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- G Deffieux, D Merlet, R Baute, G Bourgeois, M A Baute, A Neveu
- The Journal of antibiotics
- 1981

Isariins B, C and D, isolated from a strain of Isaria felina, were shown to be cyclodepsipeptides constituted by a pentapeptide cyclized through a beta-hydroxyacid. The nature of the latter and the sequence of the peptide were determined for each compound. Relations between insecticidal activity and structure of the depsipeptides were pointed out.

Let A, B be n × n complex matrices such that C = AB − BA and A commute. For n = 2, we prove that A, B are simultaneously triangularizable. For n ≥ 3, we give an example of matrices A, B such that the pair (A, B) does not have property L of Motzkin-Taussky, and such that B and C are not simultaneously triangularizable. Finally, we estimate the complexity of… (More)

- Gerald Bourgeois, Sébastien Orange
- Automated Deduction in Geometry
- 2008

- Gerald Bourgeois, Jean-Charles Faugère
- J. Mathematical Cryptology
- 2009

We present an algebraic attack on NTRU (restricted to the case where the parameter q is a power of two) using the method of the Witt vectors proposed by Silverman, Smart and Vercauteren [17]; the latter considered only the first two bits of a Witt vector attached to the recovering of the secret key in order to reduce the problem to the resolution of an… (More)

Let A, B be n × n complex matrices such that C = AB − BA and A commute. For n = 2, we prove that A, B are simultaneously triangularizable. For n ≥ 3, we give an example of matrices A, B such that the pair (A, B) does not have property L of Motzkin-Taussky, and such that B and C are not simultaneously triangularizable. Finally, we estimate the complexity of… (More)

- GERALD BOURGEOIS
- 2005

f, g ∈ L(E) where E is a k vector space of dimension d. We introduce the relation (*): exp(t.f + g) = exp(t.f) ◦ exp(g) for any t ∈ k or N; we study the connections between the relations () and f ◦g = g◦f for d = 2 or 3. Let d = 2: if k = R and if (*) is verified for t ∈ N then f ◦g = g◦f ; we obtain all the couples f , g verifying (*) on C and such as f ◦g… (More)

- Gerald Bourgeois
- ArXiv
- 2006

Résumé : on améliore une attaque algébrique de NTRU (où le paramètre q est une puissance de 2), due à Silverman, Smart et Vercauteren ; au lieu de considérer, comme les précédents, les 2 premiers bits d’un vecteur de Witt attaché à la recherche de la clé secrète, on considère ici les 4 premiers bits, ce qui fournit des équations supplémentaires de degrés 4… (More)

Let T0 = (A 0 0 · · ·A d 0) be a d-simplex, G0 its centroid, S its circumsphere, O the center of S . Let (Ai1) be the points where S intersects the lines (G0A i 0), T1 the d-simplex (A01 · · ·A d 1), and G1 its centroid. By iterating this construction, a dynamical system of dsimplices (Ti) with centroids (Gi) is constructed. For d = 2 or 3, we prove that… (More)

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