectives Semiclassical orthogonal polynomials, in particular generalized Freud polynomials, have been the main focus of this thesis. Generalized Freud polynomials are orthogonal with respect to the so-called generalized Freud inner...

Get Complete Project Material File(s) Now! » Orthogonal polynomials and their properties Orthogonal polynomials were used by R. Murphy (cf. [40]) in 1835 although he referred to them as ”reciprocal functions”. P.L. Chebyshev (cf. [16]) recognized the importance of orthogonal...

Get Complete Project Material File(s) Now! » The Algebraic Group Model A central paradigm for assessing the security of a cryptographic scheme or hardness assumption is to analyze it within an idealized model of computation. A line of work initiated...

Get Complete Project Material File(s) Now! » Reduced kinematics for the kinetic energy In order to lter local displacements, a reduced kinematics is introduced for the mass matrix. This reduced kinematics is intended to be such that the local displacements...

Get Complete Project Material File(s) Now! » Lattices in Physical Attacks If physical attacks sometimes allow the retrieval of the whole secret, in many cases, only part of the secret is revealed to the attacker. In those cases, lattice-based techniques...

Get Complete Project Material File(s) Now! » Euler characteristic Introduction to the Euler characteristic is often made with the so-called Polyhedra Formula. Among its countless contributions, Euler found out that alternative the sum of the number of vertices (V ),...

Get Complete Project Material File(s) Now! » Locally decodable and correctable codes Classical correcting algorithms allow us to retrieve a codeword c from a damaged version y of c. They usually take as input the entire noisy word y and...

Get Complete Project Material File(s) Now! » Motivation Since the 1990’s, Zeilberger’s method has been extensively studied in the literature [95, 96, 15, 92, 63, 6, 7, 65, 28, 16]. The main focus of those studies is on the efficiency...