# INSTITUT DE MATHEMATIQUES DE BOURGOGNE

UMR 5584

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## Prépublications dans HAL

Dernières parutions

Une partie des prépublications de l’Institut de Mathématiques de Bourgogne est disponible dans la collection HAL du laboratoire.

Ci-dessous les derniers dépôts des membres de l’IMB :

### [hal-01880822] Hyperboloidal slicing approach to quasi-normal mode expansions : the Reissner-Nordström case

25 septembre 2018

We study quasi-normal modes of black holes, with a focus on resonant (or quasi-normal mode) expansions, in a geometric frame based on the use of conformal compactifications together with hyperboloidal foliations of spacetime. Specifically, this work extends the previous study of Schwarzschild (...)

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### [hal-01871974] Notes on the Sagnac effect in General Relativity

11 septembre 2018

The Sagnac effect can be described as the difference in travel time between two photons traveling along the same path in opposite directions. In this paper we explore the consequences of this characterisation in the context of General Relativity. We derive a general expression for this time (...)

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### [hal-01871562] Gravitational waves and the Sagnac effect

11 septembre 2018

Light rays propagating in opposite directions around the same loop in general show a relative phase shift when recombined. This phenomenon is known as the Sagnac effect after Georges Sagnac who, in 1913, demonstrated with an interferometer on a rotating table that the phase shift depended on (...)

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### [hal-01865763] Families of solutions to the KPI equation and the structure of their rational representations of order N

7 septembre 2018

We construct solutions to the Kadomtsev-Petviashvili equation (KPI) in terms of Fredholm determinants. We deduce solutions written as a quotient of wronskians of order 2N. These solutions called solutions of order N depend on 2N − 1 parameters. They can also be written as a quotient of two (...)

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### [hal-01865442] Real structures on horospherical varieties

5 septembre 2018

We study the equivariant real structures on complex horospher-ical varieties, generalizing classical results known for toric varieties and flag varieties. In particular, we obtain a necessary and sufficient condition for the existence of such real structures and determine the number of (...)

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### [hal-01864114] Virtual braids and permutations

30 août 2018

Let VB_n be the virtual braid group on n strands and let S_n be the symmetric group on n letters. Let n, m ∈ N such that n ≥ 5, m ≥ 2 and n ≥ m. We determine all possible homomorphisms from VB_n to S_m , from S_n to VB_m and from VB_n to VB_m. As corollaries we get that Out(VB_n) is isomorphic to (...)

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### [hal-01854551] Pontryagin-Type Conditions for Optimal Muscular Force Response to Functional Electric Stimulations

6 août 2018

In biomechanics, recent mathematical force-fatigue models allow to predict the muscular response to functional electric stimulations and this opens the road to compute optimized electrical pulses trains. Such pulses are modeled as Dirac pulses and this leads to a sampled-data control problem. (...)

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### [hal-01851770] Analytic Bergman operators in the semiclassical limit

1er août 2018

Using a new quantization scheme, we construct approximate semi-classical Bergman projections on weighted L² spaces with analytic weights, and show that their kernel functions admit an asymptotic expansion in the class of analytic symbols. As a corollary, we obtain new estimates for asymptotic (...)

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### [hal-01851166] The open XXZ spin chain in the SoV framework : scalar product of separate states

29 juillet 2018

In our previous paper [1] we have obtained, for the XXX spin-1/2 Heisenberg open chain, new determinant representations for the scalar products of separate states in the quantum separation of variables (SoV) framework. In this article we perform a similar study in a more complicated case: the (...)

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### [hal-01838437] Algebraic vector bundles on the 2-sphere and smooth rational varieties with infinitely many real forms

16 juillet 2018

We construct smooth rational real algebraic varieties of every dimension ≥ 4 which admit infinitely many pairwise non-isomorphic real forms.

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### [hal-01829562] Characterization of stationary probability measures for Variable Length Markov Chains

6 juillet 2018

By introducing a key combinatorial structure for words produced by a Variable Length Markov Chain (VLMC), the longest internal suffix, precise characterizations of existence and uniqueness of a stationary probability measure for a VLMC chain are given. These characterizations turn into (...)

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### [hal-01226734] Geometric and Numerical Optimal Control with Application to Swimming at Low Reynolds Number and Magnetic Resonance Imaging.

3 juillet 2018

This series of notes have their origin into accelerated course in optimal control given to multidisciplinary Phd students in Mathematics, Physics or Control Engineering and the purpose is to present the seminal results of this theory in view of applications to concrete problems. For that we (...)

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### [hal-01826458] Infinite families of inequivalent real circle actions on affine four-space

3 juillet 2018

The main result of this article is to construct infinite families of non-equivalent equivariant real forms of linear C*-actions on affine four-space. We consider the real form of C* whose fixed point is a circle. In [F-MJ] one example of a non-linearizable circle action was constructed. Here, (...)

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### [hal-01679261] Non-integrability of the minimum-time Kepler problem

25 juin 2018

We prove that the minimum-time controlled Kepler problem is not meromorphically Liouville integrable on the Riemann surface of its Hamiltonian.

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### [hal-01819219] Is the 1-norm the best convex sparse regularization ?

21 juin 2018

The 1-norm is a good convex regularization for the recovery of sparse vectors from under-determined linear measurements. No other convex regularization seems to surpass its sparse recovery performance. How can this be explained? To answer this question, we define several notions of " best (...)

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### [hal-01810449] A Topological Invariant for Modular Fusion Categories

8 juin 2018

The modular data of a modular category C, consisting of the S-matrix and the T-matrix, is known to be a incomplete invariant of C. More generally, the invariants of framed links and knots defined by a modular category as part of a topological quantum field theory can be viewed as numerical (...)

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### [hal-01531275] Ordering Garside groups

8 juin 2018

We introduce a condition on Garside groups that we call Dehornoy structure. An iteration of such a structure leads to a left order on the group. We show conditions for a Garside group to admit a Dehornoy structure, and we apply these criteria to prove that the Artin groups of type A and I 2 (...)

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### [hal-01807041] Convergence rate of a relaxed inertial proximal algorithm for convex minimization

5 juin 2018

In a Hilbert space setting, the authors recently introduced a general class of relaxed inertial proximal algorithms that aim at solving monotone inclusions. In this paper, we specialize this study in the case of non-smooth convex minimization problems. We obtain convergence rates for the values (...)

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### [hal-01806603] Torsion of a finite base locus

4 juin 2018

We interpret geometrically the torsion of the symmetric algebra of the ideal sheaf of a zero-dimensional scheme Z defined by n + 1 equations in an n-dimensional variety. This leads us to generalise a formula of A.Dimca and S.Papadima in positive characteristic for a rational transformation with (...)

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### [hal-01806297] First and second order rational solutions to the Johnson equation and rogue waves

4 juin 2018

Rational solutions to the Johnson equation are constructed as a quotient of two polynomials in x, y and t depending on several real parameters. We obtain an infinite hierarchy of rational solutions written in terms of polynomials of degrees 2N (N + 1) in x, and t, 4N (N + 1) in y, depending on (...)

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### [hal-01802038] Algebraic models of the line in the real affine plane

29 mai 2018

We study smooth rational closed embeddings of the real affine line into the real affine plane, that is algebraic rational maps from the real affine line to the real affine plane which induce smooth closed embeddings of the real euclidean line into the real euclidean plane. We consider these up (...)

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### [hal-01720871] Optimality of 1-norm regularization among weighted 1-norms for sparse recovery : a case study on how to find optimal regularizations

23 mai 2018

The 1-norm was proven to be a good convex regularizer for the recovery of sparse vectors from under-determined linear measurements. It has been shown that with an appropriate measurement operator, a number of measurements of the order of the sparsity of the signal (up to log factors) is (...)

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### [hal-01790674] Cylinders in Mori Fiber Spaces : forms of the quintic del Pezzo threefold

15 mai 2018

Motivated by the general question of existence of open A1-cylinders in higher dimensional pro-jective varieties, we consider the case of Mori Fiber Spaces of relative dimension three, whose general closed fibers are isomorphic to the quintic del Pezzo threefold V5 , the smooth Fano threefold of (...)

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### [hal-01787553] Resolution of the symmetric algebra of a finite base locus

15 mai 2018

We provide a locally free resolution of the projectivized symmetric algebra of the ideal sheaf of a zero-dimensional scheme defined by n + 1 equations in an n-dimensional variety. The resolution is given in terms of the resolution of the ideal itself and of the Eagon-Northcott complex of the (...)

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### [hal-01653901] Sub-Riemannian geometry, Hamiltonian dynamics, micro-swimmers, Copepod nauplii and Copepod robot

4 mai 2018

The objective of this article is to present the seminal concepts and techniques of Sub-Riemannian geometry and Hamiltonian dynamics, complemented by adapted software to analyze the dynamics of the copepod micro-swimmer, where the model of swimming is the slender body approximation for Stokes (...)

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2 mai 2018

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### [hal-01312534] Orbital stability via the energy-momentum method : the case of higher dimensional symmetry groups

9 mai 2016

We consider the orbital stability of the relative equilibria of Hamiltonian dynamical systems on Banach spaces, in the presence of a multi-dimensional invariance group for the dynamics. We present a generalization of the Vakhitov-Kolokolov slope condition to this higher dimensional setting, and (...)

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### [hal-01293978] Higher Frobenius-Schur indicators for Drinfeld doubles of finite groups through characters of centralizers

8 avril 2016

We present a new approach to calculating the higher Frobenius-Schur indicators for the simple modules over the Drinfeld double of a finite group. In contrast to the formula by Kashina-Sommerhäuser-Zhu that involves a sum over all group elements satisfying a certain condition, our formula (...)

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### [hal-01299469] Families of deformations of the twelfth Peregrine breather solutions to the NLS equation with twenty two parameters

7 avril 2016

The twelfth Peregrine breather (P12 breather) solution to the focusing one dimensional nonlinear Schrödinger equation (NLS) with its twenty two real parameters deformations solutions to the NLS equation are explicitly constructed here. New families of quasi-rational solutions of the NLS equation (...)

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### [hal-01286602] A Numerical Approach to the Optimal Control and Efficiency of the Copepod Swimmer

7 avril 2016

— The objective of this article is to make a geometric and numerical analysis about the optimal displacements of a larval copepod swimming at low Reynolds number. A simplified model of locomotion is analyzed in the framework of Sub-Riemannian geometry. In particular, the role of both normal and (...)

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### [hal-01226734] Working Examples In Geometric Optimal Control

25 mars 2016

This series of notes have their origin into accelerated course in optimal control given to multidisciplinary Phd students in Mathematics, Physics or Control Engineering and the purpose is to present the seminal results of this theory in view of applications to concrete problems. For that we (...)

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### [hal-01287290] Optimal Control of an Ensemble of Bloch Equations with Applications in MRI

14 mars 2016

The optimal control of an ensemble of Bloch equations describing the evolution of an ensemble of spins is the mathematical model used in Nuclear Resonance Imaging and the associated costs lead to consider Mayer optimal control problems. The Maximum Principle allows to parameterize the optimal (...)

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### [hal-01143763] The Purcell Three-link swimmer : some geometric and numerical aspects related to periodic optimal controls

11 mars 2016

The maximum principle combined with numerical methods is a powerful tool to compute solutions for optimal control problems. This approach turns out to be extremely useful in applications, including solving problems which require establishing periodic trajectories for Hamiltonian systems, (...)

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### [hal-01286602] A Numerical Approach to the Optimal Control and Efficiency of the Copepod Swimmer

11 mars 2016

The objective of this article is to make a geometric and numerical analysis about the optimal displacements of a larval copepod swimming at low Reynolds number. A simplified model of locomotion is analyzed in the framework of Sub-Riemannian geometry. In particular, the role of both normal and (...)

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### [hal-01164543] A simple solution to the word problem for virtual braid groups

4 mars 2016

We show a simple and easily implementable solution to the word problem for virtual braid groups.

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### [hal-01280499] QUADRATIC AND PINCZON ALGEBRAS

1er mars 2016

Given a symmetric non degenerated bilinear form b on a vector space V , G. Pinczon and R. Ushirobira defined a bracket , on the space of multilinear skewsymmetric forms on V. With this bracket, the quadratic Lie algebra structure equation on (V, b) becomes simply Ω, Ω = 0. We characterize (...)

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### [hal-01197123] Generalized stochastic Lagrangian paths for the Navier-Stokes equation

23 février 2016

In the note added in proof of the seminal paper [Groups of diffeomorphisms and the motion of an incompressible fluid, Ann. of Math. 92 (1970), 102-163], Ebin and Marsden introduced the so-called correct Laplacian for the Navier-Stokes equation on a compact Riemannian manifold. In the spirit of (...)

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### [hal-01276394] Patterns of deformations of P 3 and P 4 breathers solutions to the NLS equation

23 février 2016

In this article, one gives a classification of the solutions to the one dimensional nonlinear focusing Schrödinger equation (NLS) by considering the modulus of the solutions in the (x, t) plan in the cases of orders 3 and 4. For this, we use a representation of solutions to NLS equation as a (...)

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### [hal-01159255] Autoregressive Functions Estimation in Nonlinear Bifurcating Autoregressive Models

13 février 2016

Bifurcating autoregressive processes, which can be seen as an adaptation of au-toregressive processes for a binary tree structure, have been extensively studied during the last decade in a parametric context. In this work we do not specify any a priori form for the two autoregressive functions (...)

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### [hal-01017350] Homotopy classification of ribbon tubes and welded string links

8 février 2016

Ribbon 2-knotted objects are locally flat embeddings of surfaces in 4-space which bound immersed 3-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. In this paper, we consider ribbon (...)

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### [hal-01017350] Homotopy classification of ribbon tubes and welded string links

25 janvier 2016

Ribbon 2-knotted objects are locally flat embeddings of surfaces in 4-space which bound immersed 3-manifolds with only ribbon singularities. They appear as topological realizations of welded knotted objects, which is a natural quotient of virtual knot theory. In this paper, we consider ribbon (...)

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### [hal-01254200] Adaptive Estimation for Bifurcating Markov Chains

13 janvier 2016

In a first part, we prove Bernstein-type deviation inequalities for bifurcating Markov chains (BMC) under a geometric ergodicity assumption, completing former results of Guyon and Bitseki Penda, Djellout and Guillin. These preliminary results are the key ingredient to implement nonparametric (...)

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### [hal-01251594] ADAPTIVE ESTIMATION FOR BIFURCATING MARKOV CHAINS

7 janvier 2016

In a first part, we prove Bernstein-type deviation inequalities for bifurcating Markov chains (BMC) under a geometric ergodicity assumption, completing former results of Guyon and Bitseki Penda, Djellout and Guillin. These preliminary results are the key ingredient to implement nonparametric (...)

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### [hal-01246830] Un astronome bourguignon : Alexandre Véronnet (1876-1951) (document de travail, version 1)

22 décembre 2015

Qui est donc Alexandre Véronnet ? C'est à cette question que nous allons répondre. Nous allons voir que Alexandre Véronnet est un scientifique tout à fait étonnant ayant eu un parcours particulièrement original.

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### [hal-01224526] The eleventh Peregrine breather and twenty parameters families of solutions to the NLS equation

15 décembre 2015

The Peregrine breather of order eleven (P11 breather) solution to the focusing one dimensional nonlinear Schrödinger equation (NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given : when all (...)

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### [hal-01231875] An attempt to classification of the quasi rational solutions to the NLS equation

15 décembre 2015

Based on a representation in terms of determinants of order 2N , an attempt to classification of quasi rational solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) is given and several conjectures about the structure of the solutions are also formulated. These (...)

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### [hal-01165480] ON THE LINKS-GOULD INVARIANT AND THE SQUARE OF THE ALEXANDER POLYNOMIAL

1er décembre 2015

This paper gives a connection between well chosen reductions of the Links-Gould invariants of oriented links and powers of the Alexander-Conway polynomial. We prove these formulas by showing the representations of the braid groups we derive the specialized Links-Gould polynomials from can be (...)

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### [hal-01231875] An attempt to classification of the quasi rational solutions to the NLS equation

30 novembre 2015

Based on a representation in terms of determinants of order 2N , an attempt to classification of quasi rational solutions to the one dimensional focusing nonlinear Schrödinger equation (NLS) is given and several conjectures about the structure of the solutions are also formulated. These (...)

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### [hal-01224526] The eleventh Peregrine breather and twenty parameters families of solutions to the NLS equation

6 novembre 2015

The Peregrine breather of order eleven (P11 breather) solution to the focusing one dimensional nonlinear Schrödinger equation (NLS) is explicitly constructed here. Deformations of the Peregrine breather of order 11 with 20 real parameters solutions to the NLS equation are also given : when all (...)

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### [hal-01217945] On forbidden moves and the delta move

21 octobre 2015

We consider the quotient of welded knotted objects under several equivalence relations, generated respectively by self-crossing changes, ∆ moves, self-virtualizations and forbidden moves. We prove that for welded objects up to forbidden moves or classical objects up to ∆ moves, the notions of (...)

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### [hal-01217085] On forbidden moves and the delta move

20 octobre 2015

We consider the quotient of welded knotted objects under several equivalence relations, generated respectively by self-crossing changes, ∆ moves, self-virtualizations and forbidden moves. We prove that for welded objects up to forbidden moves or classical objects up to ∆ moves, the notions of (...)

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### [hal-01143763] The Purcell Three-link swimmer : some geometric and numerical aspects related to periodic optimal controls

6 octobre 2015

The maximum principle combined with numerical methods is a powerful tool to compute solutions for optimal control problems. This approach turns out to be extremely useful in applications, including solving problems which require establishing periodic trajectories for Hamiltonian systems, (...)

Lire la suite

### [hal-01205277] Affine-ruled varieties without the Laurent cancellation property

25 septembre 2015

We describe a method to construct hypersurfaces of the complex affine $n$-space with isomorphic $\mathbbC^*$-cylinders. Among these hypersurfaces, we find new explicit counterexamples to the Laurent Cancellation Problem, i.e. hypersurfaces that are non isomorphic, although their (...)

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### [hal-01201838] COPULA’S APPROXIMATIONS : APPLICATION TO QUANTILE ESTIMATION

22 septembre 2015

Estimating high level quantiles of aggregated variables (mainly sums or weighted sums) is crucial in risk management for many application fields such as finance, insurance, environment... This question has been widely treated but new efficient methods are always welcome; especially if they (...)

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### [hal-01135794] Persistent random walks

13 septembre 2015

We consider a walker that at each step keeps the same direction with a probability that depends on the time already spent in the direction the walker is currently moving. In this paper, we study some asymptotic properties of this persistent random walk and give the conditions of recurrence or (...)

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### [hal-01197123] Generalized stochastic Lagrangian paths for the Navier-Stokes equation

11 septembre 2015

The purpose of this work is to establish a counterpart for the Navier-Stokes equation of Brenier's generalized flows for the Euler equation. We introduce a class of semi-martingales on a compact Riemannian manifold which will be generalized solutions of the Navier-Stokes equation. We prove that (...)

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### [hal-01192831] A note on Constantin and Iyer’s representation formula for the Navier–Stokes equations

4 septembre 2015

The purpose of this note is to establish a probabilistic representation formula for Navier–Stokes equations on a compact Riemannian manifold. To this end, we first give a geometric interpretation of Constantin and Iyer's representation formula for the Navier–Stokes equation, then extend it to a (...)

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### [hal-01192833] Remarks on spectral gaps on the Riemannian path space

4 septembre 2015

In this paper, we will give some remarks on links between the spectral gap of the Ornstein-Uhlenbeck operator on the Riemannian path space with lower and upper bounds of the Ricci curvature on the base manifold; this work was motivated by a recent work of A. Naber on the characterization of the (...)

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### [hal-01188470] REAL FRONTIERS OF FAKE PLANES

1er septembre 2015

In [8], we define and partially classify fake real planes, that is, minimal complex surfaces with conjugation whose real locus is diffeomorphic to the euclidean real plane $\mathbbR^2$. Classification results are given up to biregular isomorphisms and up to birational diffeomorphisms. In this (...)

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### [hal-01183351] Explicit biregular/birational geometry of affine threefolds : completions of A^3 into del Pezzo fibrations and Mori conic bundles

8 août 2015

We study certain pencils of del Pezzo surfaces generated by a smooth del Pezzo surface S of degree less or equal to 3 anti-canonically embedded into a weighted projective space P and an appropriate multiple of a hyperplane H. Our main observation is that every minimal model program relative to (...)

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### [hal-01179229] AUTOMORPHISM GROUPS OF KORAS-RUSSELL THREEFOLDS OF THE SECOND KIND

23 juillet 2015

We determine the automorphism groups of Koras-Russell threefolds of the second kind. In particular we show that these groups are semi-direct products of two subgroups, one given by the multiplicative group and the other isomorphic to a polynomial ring in two variables with the addition law. We (...)

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### [hal-01178953] Rigid affine surfaces with isomorphic A2-cylinders

22 juillet 2015

We construct families of smooth affine surfaces with pairwise non isomorphic A 1-cylinders but whose A 2-cylinders are all isomorphic. These arise as complements of cuspidal hyperplane sections of smooth projective cubic surfaces.

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### [hal-01176073] On usual, virtual and welded knotted objects up to homotopy

17 juillet 2015

We consider several classes of knotted objects, namely usual, virtual and welded pure braids and string links, and two equivalence relations on those objects, induced by either self-crossing changes or self-virtualizations. We provide a number of results which point out the differences between (...)

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### [hal-01176009] La méthode d’itération rationnelle de Georges Lemaître (document de travail)

17 juillet 2015

En 1942, le célèbre astronome et physicien belge Georges Lemaître (1894-1966) publie dans le Bulletin de la classe des sciences de l'Académie Royale de Belgique, un article dans lequel il formule une méthode qu'il nomme itération rationnelle. Il redécouvre à la fois le processus du Delta 2 de Aitken et (...)

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### [hal-01175667] A note on the restricted universal enveloping algebra of a restricted Lie-Rinehart Algebra

12 juillet 2015

Lie-Rinehart algebras, also known as Lie algebroids, give rise to Hopf algebroids by a universal enveloping algebra construction, much as the universal enveloping algebra of an ordinary Lie algebra gives a Hopf algebra, of infinite dimension. In finite characteristic, the universal enveloping (...)

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### [hal-01175154] Fake Real Planes : exotic affine algebraic models of $\mathbb{R}^{2}$

11 juillet 2015

We study real rational models of the euclidean affine plane $\mathbbR^2$ up to isomorphisms and up to birational diffeomorphisms. The analogous study in the compact case, that is the classification of real rational models of the real projective plane $\mathbbR\mathbbP^2$ is well known: up to (...)

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### [hal-01107470] Hausdorff volume in non equiregular sub-Riemannian manifolds

2 juillet 2015

In this paper we study the Hausdorff volume in a non equiregular sub-Riemannian manifold and we compare it with a smooth volume. We first give the Lebesgue decomposition of the Hausdorff volume. Then we study the regular part, show that it is not commensurable with the smooth volume, and give (...)

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### [hal-01169229] METHODS TO COMPUTE RING INVARIANTS AND APPLICATIONS : A NEW CLASS OF EXOTIC THREEFOLDS

30 juin 2015

We develop some methods to compute the Makar-Limanov and Derksen invariants, isomorphism classes and automorphism groups for k-domains B, which are constructed from certain Russell k-domains. We propose tools and techniques to distinguish between k-domains with the same Makar-Limanov and (...)

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### [hal-01162407] A note about the geometric optimal control of the copepod swimmer

20 juin 2015

The objective of this note is to made preliminary remarks concerning the optimal locomotion of the Copepod swimmer described by a simple model concerning swimming at low Reynolds number, in the framework of Sub-Riemannian geometry. In particular the role of both normal and abnormal geodesics is (...)

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### [hal-01165480] ON THE LINKS-GOULD INVARIANT AND THE SQUARE OF THE ALEXANDER POLYNOMIAL

20 juin 2015

This paper gives a connection between well chosen reductions of the Links-Gould invariants of oriented links and powers of the Alexander-Conway polynomial. We prove these formulas by showing the representations of the braid groups we derive the specialized Links-Gould polynomials from can be (...)

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### [hal-01165324] Tenth order solutions to the NLS equation with eighteen parameters

20 juin 2015

We present here new solutions of the focusing one dimensional non linear Schrödinger equation which appear as deformations of the Peregrine breather of order 10 with 18 real parameters. With this method, we obtain new families of quasi-rational solutions of the NLS equation, and we obtain (...)

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### [hal-00940106] Virtual braids from a topological viewpoint

20 juin 2015

Virtual braids are a combinatorial generalization of braids. We present abstract braids as equivalence classes of braid diagrams on a surface, joining two distinguished boundary components. They are identified up to isotopy, compatibility, stability and Reidemeister moves. We show that virtual (...)

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### [hal-01164543] A simple solution to the word problem for virtual braid groups

18 juin 2015

We show a simple and easily implementable solution to the word problem for virtual braid groups.

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### [hal-00521135] Genèse et diffusion d’un théorème de Robert de Montessus de Ballore sur les fractions continues alg\’ebriques.

30 mai 2015

En 1902, Robert de Montessus de Ballore démontre la convergence d'une fraction continue algébrique associée à une fonction analytique à l'origine et méromorphe dans un domaine contenant l'origine. Aujourd'hui ce théorème est encore cité. Et le nom Montessus de Ballore sert à nommer des généralisations (...)

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