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Microscopic origins of shear stress in dense fluid-grain mixturesApr 10 2015Apr 14 2015A numerical model is used to simulate rheometer experiments at constant normal stress on dense suspensions of spheres. The complete model includes sphere-sphere contacts using a soft contact approach, short range hydrodynamic interactions defined by frame-invariant ... More

Pore-scale modeling of fluid-particles interaction and emerging poromechanical effectsApr 17 2013A micro-hydromechanical model for granular materials is presented. It combines the discrete element method (DEM) for the modeling of the solid phase and a pore-scale finite volume (PFV) formulation for the flow of an incompressible pore fluid. The coupling ... More

Pore-scale simulations of drainage in granular materials: finite size effects and the representative elementary volumeJan 05 2016A pore-scale model is introduced for two-phase flow in dense packings of polydisperse spheres. The model is developed as a component of a more general hydromechanical coupling framework based on the discrete element method, which will be elaborated in ... More

A minimal coupled fluid-discrete element model for bedload transportMay 19 2016A minimal Lagragian two-phase model to study turbulent bedload transport focusing on the granular phase is presented, and validated with experiments. The model intends to describe bedload transport of massive particles in fully rough flows at relatively ... More

A Hybrid multiphase model based on lattice Boltzmann method direct simulationsJun 11 2019By means of the multicomponent Shan-Chen lattice Boltzmann method (LBM), we investigate the multiphase flow through porous media. Despite the excellent accuracy of the LBM, large domains result in unaffordable computational expenses. The Hybrid model ... More

On the capillary stress tensor in wet granular materialsMay 05 2011This paper presents a micromechanical study of unsaturated granular media in the pendular regime, based upon numerical experiments using the discrete element method, compared to a microstructural elastoplastic model. Water effects are taken into account ... More

Additivity of on-line decision complexity is violated by a linear term in the length of a binary stringAug 31 2009We show that there are infinitely many binary strings z, such that the sum of the on-line decision complexity of predicting the even bits of z given the previous uneven bits, and the decision complexity of predicting the uneven bits given the previous ... More

Infinite dimensional Riemannian symmetric spaces with fixed-sign curvature operatorApr 26 2012Oct 04 2014We associate to any Riemannian symmetric space (of finite or infinite dimension) a L$^*$-algebra, under the assumption that the curvature operator has a fixed sign. L$^*$-algebras are Lie algebras with a pleasant Hilbert space structure. The L$^*$-algebra ... More

On the existence of stable compact leaves for transversely holomorphic foliationsMar 31 2012A transversely holomorphic foliation on a compact complex manifold, exhibits a compact stable leaf if and only if the set of compact leaves is not a zero measure subset of the manifold.

Quelques calculs de sommes de GaussAug 13 2011We observe that the Galois action on local constants associated to Galois representations of a local field yields information on their arithmetic nature, for example provides an upper bound to their order when they are roots of unity. It also yields information ... More

Around Quillen's theorem AAug 11 2011Jul 02 2014New version, including a variant of Quillen's proof of the Solomon-Tits theorem.

On the generalised Tate conjecture for products of elliptic curves over finite fieldsJan 10 2011We prove the generalised Tate conjecture for H^3 of products of elliptic curves over finite fields, by slightly modifying an argument of M. Spiess concerning the Tate conjecture. We prove it fully if the elliptic curves run among at most 3 isogeny classes. ... More

Number of points of function fields over finite fieldsOct 14 2002Oct 30 2002This is a revised and slightly expanded version. We point out that in the previous summary, "without cohomology" should really read "almost without cohomology" because of the proof of Lemma 2, that the idea to consider effective motives divisible by the ... More

Absence of spontaneous magnetic order at non-zero temperature in one- and two-dimensional Heisenberg and XY systems with long-range interactionsMay 06 2001May 27 2002The Mermin-Wagner theorem is strengthened so as to rule out magnetic long-range order at T>0 in one- or two-dimensional Heisenberg and XY systems with long-range interactions decreasing as R^{-alpha} with a sufficiently large exponent alpha. For oscillatory ... More

Non-quantized Dirac monopoles and strings in the Berry phase of anisotropic spin systemsApr 26 2004Aug 31 2004The Berry phase of an anisotropic spin system that is adiabatically rotated along a closed circuit C is investigated. It is shown that the Berry phase consists of two contributions: (i) a geometric contribution which can be interpreted as the flux through ... More

Interlayer exchange coupling: Preasymptotic correctionsAug 10 1998Sep 03 1999In the asymptotic limit, the interlayer exchange coupling decays as $D^{-2}$, where $D$ is the spacer thickness. A systematic procedure for calculating the preasymptotic corrections, i.e., the terms of order $D^{-n}$ with $n \ge 3$, is presented. The ... More

Performance Bounds for Lambda Policy Iteration and Application to the Game of TetrisNov 05 2007Oct 11 2011We consider the discrete-time infinite-horizon optimal control problem formalized by Markov Decision Processes. We revisit the work of Bertsekas and Ioffe, that introduced $\lambda$ Policy Iteration, a family of algorithms parameterized by $\lambda$ that ... More

Nonstandard Intuitionistic InterpretationsDec 22 2015We present a notion of realizability and a functional interpretation in the context of intuitionistic logic, both incorporating nonstandard principles. The functional interpretation that we present corresponds to the intuitionistic counterpart of an interpretation ... More

Lévy mixing related to distributed order calculus, subordinators and slow diffusionsJun 18 2014May 19 2015The study of distributed order calculus usually concerns about fractional derivatives of the form $\int_0^1 \partial^\alpha u \, m(d\alpha)$ for some measure $m$, eventually a probability measure. In this paper an approach based on L\'evy mixing is proposed. ... More

Motifs et adjointsJun 28 2015Nov 23 2015We show in many cases the existence of adjoints to extension of scalars on categories of motivic nature, in the framework of field extensions. This is to be contrasted with the more classical situation where one deals with a finite type morphism of schemes. ... More

Bounded-degree factors of lacunary multivariate polynomialsDec 11 2014Jan 29 2016In this paper, we present a new method for computing bounded-degree factors of lacunary multivariate polynomials. In particular for polynomials over number fields, we give a new algorithm that takes as input a multivariate polynomial f in lacunary representation ... More

Computing low-degree factors of lacunary polynomials: a Newton-Puiseux approachJan 19 2014Jun 24 2014We present a new algorithm for the computation of the irreducible factors of degree at most $d$, with multiplicity, of multivariate lacunary polynomials over fields of characteristic zero. The algorithm reduces this computation to the computation of irreducible ... More

Signal-wise performance attribution for constrained portfolio optimisationApr 18 2014Aug 06 2014Performance analysis, from the external point of view of a client who would only have access to returns and holdings of a fund, evolved towards exact attribution made in the context of portfolio optimisation, which is the internal point of view of a manager ... More

On some p-adic power series attached to the arithmetic of $\mathbb Q(ζ\_p).$Oct 14 2005In this paper, we prove that the derivative of the Iwasawa power series associated to p-adic L-functions of $\mathbb Q(\zeta\_p)$ are not divisible by p. This extends previous results obtained by Ferrero and Washington in 1979.

The critical random barrier for the survival of branching random walk with absorptionNov 11 2009We study a branching random walk on $\r$ with an absorbing barrier. The position of the barrier depends on the generation. In each generation, only the individuals born below the barrier survive and reproduce. Given a reproduction law, Biggins et al. ... More

Operationalization of Basic Observables in MechanicsApr 10 2015Dec 03 2015This novel approach to the foundation of the physical theory begins with Hermann von Helmholtz fundamental analysis of basic measurements. We explain the mathematical formalism from the operationalization of basic observables. According to Leibniz resp. ... More

Resolution and Datalog Rewriting Under Value Invention and Equality ConstraintsDec 02 2012This paper present several refinements of the Datalog +/- framework based on resolution and Datalog-rewriting. We first present a resolution algorithm which is complete for arbitrary sets of tgds and egds. We then show that a technique of saturation can ... More

Propositional dynamic logic for searching games with errorsJan 28 2014We investigate some finitely-valued generalizations of propositional dynamic logic with tests. We start by introducing the (n+1)-valued Kripke models and a corresponding language based on a modal extension of {\L}ukasiewicz many-valued logic. We illustrate ... More

Approximate Policy Iteration Schemes: A ComparisonMay 12 2014We consider the infinite-horizon discounted optimal control problem formalized by Markov Decision Processes. We focus on several approximate variations of the Policy Iteration algorithm: Approximate Policy Iteration, Conservative Policy Iteration (CPI), ... More

Singular integrals and Hardy type spaces for the inverse Gauss measureJan 26 2018Let $\gamma_{-1}$ be the absolutely continuous measure on $\mathbb{R}^n$ whose density is the reciprocal of a Gaussian and consider the natural weighted Laplacian $\mathcal{A}$ on $L^2(\gamma_{-1})$. In this paper, we prove boundedness and unboundedness ... More

Cycles of Sums of IntegersMay 05 2019We study the period of the linear map $T:\textbf{Z}_m^n\rightarrow \textbf{Z}_m^n:(a_0,\dots,a_{n-1})\mapsto(a_0+a_1,\dots,a_{n-1}+a_0)$ as a function of $m$ and $n$, where $\textbf{Z}_m$ stands for the ring of integers modulo $m$. This map being a variant ... More

Cubical informal type theory: the higher groupoid structureJun 22 2018Following a project of developing conventions and notations for informal type theory carried out in the homotopy type theory book for a framework built out of an augmentation of constructive type theory with axioms governing higher-dimensional constructions ... More

Localization on 5 sites for vertex reinforced random walks: Towards a characterizationMay 15 2019We continue the investigation of the localization phenomenon for a Vertex Reinforced Random Walk on the integer lattice. We provide some partial results towards a full characterization of the weights for which localization on 5 sites occurs with positive ... More

Jordan derivations on triangular matrix ringsOct 26 2014Oct 28 2014Guided by the research line introduced by Martindale III in [1] on the study of the additivity of maps, this article aims establish condi- tions on triangular matrix rings in order that an map ' satisfying '(ab + ba) = '(a)b + a'(b) + '(b)a + b'(a) for ... More

Constructing a class of solutions for the Hamilton-Jacobi equation in field theorySep 12 2007A new approach leading to the formulation of the Hamilton-Jacobi equation for field theories is investigated within the framework of jet-bundles and multi-symplectic manifolds. An algorithm associating classes of solutions to given sets of boundary conditions ... More

Collapses, products and LC manifoldsNov 24 2009May 16 2010Durhuus and Jonsson (1995) introduced the class of "locally constructible" (LC) triangulated manifolds and showed that all the LC 2- and 3-manifolds are spheres. We show here that for each d>3 some LC d-manifolds are not spheres. We prove this result ... More

Implementation without commitment in moral hazard environmentsMar 05 2013Sep 16 2013Interdependent-choice equilibrium is defined as an extension of correlated equilibrium in which the mediator is able to choose the timing of her signals, and observe the actions taken by the players. The set of interdependent-choice equilibria is a nonempty, ... More

On the Abel-Radon transform of locally residual currentsFeb 22 2010First we recall the definition of locally residual currents and their basic properties. We prove in this first section a trace theorem, that we use later. Then we define the Abel-Radon transform of a current ${\cal R}(\alpha)$, on a projective variety ... More

La théorie des invariants des formes quadratiques ternaires revisitéeMay 27 2008The simultaneous invariants of 2, 3, 4 and 5 ternary quadratic forms under the group $\SL(3, {\Bbb C})$ were given by several authors (P. Gordan, C. Ciamberlini, H.W. Turnbull, J.A Todd), utilizing the symbolic method. Using the Jordan algebra structure ... More

Heat Kernels and CyclesMay 26 2005We use the heat kernel (on differential forms) on a compact Riemannian manifold to assign a real number to a k-tuple of cycles on the manifold satisfying certain conditions. If k is 2, this number is the ordinary topological linking number, an integer ... More

A family of $ω_1$ many topological types of locally finite treesApr 15 2016Two rooted locally finite trees are considered equivalent if both can be embedded into each other as topological minors by means of tree-order preserving mappings. By exploiting Nash-William's Theorem, Matthiesen provided a non-constructive proof of the ... More

Matching Estimators with Few Treated and Many Control ObservationsSep 11 2019We analyze the properties of matching estimators when there are few treated, but many control observations. We show that, under standard assumptions, the nearest neighbor matching estimator for the average treatment effect on the treated is asymptotically ... More

The Poisson boundary of triangular matrices in a number fieldDec 11 2006Sep 19 2008The aim of this note is to describe the Poisson boundary of the group of invertible triangular matrices with coefficients in a number field. It generalizes to any dimension and to any number field a result of Brofferio concerning the Poisson boundary ... More

Random walk on a building of type $\tilde{A}_r$ and Brownian motion of the Weyl chamberNov 17 2006May 25 2009In this paper we study a random walk on an affine building of type $\tilde{A}_r$, whose radial part, when suitably normalized, converges to the Brownian motion of the Weyl chamber. This gives a new discrete approximation of this process, alternative to ... More

Stochastic homogenization of nonconvex Hamilton-Jacobi equations: a counterexampleDec 20 2015Sep 07 2016We provide an example of a Hamilton-Jacobi equation in which stochastic homogenization does not occur. The Hamiltonian involved in this example satisfies the standard assumptions of the literature, except that it is not convex.

m-sophisticationJan 26 2010The m-sophistication of a finite binary string x is introduced as a generalization of some parameter in the proof that complexity of complexity is rare. A probabilistic near sufficient statistic of x is given which length is upper bounded by the m-sophistication ... More

Influence tests I: ideal composite hypothesis tests, and causal semimeasuresDec 14 2009Ratios of universal enumerable semimeasures corresponding to hypotheses are investigated as a solution for statistical composite hypotheses testing if an unbounded amount of computation time can be assumed. Influence testing for discrete time series is ... More

The geometric mean of two matrices from a computational viewpointDec 30 2011The geometric mean of two matrices is considered and analyzed from a computational viewpoint. Some useful theoretical properties are derived and an analysis of the conditioning is performed. Several numerical algorithms based on different properties and ... More

Distributions vectorielles homogènes sur une algèbre de JordanMay 15 2007We study distributions on a Euclidean Jordan algebra V with values in a finite dimensional representation space for the identity component G of the structure group of V and homogeneous equivariance condition. We show that such distributions exist if and ... More

Bounds on the mass gap of the ferromagnetic XXZ chainJan 20 1995We prove rigorous lower and upper bounds for the mass gap of the ferromagnetic spin 1/2 XXZ chain. The two bounds coincide asymptotically in the Ising limit $\Delta\to\infty$. Near the isotropic point, $\Delta=1$, the estimates are good enough to determine ... More

Homology of generalized partition posetsMay 16 2004Aug 31 2006We define a poset of partitions associated to an operad. We prove that the operad is Koszul if and only if the poset is Cohen-Macaulay. In one hand, this characterisation allows us to compute the homology of the poset. This homology is given by the Koszul ... More

Periodic Orbit TheoryMar 23 1993[[ RM: A review paper on cycle expansions. I quote the introduction: in section (2) ]] I will summarize Gutzwiller's theory for the spectrum of eigenenergies and extend it to diagonal matrix elements as well. The derivation of the associated zeta function ... More

Geometrically constrained magnetic wallApr 26 1999Sep 20 1999The structure and properties of a geometrically constrained magnetic wall in a constriction separating two wider regions are investigated theoretically. They are shown to differconsiderably from those of an unconstrained wall, so that the geometrically ... More

Thermo-Rotational Instability in Plasma Disks Around Compact ObjectsFeb 12 2008Differentially rotating plasma disks, around compact objects, that are imbedded in a ``seed'' magnetic field are shown to develop vertically localized ballooning modes that are driven by the combined radial gradient of the rotation frequency and vertical ... More

Improved and Generalized Upper Bounds on the Complexity of Policy IterationJun 03 2013Feb 10 2016Given a Markov Decision Process (MDP) with $n$ states and a totalnumber $m$ of actions, we study the number of iterations needed byPolicy Iteration (PI) algorithms to converge to the optimal$\gamma$-discounted policy. We consider two variations of PI: ... More

On the Use of Non-Stationary Policies for Infinite-Horizon Discounted Markov Decision ProcessesMar 25 2012Mar 30 2012We consider infinite-horizon $\gamma$-discounted Markov Decision Processes, for which it is known that there exists a stationary optimal policy. We consider the algorithm Value Iteration and the sequence of policies $\pi_1,...,\pi_k$ it implicitely generates ... More

Stability and instability of the Einstein-Lichnerowicz constraint systemFeb 14 2015We investigate the relevance of the conformal method by investigating stability issues for the Einstein-Lichnerowicz conformal constraint system in a nonlinear scalar-field setting. We prove the stability of the system with respect to arbitrary perturbations ... More

Exact high temperature expansion of the one-loop thermodynamic potential with complex chemical potentialNov 11 2013Jan 10 2014We present a derivation of an exact high temperature expansion for a one-loop thermodynamic potential $\Omega(\tilde{\mu})$ with complex chemical potential $\tilde{\mu}$. The result is given in terms of a single sum the coefficients of which are analytical ... More

A conjectured class of scale-invariant distances on inner product spacesJan 07 2014Jan 09 2014Let $V$ be an inner product space, and $x, y \in V$; the conjecture is made that, for any $p \in [1, \infty]$, the function $d_p(x, y):=\|x-y\|/(\|x\|^p+ \|y\|^p)^{1/p}$ is a distance on $V$.

Non-vanishing at m -> 0 of the 1-loop self-mass of an electron of mass m propagating in a graphene-like medium in a constant external magnetic fieldJul 04 2016The 1-loop self-energy of a Dirac electron of mass m propagating in a thin medium simulating graphene in an external magnetic field B is investigated in Quantum Field Theory. Equivalence is shown with the so-called reduced QED_{3+1} on a 2-brane. Schwinger-like ... More

The permanent spatial decomposition of the wave functionOct 26 2009Permanent spatial decomposition (PSD) is the (hypothesized) property of the wave function of a macroscopic system of decomposing into localized permanently non-overlapping parts when it spreads over a macroscopic region. The typical example of this phenomenon ... More

Lacunaryx: Computing bounded-degree factors of lacunary polynomialsJun 11 2015Feb 18 2016In this paper, we report on an implementation in the free software Mathemagix of lacunary factorization algorithms, distributed as a library called Lacunaryx. These algorithms take as input a polynomial in sparse representation, that is as a list of nonzero ... More

Acceptable Complexity Measures of TheoremsSep 30 2009In 1931, G\"odel presented in K\"onigsberg his famous Incompleteness Theorem, stating that some true mathematical statements are unprovable. Yet, this result gives us no idea about those independent (that is, true and unprovable) statements, about their ... More

Potential model of a 2D Bunsen flameJul 10 2006The Michelson Sivashinsky equation, which models the non linear dynamics of premixed flames, has been recently extended to describe oblique flames. This approach was extremely successful to describe the behavior on one side of the flame, but some qualitative ... More

Stationary solutions and Neumann boundary conditions in the Sivashinsky equationApr 17 2006New stationary solutions of the (Michelson) Sivashinsky equation of premixed flames are obtained numerically in this paper. Some of these solutions, of the bicoalescent type recently described by Guidi and Marchetti, are stable with Neumann boundary conditions. ... More

Projected site-occupation embedding theory: a rigorous embedding combining wavefunction theory and density functional theoryFeb 15 2019Site-occupation embedding theory (SOET) [B. Senjean et al., Theo. Chem. Acc. (2018) 137:169] is an in-principle exact embedding method combining wavefunction theory and density functional theory that yields promising results when applied to the one-dimensional ... More

Symmetry and Complete Regularity: Kopperman's duality {\it à la quantale}Nov 02 2016Nearly three decades from his celebrated result, we study a modern refinement and strengthening of Kopperman's full metrisabilty of all topological spaces. Within this new theory of \emph{V-spaces}, developed by Flagg and Weiss, we investigate several ... More

Discussion of: Brownian distance covarianceOct 05 2010Discussion on "Brownian distance covariance" by G\'abor J. Sz\'ekely and Maria L. Rizzo [arXiv:1010.0297]

On the p-adic Leopoldt Transform of a power seriesSep 18 2007In this paper we give a bound for the Iwasawa lambda invariant of an abelian number field attached to the cyclotomic Z_p-extension of that field. We also give some properties of Iwaswa power series attached to p-adic L-functions.

Tachyons and EPR correlationsDec 22 2005No causal paradoxes will occur if a preferred reference frame for tachyons propagation is assumed, and results of Bell's inequality experiments may be well explained without using any telepathyc effect. We can read G. Faraci's and others' results, Lettere ... More

On the cohomology of Kaehler groupsMay 17 2010This is the geometric part of two papers on the cohomology of Kaehler groups. Using non-Abelian Hodge theory we show that if a finitely presented group with an unbounded complex linear morphism is the fundamental group of a compact Kaehler manifold then ... More

Uniform van Lambalgen's theorem fails for computable randomnessOct 02 2015Feb 02 2018We show that there exists a bitsequence that is not computably random for which its odd bits are computably random and its even bits are computably random relative to the odd bits. This implies that the uniform variant of van Lambalgen's theorem fails ... More

Hilbert functions and geometryApr 06 2004Apr 13 2004This note is devoted to the study of the links between the Hilbert function of a subscheme X of the projective space, and its geometric properties. We will assume that X is arithmetically Cohen-Macaulay, which allows us to characterize its Hilbert function ... More

Physical Determination of the ActionJun 28 2013Dec 04 2015The objective is a foundation of physics from the operationalization of its basic observables. We begin with classical and relativistic kinematics. Seizing on a programmatic proposal by Heinrich Hertz we arrive via quantification of energy-momentum at ... More

Operationalization of Relativistic MotionMay 11 2012Dec 03 2015We demonstrate the definition of basic observables from physical operations, the key to overcome hidden stumbling blocks and apparent paradoxes from unscrutinized (classical) formalisms. We develop Helmholtz program of basic measurements for relativistic ... More

Bounded harmonic functions for the Heckman--Opdam LaplacianSep 24 2008Oct 21 2008We describe the set of bounded harmonic functions for the Heckman--Opdam Laplacian, when the multiplicity function is larger than 1/2. We prove that this set is a vector space of dimension the cardinality of the Weyl group. We give some consequences in ... More

Characterization of transiting exoplanets: analyzing the impact of the host star on the planet parametersApr 13 2016In this PhD dissertation, I discuss issues of the Radial Velocities (RV) and transit methods. These techniques allow us to derive the mass and radius of an exoplanet, necessary to model its bulk structure and to have insight on its formation. To do this, ... More

A proof of Kummer's theoremApr 14 1999Apr 15 1999Following suggestions of T. H. Koornwinder, we give a new proof of Kummer's theorem involving Zeilberger's algorithm, the WZ method and asymptotic estimates. In the first section, we recall a classical proof given by L. J. Slater. The second section discusses ... More

Almost homogeneous curves over an arbitrary fieldMar 28 2017We classify the pairs $(C,G)$ where $C$ is a seminormal curve over an arbitrary field $k$ and $G$ is a smooth connected algebraic group acting faithfully on $C$ with a dense orbit, and we determine the equivariant Picard group of $C$. We also give a partial ... More

Weak hamiltonian Wilson Coefficients from Lattice QCDDec 26 2017In this work we present a calculation of the Wilson Coefficients $C_1$ and $C_2$ of the Effective Weak Hamiltonian to all-orders in $\alpha_s$, using lattice simulations. Given the current availability of lattice spacings we restrict our calculation to ... More

Spectral GeometryDec 16 2017The goal of these lectures is to present the few fundamentals of noncommutative geometry looking around its spectral approach. Strongly motivated by physics, in particular by relativity and quantum mechanics, Chamseddine and Connes have defined an action ... More

Hodge loci and atypical intersections: conjecturesNov 26 2017We present a conjecture on the geometry of the Hodge locus of a (graded polarizable, admissible) variation of mixed Hodge structure over a complex smooth quasi-projective base, generalizing to this context the Zilber-Pink Conjecture for mixed Shimura ... More

Topological properties of Wazewski dendrite groupsMar 13 2019Mar 28 2019Homeomorphism groups of generalized Wa\.zewski dendrites act on the infinite countable set of branch points of the dendrite and thus have a nice Polish topology. In this paper, we study them in the light of this Polish topology. The group of the universal ... More

On the Properties of the Synthetic Control Estimator with Many Periods and Many ControlsJun 16 2019We consider the asymptotic properties of the Synthetic Control (SC) estimator when both the number of pre-treatment periods and control units are large. If potential outcomes follow a linear factor model, we provide conditions under which the factor loadings ... More

Albanese kernels and Griffiths groupsNov 12 2017Apr 29 2018We describe the Griffiths group of the product of a curve $C$ and a surface $S$ as a quotient of the Albanese kernel of $S$ over the function field of $C$. When $C$ is a hyperplane section of $S$ varying in a Lefschetz pencil, we prove the nonvanishing ... More

Lieb-Robinson bounds and the existence of infinite system dynamicsSep 15 2009We present a recent result on the existence of the dynamics in the thermodynamic limit of a class of anharmonic quantum oscillator lattices, which was obtained using Lieb--Robinson bounds.

Théorème de Chebotarev effectifNov 22 2013Let K be a number field, and L be a finite normal extension of K with Galois group G. It is known that the number of Frobenius automorphisms corresponding to prime ideals, whose norms are less than x, is equivalent to the logarithmic integral as x tends ... More

Linear Differential Equations as a Data-StructureNov 21 2018A lot of information concerning solutions of linear differential equations can be computed directly from the equation. It is therefore natural to consider these equations as a data-structure, from which mathematical properties can be computed. A variety ... More

A Tauberian theorem for nonexpansive operators and applications to zero-sum stochastic gamesJan 26 2015Feb 23 2015We prove a Tauberian theorem for nonexpansive operators, and apply it to the model of zero-sum stochastic game. Under mild assumptions, we prove that the value of the lambda-discounted game v_{lambda} converges uniformly when lambda goes to 0 if and only ... More

Smoothing discrete Morse theoryDec 04 2012Dec 10 2014After surveying classical notions of PL topology of the Seventies, we clarify the relation between Morse theory and its discretization by Forman. We show that PL handles theory and discrete Morse theory are equivalent, in the sense that every discrete ... More

An approach between the multiplicative and additive structure of a Jordan ringApr 18 2018Let J and J' be Jordan rings. We prove under some conditions that if J contains a nontrivial idempotent, then n-multiplicative maps and n-multiplicative derivations from J to J' are additive maps.

Effective multiplicity for the Einstein-scalar field Lichnerowicz equationJul 09 2013We prove the stability of the Einstein-scalar field Lichnerowicz equation under subcritical perturbations of the critical nonlinearity in dimensions 3, 4 and 5. As a consequence, we obtain the existence of a second solution to the equation in several ... More

Multiplicative properties of the multiplicative groupJun 08 2017Nov 02 2017We give a few properties equivalent to the Bloch-Kato conjecture (now the norm residue isomorphism theorem).

Divisibility properties of motivic cohomologyJan 18 2018We extend results of Colliot-Th\'el\`ene and Raskind on the $\mathcal{K}_2$-cohomology of smooth projective varieties over a separably closed field $k$ to the \'etale motivic cohomology of smooth, not necessarily projective, varieties over $k$. Some consequences ... More

General limit value in zero-sum stochastic gamesOct 20 2014Nov 11 2015Bewley and Kohlberg (1976) and Mertens and Neyman (1981) have proved, respectively, the existence of the asymptotic value and the uniform value in zero-sum stochastic games with finite state space and finite action sets. In their work, the total payoff ... More

Majorana's stellar representation for the local polarization of harmonic electromagnetic and gravitational wavesMar 20 2019The local polarization of electromagnetic (EMW) and gravitational waves (GW) is discussed from an operational point of view, in which all the relevant mathematical framework is constructed in terms of measurements of the power absorbed by a local detector. ... More

Homotopy theory of homotopy algebrasNov 20 2014Feb 07 2016This paper studies the homotopy theory of algebras and homotopy algebras over an operad. It provides an exhaustive description of their higher homotopical properties using the more general notion of morphisms called infinity-morphisms. The method consists ... More

Convergence of the solutions of the discounted Hamilton-Jacobi equation: a counterexampleJan 18 2018Jan 19 2018This paper provides a counterexample about the asymptotic behavior of the solutions of a discounted Hamilton-Jacobi equation, as the discount factor vanishes. The Hamiltonian of the equation is a 1-dimensional continuous and coercive Hamiltonian.

Non-linear model equation for three-dimensional Bunsen flamesJul 10 2006The non linear description of laminar premixed flames has been very successful, because of the existence of model equations describing the dynamics of these flames. The Michelson Sivashinsky equation is the most well known of these equations, and has ... More

Supernovae and CosmologyFeb 28 2008The extreme luminosity and their fairly unique temporal behaviour have made supernovae a superb tool to measure distances in the universe. As complex astrophysical events they provide interesting insights into explosion physics, explosive nucleosynthesis, ... More