Institute Of Mathematiques Of Jussieu Paris Rive Gauche

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Institute Of Mathematiques Of Jussieu Paris Rive Gauche

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Delisle L.,Institute Of Mathematiques Of Jussieu Paris Rive Gauche
Journal of Mathematical Physics | Year: 2017

We present a bilinear Hirota representation of the N = 2 supersymmetric extension of the Korteweg-de Vries equation. This representation is deduced using binary Bell polynomials, hierarchies, and fermionic limits. We, also, propose a new approach for the generalisation of the Hirota bilinear formalism in the N = 2 supersymmetric context.


Delisle L.,Institute Of Mathematiques Of Jussieu Paris Rive Gauche | Hussin V.,University of Montréal | Zakrzewski W.J.,Durham University
Journal of Physics: Conference Series | Year: 2015

We investigate the geometric characteristics of constant Gaussian curvature surfaces obtained from solutions of the G(m, n) sigma model. Most of these solutions are related to the Veronese sequence. We show that we can distinguish surfaces with the same Gaussian curvature using additional quantities like the topological charge and the mean curvature. The cases of G(1,n) = CPn-1 and G(2,n) are used to illustrate these characteristics. © Published under licence by IOP Publishing Ltd.


Delisle L.,Institute Of Mathematiques Of Jussieu Paris Rive Gauche | Hussin V.,University of Montréal | Zakrzewski W.J.,Durham University
Journal of Mathematical Physics | Year: 2016

A new approach for the construction of finite action solutions of the supersymmetric CPN-1 sigma model is presented. We show that this approach produces more non-holomorphic solutions than those obtained in previous approaches. We study the CP2 model in detail and present its solutions in an explicit form. We also show how to generalise this construction to N > 3. © 2016 AIP Publishing LLC.


Leducq E.,Institute Of Mathematiques Of Jussieu Paris Rive Gauche | Leducq E.,University Paris - Sud
Designs, Codes, and Cryptography | Year: 2015

Jedlicka, Hernando and McGuire proved that Gold and Kasami functions are the only power mappings which are APN on infinitely many extensions of (Formula presented.). For p an odd prime, we prove that the only power mappings (Formula presented.) such that (Formula presented.) which are PN on infinitely many extensions of (Formula presented.) are those such that (Formula presented.), l positive integer. As Jedlicka, Hernando and McGuire, we prove that (Formula presented.) has an absolutely irreducible factor by using Bézout’s theorem. © 2013, Springer Science+Business Media New York.


Michel P.,Institute Of Mathematiques Of Jussieu Paris Rive Gauche | Michel P.,Cergy-Pontoise University
Logical Methods in Computer Science | Year: 2015

By introducing the busy beaver competition of Turing machines, in 1962, Rado defined noncomputable functions on positive integers. The study of these functions and variants leads to many mathematical challenges. This article takes up the following one: How can a small Turing machine manage to produce very big numbers? It provides the following answer: mostly by simulating Collatz-like functions, that are generalizations of the famous 3x+1 function. These functions, like the 3x+1 function, lead to new unsolved problems in number theory. © 2015 Logical Methods in Computer Science.


Finkel O.,Institute Of Mathematiques Of Jussieu Paris Rive Gauche | Skrzypczak M.,University of Warsaw
Information Processing Letters | Year: 2014

We show that there are Σ30-complete languages of infinite words accepted by non-deterministic Petri nets with Büchi acceptance condition, or equivalently by Büchi blind counter automata. This shows that ω-languages accepted by non-deterministic Petri nets are topologically more complex than those accepted by deterministic Petri nets. © 2013 Elsevier B.V.


Delisle L.,Institute Of Mathematiques Of Jussieu Paris Rive Gauche
Journal of Physics A: Mathematical and Theoretical | Year: 2016

We present a characterization of Maurer-Cartan 1-superforms associated to the two-dimensional supersymmetric ℂpN-1 sigma model. We, then, solve the associated linear spectral problem and use its solutions to describe an integrable system for a su(N)-valued map. © 2016 IOP Publishing Ltd.


Finkel O.,Institute Of Mathematiques Of Jussieu Paris Rive Gauche
Information Processing Letters | Year: 2015

In this short note, we give the exact complexity of the infinite Post Correspondence Problem, showing that it is Π10-complete. Surprisingly, it turns out that the infinite Post Correspondence Problem is not "more complex" than the Post Correspondence Problem, which is known to be Σ10-complete, but has the exact dual complexity. This gives an answer to a question of Simonnet [15]. © 2015 Elsevier B.V. Allrightsreserved.

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