Séminaires de mathématique (Prépublications)

Pour les prépublications à partir de 2005, veuillez vous référer à la page Séminaires de mathématique (prépublications).

• 245 - séminaire - A. CARBONI, E.M. VITALE - Regular and exact completions (19/01/1995)
  
  A paraître dans : Journal of Pure and Applied Algebra.
  
  The regular and exact completions of categories with weak limits areproved to exist and to be determined by an appropriate universal property.Several examples are discussed, and in particular the class of examples givenby categories monadic over a power of Set: any such a category is in fact theexact completion of the full subcategory of free algebras. Applications toGrothendieck toposes and geometric morphisms, and to epireflective hullsare also discussed.
  
  
• 246 - séminaire - A.P. MAGNUS - Special non uniform lattice (snul) orthogonal polynomials on discrete dense sets of points (27/02/1995)
  
  Publié dans : J. Comp. Appl. Math. 65(1995), pages 253-265.
  
  Difference calculus compatible with polynomials(i.e., such that the divided difference operator of first order appliedto any polynomial must yield a polynomial of lower degree) can only bemade on special lattices well known in contemporary q-calculus.Orthogonal polynomials satisfying difference relations on such latticesare presented. In particular, lattices which are dense on intervals(|q|? are considered
  
  
• 247 - séminaire - K. PEIFFER, A. Ya SAVCHENKO - On passive stabilization (18/01/1995) - DVI  - PS 
  
  The attitude of a satellite is often controlled by reactive forcesrequiring some additional energy. But it can also be stabilized bymeans of some piece of the satellite moving in anonideal fluid as an oscillator with damping. This does not require additionalenergy and is called "passive stabilization". Moreover the relative motiontends asymptotically to zero together with the satellite finding the desiredposition. Here we consider passive stabilization for hamiltonian systems froma mathematical point of view and show that stabilization can sometimes beobtained bynonlinear terms.
  
  
• 248 - séminaire - C. TROESTLER, M. WILLEM - Nontrivial solution of a semilinear Schrödinger equation (12/05/1995)
  
  A paraître dans : Communications in P.D.E..
  
  This paper develops a method to deal with strongly indefinite functionals whose gradients are Fredholm operators of index 0 and map weakly convergent sequences to weakly convergent sequences. We show how these results apply to a Z^N-invariant semilinear Schrödinger equation on R^N.
  
  
• 249 - séminaire - A. CAPIETTO, J. MAWHIN, F. ZANOLIN - On the existence of two solutions with a prescribed number of zeros for a superlinear two-point boundary value problem (23/05/1995) - DVI  - PS 
  
  The aim of this not is to show how to refine an abstractcontinuation of the authors in order to prove, for eachsufficient positive number k the existence of at leasttwo solutions for a class of forced superlinear secondorder ordinary differential equations submitted toDirichlet conditions.
  
  
• 45 - recherche - M. HENRARD - Duality theorems for functional differential equations and application to superlinear problems (16/01/1995)
  
  Publié dans : Differential Equations and Dynamical Systems 3(1)(1995), pages 43-60.
  
  A lot of existence and multiplicity results has been obtained for forcedsuperlinear equation of the form x''(t) + f(x(t)) ?(t,x(t),x'(t)) with various boundary conditions.In this paper, those results are extended to the functional differentialequation x''(t) + f(x(t)) ?(t,x_t,(x')_t) with boundary conditions of the type x_0 + Nx_1 ?(x) ;   h(x) ? To obtain those results, duality theorems between thetopological degree of the ordinary differential equation and the degreeof the functional one are stated. Those duality results are applied inthe case where the boundary conditions reduced in some way toSturm-Liouville boundary conditions or to linear boundary conditions.
  
  
• 46 - recherche - K. BEN NAOUM, C. DE COSTER - On the existence and multiplicity of positive solutions of the p-Laplacian separated boundary value problem. (1/04/1995) - DVI 
  
  Using the lower and upper solutions method together with degree theory, we study the existence and multiplicity of positive solutions for the p-Laplacian separated boundary value problem. The nonlinearity satisfies assumptions related to the classically called sublinear, superlinear, sub-superlinear, orsuper-sublinear case. Our results improve the recent ones of L.H. Erbe - H. Wang (J. Math. Anal. Appl. 184(1994), 640-648) and L.H. Erbe - S. Hu - H. Wang (Proc. A.MS. 120(1994), 743-748).
  
  
• 47 - recherche - Y. FELIX - Théorie homotopique des modules semi-libres (10/06/1995) - DVI 
  
  Ce texte consiste en une présentation des propriétés homotopiques des modules différentiels
  
  
• 250 - séminaire - Th. DE PAUW - A concept of generalized absolute continuity for theF-integral (10/08/1995)
  
  Publié dans : Real Analysis Exchange 22(1)(1996-97), pages 350-361.
  
  We define a concept of generalized absolute continuity for additivefunctions of figures. This makes it possible to give a descriptivedefinition of the F-integral introduced by Washek Pfeffer in order tointegrate divergence of vector fields with singularities.Finally, we discuss a possible extension to additive functions ofsets of bounded variation.
  
  
• 251 - séminaire - Y. DING, S. LI, M. WILLEM - Periodic solutions of symmetric wave equations (9/10/1995) - DVI 
  
  We consider the problemu_{tt} - u_{xx} ?f(x,t,u), u(0,t) ? ?(pi,t), u(x,t+2pi) ?(x,t). We assume that f is odd and nondecreasing in u.We prove the existence of infinitely many solutions when f is either superlinear or sublinear and coercive.
  
  
• 48 - recherche - J.M.-S. LUBUMA, S. NICAISE - Finite element method for elliptic problems with edge corners (17/11/1995) - DVI 
  
  One considers a linear elliptic boundary value problem of order 2m on a three-dimensional infinite cylinder of polygonal section. From the known behaviour of the solution near the edges, section 2 of the paper states the needed singular decomposition. Section 3 is devoted to the discrete function spaces which will be needed. The approximation of the elliptic problem is analyzed in section 4 with emphasis on the following aspects: optimally (sec. 4.1) and slowly (sec. 4.3, 4.4) convergent schemes, computation of discrete solutions (sec. 4.2).
  
  
• 49 - recherche - Th. DE PAUW - Topologies for the space of BV-integrable functions in RN (11/12/1995)
  
  Publié dans : Journal of Functional Analysis 1(144)(1997), pages 190-231.
  
  We introduce two topologies on the space of BV-integrablefunctions in R^N. Among the studied properties are barrellednessand integral representation of linear continuous functionals. In onecase, we characterize the dual space. We show the relations withthe study of multipliers. Finally, we also introduce and study atopology on the space of bounded BV functions in R^N.
  
  
• 252 - séminaire - F. BORCEUX, C. QUINTEIRO - A theory of enriched sheaves (12/12/1995) - DVI  - PS 
  
  Publié dans : Cahiers de topologie et géométrie différentielle catégorique XXXVII(2)(1996), pages 145-162.
  
  We fix a regular, locally finitely presentable, symmetricmonoidal closed category V in the sense of Kelly. Given asmall V-category C, we define the notion ofGrothendieck V-topology on C and prove the existenceand the V-exactness of the corresponding associated sheaffunctor. There are bijections between the GrothendieckV-topologies on C, the V-localizations of theV-category [C*,V] of V-presheaves and the V-universalclosure operations on [C*,V] .
  
  
• 253 - séminaire - P. HABETS, L. SANCHEZ - A two-point problem with nonlinearity depending only of the derivative (12/12/1995) - DVI 
  
  We study the existence and multiplicity of solutions for a two-point boundary value problem at resonance in the first eigenvalue; thenonlinearity depends only on the first derivative and has finite limitsat ± ?
  
  
• 50 - recherche - F. BORCEUX, C. QUINTEIRO - Enriched accessible categories (19/12/1995)
  
  A paraître dans : Bulletin of the Australian Mathematical Society.
  
  We consider category theory enriched in a locally finitelypresentable symmetric monoidal closed category V. We define theV-filtered colimits as those colimits weighted by a V-flatpresheaf and consider the corresponding notion of V-accessiblecategory. We prove that V-accessible categories coincide with thecategories of V-flat presheaves and also with the categories ofV-points of the categories of V-presheaves. Moreover, theV-locally finitely presentable categories are exactly theV-cocomplete finitely accessible ones. To prove this last result, weshow that the Cauchy completion of a small V-category C isequivalent to the category of V-finitely presentable V-flatpresheaves on C. 
  
  
• 51 - recherche - A.K. BEN NAOUM - On the Dirichlet problem for the nonlinear wave equation in bounded domains with corner points (12/01/1996) - DVI 
  
  Using Mawhin's coincidence topological degree arguments and fixed point theory fornon-expansive mappings results, we discuss the solvability of the Dirichlet problem for thesemilinear equation of the vibrating string u_{xx}-u_{yy} + f(x,y,u)?in bounded domainwith corner points. When the winding number associated to the domain is rational we improve and extend some results of Lyashenko (On the Dirichlet problem for the nonlinear equation of the vibrating string. I, J. Math. Kyoto Univ. 33-2 (1993) 543-570) and Lyashenko-Smiley (preprint). The case where thewinding number is irrational is also examined.
  
  
• 254 - séminaire - A.K. BEN NAOUM - Some results on the Markov number from the theory of diophantine approximations (12/01/1996) - DVI  - PS 
  
  Two reals numbers alpha, beta are said to be equivalent, if there exist integers a, b, c, d, such that |ad - bc| ? and beta ?frac{a alpha+ b}{c alpha+ d}. Now let M(alpha) be the Markov number (defined below) associated to an irrational number alpha. There is an old result which states that if alpha and beta are two equivalent irrational numbers, then M(alpha) ?(beta). In this note, first we generalize this result, proving that if beta ?frac{a alpha+ b} {c alpha + d} with ad - bc ? 0, and a, b, c, d e Z, then M(alpha) ? M(beta) |ad - bc| . As consequence, M(alpha) is finite if and only if M(beta) is finite and we show that this result can be related to other ones on the quadratic form Q_{alpha} (m,n) :?alpha m)^{2} - n^{2} in which m and n are integers, not both zero, and alpha is an irrational number. 
  
  
• 255 - séminaire - M. WILLEM - On the generalized Kadomtsev-Petviashvili equation (22/01/1996) - DVI  - PS 
  
  The existence of solitary waves w(t,x,y) ?(x-ct,y) of the GeneralizedKadomtsev-Petviashvili equationw_t + w_{xxx} + (f(w))_x ?^{-1}_x w_{yy}is proved in the case of a nonhomogeneous nonlinearity f . Non existenceresults follow also from the identity 1/2 int_{R^2} [u^2_x+ (D^{-1}_2 u_y)^2] ?3 int_{R^2} F(u) where F(u) ?int^u_0 f(s) ds.
  
  
• 257 - séminaire - Calin POPESCU - Non-isomorphic U(H(L)) and H(U(L)) (19/02/1996) - DVI 
  
  We present a very simple, but quite general pattern for constructing, for any given natural m, (m+2)-nilpotent differential graded Lie algebras L(m) over a commutative ring R in which 2 is a unit,with R-free underlying module L(m) and R-free homology H(L(m)), both of finite type, but non-isomorphic R-modules U(H(L(m))) and H(U(L(m))) or even H(U(L(m)))/torsion, when this latter makes sense (e.g., if R is a domain).
  
  
• 256 - séminaire - Th. KAHL - An axiomatic approach to Lusternik-Schnirelmann category type homotopy invariants (25/01/1996) - DVI  - PS 
  
  In the course of the investigation of the Lusternik-Schnirelmann category (cat) several related numerical homotopy invariants have been defined. It would be interesting to know in how far the theory of these invariants can be developed in an axiomatic framework. In this text we define axiomatically a notion of “LS-invariants” which covers cat and the strong category (Cat) and derive some fundamental properties of these invariants from the axioms. This is done in the framework of axiomatic homotopy theory. We also show that Cornea’s cone-length (Cl) is a LS-invariant. As LS-invariants are always ? Cat, we obtain the abstract version of Cornea’s recent result that Cl ¸at.
  
  
• 52 - recherche - C. DE COSTER, P. HABETS - Upper and lower solutions in the theory of ode boundary value problems : classical and recent results (12/04/1996) - DVI 
  
  This text is a set of lecture notes on upper and lower solutions. It emphasizesthe existence of solutions of Caratheodory type to the Dirichlet and the periodic boundary value problem. The first section presents the method and itsrelation with degree theory and variational approach. Some attention is givento examples and applications. Further sections are devoted to systems withsingularities, to the Ambrosetti-Prodi problem and to lower and upper solutionsin the reversed order.
  
  
• 258 - séminaire - D. HAILE, J.-P. TIGNOL - Algebras with involution that become hyperbolic under a given extension (24/04/1996) - DVI  - PS 
  
  A central simple algebra with involution over a field F of characteristic different from 2 is called hyperbolic if it can be represented as the endomorphism algebra of a hyperbolic space. If pi in F[t] is a monic separable polynomial of even degree 2n, we let F(pi) ?[t] / (pi). In a previous paper by the second author it was shown that there is an algebra H_{pi} with involution sigma_{pi} which has the following property : a central simple F-algebra with involution (A,sigma) becomes hyperbolic under scalar extension to F(pi) if and only if there is a homomorphism of F-algebras with involution (H_{pi}, sigma_{pi}) (A,sigma). In the present paper, a quadratic form theoretic formulation of this hyperbolicity criterion is given and the structure of the algebra H_{pi} is determined. It is shown that H_{pi} contains a free algebra on two generators if n > 2 and that H_{pi} is an order in a quaternion algebra if n Ú.
  
  
• 259 - séminaire - M. GAUDENZI, P. HABETS - Nonselfadjoint 4-th order Boundary Value Problems (20/05/1996) - DVI 
  
  We consider a nonselfadjoint two points boundary value problemfor a fourth order ordinary differential equation.We prove existence of solutions in case the nonlinearity f(t,u) is such that theratio f(t,u)/u lies, for |u| large, below the first eigenvalue of thecorresponding linear problem or between the two first ones. We also prove that,contrary to the selfadjoint case, this result does not extend to other pairs ofsuccessive eigenvalues.
  
  
• 260 - séminaire - C. DE COSTER, M. GAUDENZI - On the existence of infinitely many solutions for superlinear n-th order boundary value problems (22/05/1996) - DVI 
  
  We are concerned with the study of an n^th order superlinear equation with two point boundary conditions and we provide the existence of infinitely many solutions with different nodal properties. The boundary value problem is not variational and the technique is based on a combination of the shooting method with n-th order Sturmian theory.
  
  
• 261 - séminaire - M. HENRARD, F. SADYRBAEV - Multiplicity results for fourth order two-point boundary value problems with asymmetric nonlinearities (12/06/1996) - DVI 
  
  
  
  
• 54 - recherche - J. MAWHIN - Bounded solutions of nonlinear ordinary differential equations (20/06/1996) - DVI  - PS 
  
  
  
  
• 55 - recherche - J. MAWHIN - Nonlinear complex-valued differential equations with periodic, Floquet or nonlinear boundary conditions (20/06/1996) - DVI  - PS 
  
  After reviewing recent work on periodic solutions of some complex-valued differential equations, this paper shows that the consideration of some Floquet-type boundary conditions allows a new approach of some of the known results for periodic solutions. Associated nonlinear boundary conditions are also considered.
  
  
• 262 - séminaire - J. MAWHIN, J.R. Jr. WARD - Bounded solutions of some second order nonlinear differential equations (20/06/1996) - DVI  - PS 
  
  
  
  
• 53 - recherche - Z.-Q. WANG, M. WILLEM - A multiplicity result for the generalized Kadomtsev-Petviashvili equation (7/06/1996) - DVI 
  
  A solitary wave of the generalized Kadomtsev-Petviashviliequationw_t + w_{xxx} + (f(w))_x ?_x^{-1} w_{yy}is a solution of the formw(t,x,y) ?(x-ct,y).Under some assumptions, we prove the existence of two geometrically distinctsolitary waves by variational methods.
  
  
• 56 - recherche - P. CALDIROLI, C. DE COSTER - Multiple homoclinics for a class of singular Hamiltonian systems (1/10/1996) - DVI 
  
  We consider a Hamiltonian system ü+nabla V(u)?where the potential V : Bbb R^N S -> Bbb R has a unique strict global maximum at a point p in Bbb R^N and a singular set S subset Bbb R^N {p} such that Bbb R^N S is open, path-connected and the fundamental group G ?pi_1 (Bbb R^N S) is non trivial.Under some compactness conditions on V at infinity and around the singular set S we study the existence of homoclinic orbits to p which link with S. When V and G satisfy suitable geometrical conditions, we can prove the existence of multiple homoclinics, each one belonging to a different homotopy class of G.
  
  
• 263 - séminaire - P. HABETS, E. SERRA, M. TARALLO - Multiplicity results for boundary value problems with potentials oscillating around resonance (2/10/1996) - DVI  - PS 
  
  
  
  
• 57 - recherche - J. MAWHIN - Bound sets and Floquet boundary value problems for nonlinear differential equations (25/11/1996) - DVI 
  
  
  
  
• 58 - recherche - J. MAWHIN - Leray-Schauder continuation theorems in the absence of a priori bounds (16/12/1996) - DVI  - PS 
  
  
  
  
• 59 - recherche - M. CHERPION, C. DE COSTER, P. HABETS - Monotone iterative methods for boundary value problems (24/01/1997) - DVI  - PS 
  
  We consider a second order ordinary differential equation Lu ? (t,u,u’) together with Dirichlet boundary conditions, where L is a phi-Laplacian and f (t,u,u’) is a Carathéodory function.We Study two monotone approximation schemes associated with upper and lower solutions. The first one provides sequences of lower and upper solutions which converge to minimal and maximal solutions of the problem. However these approximations are generally not explicitely computable. The second one gives a method of approximations which is explicit, but provides only bounds on the solutions. In this last case, we also give assumptions which imply the bounds are equal, in which case they are solutions of the problem.Independently of these approximation schemes, we prove existence of minimal and maximal solutions between upper and lower solutions. We also give some maximum principles to obtain uniqueness of solution for such problems
  
  
• 60 - recherche - P.E. PARENT - Les groupes d’évalutation de Gottlieb et les espaces de Ganea (6/02/1997) - DVI 
  
  It is a well known fact that given a continuous map f from X to Y theimage of an element x in the Gottlieb group G(X) of X under the induced map f_# is not in general contained in G(Y). Following the idea of D.H. Gottlieb, we will show that f_#(x) is in fact contained in a generalized Gottlieb group G(f) which satisfy the same kind of factorisation as for the usual Gottlieb group. We use this fact to give a short proof of Gottlieb's result that G(X) is a homotopy type invariant.On the other hand, it is also known that the Gottlieb elements are annihilators under Whitehead product, but in general not all annihilators are Gottlieb (e.g. X?^2). We will show that for X a CW-complex, 1-connected, of finite type the two concepts coincide rationally when we take the generalized Gottlieb group G(p_1), where p_1 is Ganea's first application.
  
  
• 264 - séminaire - D. SMETS, M. WILLEM - Solitary waves with prescribed speed on infinite lattices (14/10/1996) - DVI  - PS 
  
  Using a refined version of the mountain pass theorem, we prove the existance of monotone solitary waves with prescribed speed on infinite lattices. In particular, our results are applicable to cubic and quartic systems and to Toda lattices.
  
  
• 265 - séminaire - J. BLOT, P. CIEUTAT, J. MAWHIN - Almost periodic oscillations of monotone second order systems (25/11/1996) - DVI 
  
  
  
  
• 267 - séminaire - C. POPESCU - On UHL and HUL (9/12/1996) - DVI 
  
  Let R be a principal idea domain of characteristic zero, containing 1/2, and let r ? (R) be the least non-invertible prime in R. Our main result is the following :Let (L,d) be a connected differential non-negatively graded Lie algebra over R, whose underlying module is R-free of finite type. If ad^{r-1} (x) (dx) ?, for all x in L_{even}, then the natural morphism UFHL ---> FHUL is an isomorphism of graded Hopf algebras; as usual, F stands for free part, H for homology, and U for universal enveloping algebra.Related facts and examples are also considered.
  
  
• 268 - séminaire - A.P. MAGNUS - Freud’s equations for orthogonal polynomials as discrete Painlevé equations (9/12/1996) - DVI  - PS 
  
  We consider orthogonal polynomials p_n with respect to an exponential weight function w(x) ?xp (-P(x)) .The related equations for the recurrence coefficientshave been explored by many people, starting essentially with Laguerre,in order to study special continued fractions, recurrence relations, andvarious asymptotic expansions (G. Freud's contribution).Most striking example is n Útw_n+w_n(w_{n+1}+w_n+w_{n-1}) for therecurrence coefficients p_{n+1} ?p_n-w_n p_{n-1} of the orthogonalpolynomials related to the weight w(x) ?xp (-4(tx^2+x^4)) .This example appears in practically all the quoted references.The connection with discrete Painlevé equations is described here.
  
  
• 269 - séminaire - D. BOURN, G. JANELIDZE - Protomodularity, Descent, and Semidirect Products (12/11/1996) - DVI 
  
  Using Descent theory we give various forms of short five-lemma in protomodularcategories, known in the case of exact protomodular categories. We alsodescribe the situation where the notion of a semidirect product can be definedcategorically.
  
  
• 266 - séminaire - Y. FELIX, S. HALPERIN, J.M. LEMAIRE - The rational LS category of products and Poincare duality complexes (28/11/1996) - DVI 
  
  A new characterization of rational L.S. category, cat_0 (x), is given from which two theorems follow.Theorem 1 : cat_0 (XxY) ¸at_0 (X) + cat_0 (Y).Theorem 2 : If X is a Poincaré duality complex, then cat_0 (X) ?_0 (X), where e_0 is Toorner’s invariant.
  
  
• 270 - séminaire - A. SERHIR - Niveau hermitien de certaines algèbres de quaternions (27/02/1997) - DVI  - PS 
  
  Let D?frac{a,b}{F}) a quaternion divisior algebraover a field F of characteristic neq 2.Denote 1, i, j, k the basis of D, such that i^2? j^2? ij?i?and wedge : D ---> D the involution given by hat i?, hat j?(and hat k?.In [LE] D. LEWIS asks the following question : Does there exist a quadratic Pfister form [S p. 72] varphi such that the hermitian form varphi otimes D is isotropic over (D, wedge) but not hyperbolic ?In this note, we show that the answer of this question is negative, so that the hermitien level [§I], when it is finite, of (D, wedge) is a power of two. This result holds for quaternion algebras with standard involution [LE].
  
  
• 61 - recherche - M. DUHOUX - Maximum and anti-maximum principles for singular Sturm-Liouville problems (18/02/1997) - DVI  - PS 
  
  The maximum and anti-maximum principles are extended to the case of eigenvalue Sturm-Liouville problems -(r(t)u’)’ + p(t)u ?lambda m(t)u + h(t), with boundary conditions of Dirichlet type (if possible) on a bounded interval [a,b]. The function r is assumed to be continous and >0 on ]a,b[ , but the function 1/r is not necessarily integrable on [a,b]. The conditions on the functions p, m and h depend on the integrability or non-integrability of 1/r on [a,c] and/or [c,b], for some c in ]a,b[ . The weight function m is not necessarily of constant sign.
  
  
• 62 - recherche - M. DUHOUX - Nonlinear singular Sturm-Liouville problems (9/06/1997) - DVI 
  
  
  
  
• 63 - recherche - Y. DING, M. WILLEM - Homoclinic orbits of a Hamiltonian system (20/06/1997) - DVI 
  
  
  
  
• 271 - séminaire - Z.-Q. WANG, M. WILLEM - Singular minimization problems (11/03/1997) - DVI  - PS 
  
  
  
  
• 272 - séminaire - S. LI, M. WILLEM - Multiple solutions for asymptotically linear boundary value problems in which the nonlinearity crosses at least one eigenvalue (10/06/1997) - DVI  - PS 
  
  
  
  
• 64 - recherche - Th. DE PAUW - On SBV dual (12/05/1997)
  
  A paraître dans : Indiana University Mathematics Journal.
  
  This paper addresses the question of describing the dual of the  space of functions having bounded variation in R^n. In particular, we are interested in how a linear continuous  functional acts on the jump part of the distributional derivative  of a BV function. It is shown that representing this action as the flux of a  H^{n-1} -measurable vector field through the jump set  is independent of ZFC . Analogous undecidable results about various spaces of currents are  stated.  Finally, we apply our results to get an improvement of Whitney's  integral representation of flat cochains.
  
  
• 273 - séminaire - M. GRAN - Internal categories in Mal’cev categories (1/08/1997) - DVI  - PS 
  
  
  
  
• 274 - séminaire - G. BANGEREZAKO - Discrete Darboux transformation for discrete polynomials of hypergeometric type (7/10/1997) - DVI  - PS 
  
  
  
  
• 275 - séminaire - LAVENDHOMME R., NISHIMURA H. - On differential forms in synthetic differential geometry (29/10/1997) - DVI  - PS 
  
  
  
  
• 276 - séminaire - ILIEV P. - Tau-functions solutions to a q-Deformation of the KP hierarchy (12/11/1997) - DVI  - PS 
  
  
  
  
• 65 - recherche - P.E. PARENT - Algebraic LS category (12/11/1997) - DVI  - PS 
  
  
  
  
• 66 - recherche - M. HENRARD - Homoclinic and multipump solutions for perturbed second order systems using topological degree^12 (19/12/1997) - DVI 
  
  
  
  
• 278 - séminaire - P. ILIEV - Solutions to Frenkel’s deformation of the KP hierarchy (3/02/1998) - DVI 
  
  
  
  
• 279 - séminaire - P. HABETS, P.J. TORRES - Some multiplicity results for periodic solutions of a Rayleigh differential equation (3/03/1998) - DVI 
  
  
  
  
• 67 - recherche - D. SMETS - Travelling Waves for an infinite Lattice : Multibump Type Solutions (22/01/1998) - DVI  - PS 
  
  
  
  
• 68 - recherche - A. DELIGIANNIS - Espaces de Ganea et comonades (27/03/1998) - DVI  - PS 
  
  
  
  
• 280 - séminaire - K.PEIFFER, A.Ya. SAVCHENKO - On the asymptotic behavior of a passively stabilized system with one critical variable (22/04/1998) - DVI 
  
  
  
  
• 281 - séminaire - C. POPESCU - Characteristic zero loop space homology for certain two-cones (22/04/1998) - DVI  - PS 
  
  
  
  
• 282 - séminaire - M. HENRARD - A very degenerate poincare-melnikov function (19/05/1998) - DVI  - PS 
  
  
  
  
• 283 - séminaire - J. MAWHIN - Remarques sur les solutions bornées ou presque périodiques de l’équation du pendule force (19/05/1998) - DVI  - PS 
  
  
  
  
• 69 - recherche - L.VANDERPUTTEN - Mesures standards definies par des densites non-standards (19/05/1998) - DVI 
  
  
  
  
• 70 - recherche - J. MAWHIN - Seventy-five years of global analysis around the forced pendulum equation (19/05/1998) - DVI  - PS 
  
  
  
  
• 284 - séminaire - J.M. Alonso, J. Mawhin, R. Ortega - Bounded Solutions of Second order Semilinear Evolution Equations and Applications to the Telegraph Equation (17/07/1998) - DVI  - PS 
  
  
  
  
• 71 - recherche - M. DUHOUX - Green functions and the property of positivity for singular second order boundary value problems (28/08/1998) - DVI  - PS 
  
  
  
  
• 72 - recherche - A. SERHIR - Sur le discriminant et la forme trace d’une involution orthogonale en degré 4 (28/08/1998) - DVI  - PS 
  
  
  
  
• 73 - recherche - A.SERHIR - Niveau hermitien d’un algèbre de quaternions à division munie d’une involution de deuxième espèce (28/08/1998) - DVI  - PS 
  
  
  
  
• 285 - séminaire - M. DUHOUX - Strongly singular Sturm-Liouville problems (28/08/1998) - DVI  - PS 
  
  
  
  
• 286 - séminaire - A.SERHIR - Sommes de carrés hermitiens dans une algèbre simple centrale à involution (28/08/1998) - DVI  - PS 
  
  
  
  
• 287 - séminaire - L. HAINE - J.P. SEMENGUE - The jacobi polynomial ensemble and the Painlevé VI equation (18/09/1998) - DVI  - PS 
  
  
  
  
• 288 - séminaire - M.CHERPION - C. DE COSTER - Existence of solutions for first order singular problems (18/09/1998) - DVI  - PS 
  
  
  
  
• 289 - séminaire - I. DEJAIFFE, D.W. LEWIS, J-P. TIGNOL - Witt equivalence of central simple algebras with evolution (21/10/1998) - DVI  - PS 
  
  
  
  
• 74 - recherche - D.W. LEWIS, J-P. TIGNOL - Classification theorems for central simple algebras with evolution (21/10/1998) - DVI  - PS 
  
  
  
  
• 277 - séminaire - C. POPESCU - On the homology of Free Lie Algebras (23/11/1997) - DVI 
  
  
  
  
• 290 - séminaire - C. POPESCU - Characteristic zero loop space homology of two-cones (23/11/1998) - DVI  - PS 
  
  
  
  
• 291 - séminaire - P. KOULMANN - Dimension minimale de matrices symétriques ou antisymétriques de polynome minimal donné (22/01/1999) - DVI  - PS 
  
  
  
  
• 75 - recherche - G.DINCA - P. JEBELEAN - J. MAWHIN - Variational and Topological Methods for Dirichlet Problems with P-Laplacian (25/06/1999) - DVI  - PS 
  
  
  
  
• 76 - recherche - L. HAINE - P. IILIEV - Commutative rings of difference operators and an adelic flag manifold (15/10/1999) - DVI  - PS 
  
  We show that maximal rank 1 commutative rings of difference operators can be systematically constructed from their differential analogues by making an appropriate shift in the variables of the tau function of the KP hierarchy. When the spectrum of the ring is a unicursal curve, the operators in the ring enjoy a bispectral property reminiscent of the familiar bispectral property satisfied by the classical orthogonal polynomials. As an illustration, the tau functions leading to the rings with spectral curves $y^2?{2K+1}(r+1)$, $K?2,3,dotsc$ are explicitly characterized.
  
  
• 77 - recherche - P. ROSELLI - The Riesz Approach to Lebesgue Integral: Abstract and concrete settings (15/04/1900) - DVI  - PS 
  
  
  
  
• 292 - séminaire - I.J. LE CREURER - Descent for models of finite limit sketches (1/04/1999) - DVI  - PS 
  
  Given a category cal C with finite limits,we give sufficient conditions for the morphisms of various well known internal structures, which are models of finite limit sketches, to be of 0,1 or 2-descent, expressed in terms of the 0,1 and 2-descent morphisms of the base category cal C. In many cases these sufficient conditions in fact characterize the classes 0,1 and 2-descent morphisms in the category of models. 
  
  
• 293 - séminaire - I.J. LE CREURER - Embedding theorem for universal colimits (2/04/1999) - DVI  - PS 
  
  Certain classes of universal colimits in a small category cal C with pullbacks can be utilized to construct sub-canonical Grothendieck topologies on cal C. We give a sufficient conditions on such a class such that the embedding cal C into the category of sheaves preserves these universal colimits.We obtain as corollaries Barr's full exact embedding of a regular category into a Grothendieck topos and the full left exact embedding of a small lextensive category into a Grothendieck topos which preserves finite coproducts. Using this embedding theorem, we give a different proof of the known result that the classes of descent and effective descent morphisms, in a locally small category with finite limits, are closed under composition
  
  
• 294 - séminaire - A.K. BEN-NAOUM - C. FABRY - Structure of the FUCIK spectrum and existence of solutions for equations with asymmetric nonlinearities (15/05/1999) - DVI  - PS 
  
  
  
  
• 295 - séminaire - R. LAVENDHOMME - Deformations of algebraic structures in synthetic differential geometry (30/06/1999) - DVI  - PS 
  
  The theory of deformations of algebraic structures is revisited from the point of view of S.D.G., that is with the systematic use of nilpotent infinitesimals. This leads to more direct calculations in classical cases, but also we propose an extension of the concept to some non abelian situations. We show that cocycle conditions appear as a slope, or a derivative, of fonctoriality conditions in the Lawvere' s definition of algebraic theories
  
  
• 296 - séminaire - D. BLANC - Homotopy operations and homotopy type (30/09/1999) - DVI  - PS 
  
  These notes provide an overview of some recent work towards defining a complete set of algebraic homotopy invariants for the homotopy type of a space X, starting from the homotopy Pa pis X. The first part consists of a quick review of basic unstable homotopy theory, homotopy operations, and homotopical algebra, with an emphasis on the simplicial methods which are needed to construct our invariants. The second part describes the invariants, taking value in appropriate Quillen cohomology groups: these consist of two inductively-defined sequences of cohomology classes, one for determining whether an (abstract) Pa can be realized in the first place, and the other to distinguish between different realizations. We also provide a dual obstruction theory, for determining the mod p homotopy type of X, starting with the unstable homology coalgebra Hi{ast}{X}{BF_{p}}
  
  
• 297 - séminaire - P. HABETS - M. GAUDENZI - Existence and multiplicity of positive solutions for boundary value problems of 2D order ode (30/09/1999) - DVI  - PS 
  
  We study the existence and multiplicity of positive solutions of theboundary value problem u''+sf(t,u)? u(0)?1)?where s is a positive parameter and f is a non-negative function. We indicate examples with more than two solutions.
  
  
• 298 - séminaire - A. DELIGIANNIS - La catégorie des An-espaces en tant que catégorie de fibration (30/10/1999) - DVI  - PS 
  
  Nous munissons la catégorie anc des an d'une structure de catégorie de fibration compatible avec le foncteur oubli U:anc rightarrow CW^{*}, i.e. f est une équivalence faible (resp. fibration) dans anc ssi U(f) est une équivalence faible (resp. fibration) dans CW^{*}.Nous montrons aussi que la notion d'homotopie définie par la structure de catégorie de fibration sur a correspond à celle que nous avions construite "à la main" dans cite{ath2}.
  
  
• 299 - séminaire - A. DELIGIANNIS - Une fibration à la Ganea simpliciale (30/09/1999) - DVI  - PS 
  
  Über eine filtrierung der simplizialen Bar-Konstruktion definieren wir neue Ganea-Abbildungen
  
  
• 300 - séminaire - P. ILIEV - Q-KP hierarchy, bispectrality and Calogero-Moser systems (30/09/1999) - DVI  - PS 
  
  We show that there is a one-to-one correspondence,between the q-tau functions of a q-deformation of the KP hierarchy and the planes in Sato Grassmannian Gr. Using this correspondence, we define a subspace Gr_q^{ad} of Gr, which is a q-deformation of Wilson's adelic Grassmannian Gr^{ad}. From each plane W in Gr_q^{ad} we construct a bispectral commutative algebra cA^q_W of q-difference operators, which extends to the case q neq 1all rank one solutions to the bispectral problem. The common eigenfunction Psi(x,z) for the operators from cA^q_W is a q wave (Baker-Akhiezer) function for a rational (in x) solution to the q-KP hierarchy. The poles of these solutions are governed by a certain q-deformation of the Calogero-Moser hierarchy.
  
  
• 301 - séminaire - M. GRAN - E.M. VITALE - Localizations of Maltsev varieties (30/10/1999) - DVI  - PS 
  
  We give an abstract characterization of categories which arelocalizations of Maltsev varieties. These results can be applied tocharacterize localizations of naturally Maltsev varieties.
  
  
• 302 - séminaire - C. NKUIMI-JUGNIA - Reticulated Categories (The embedding theorems) () - DVI  - PS 
  
  We prove Freyd-Lubkin-Mitchell-Barr type embedding theorems for categories enriched over the join complete semilattices. These results appear in the dissertation of the author.Key words: join complete semilattices, modules over a quantale, enriched category, algebraic categories, embeddings, regular categories, lambda family of regular epimorphisms, infty-regular categories. 
  
  
• 303 - séminaire - C. NKUIMI-JUGNIA - Amalgamation property and epimorphisms in the Category of modules over a quantale (15/05/1900) - DVI  - PS 
  
  In this work we show that the category of modules over a quantale has theamalgamation property; we use it to show that epimorphisms in this category are onto morphisms.Key words: amalgamation, module, quantale, equationallypresentable, algebraic categories. 
  
  
• 304 - séminaire - L. HAINE - P. ILIEV - A rank 1 analogue of the Krall polynomials (15/05/1900) - DVI  - PS 
  
  Krall's polynomials are orthogonal polynomials that are also eigenfunctions of a differential operator. We exhibit an analogue of Krall's polynomials within the context of rank 1 commutative rings of difference operators. The corresponding spectral curves are unicursal curves with equationsv^{2}?{2R+1}(u+1)^{2S+1},R?1,2,..., S?1,2,...,Our rank 1 analogues of Krall's polynomials are rational functions, which satisfy an orthogonality relation on the circle.The proof of the orthogonality relations combines the discrete KPbilinear identities, the cuspidal character of the singularities of the spectralcurves, together with an extra symmetry of the problem
  
  
• 305 - séminaire - M. WILLEM - W. ZOU - On a semilinear Dirichlet Problem and a Nonlinear Schrödinger Equation With Periodic Potential (20/03/1900) - DVI  - PS 
  
  
  
  
• 306 - séminaire - J. CHABROWSKI - M. WILLEM - Least energy solutions of a critical Neumann Problem with a weight (30/07/1900) - DVI  - PS 
  
  We investigate the effect of the coefficient of the critical nonlinearity for the Neumann problem on the existence of least energy solutions. As a by-product we establish a Sobolev inequality with interior norm.
  
  
• 307 - séminaire - R. SKIP GARIBALDI - A. QUÉGUINER-MATHIEU - J.-P. TIGNOL - Involutions and trace forms on exterior powers of a central simple algebra (30/07/1900) - DVI  - PS 
  
  For A a central simple algebra of degree 2n, the n th exterior poweralgebra lambda^n A is endowed with an involution which provides an interesting invariant of A. In the case where A is isomorphic to Q xB for some quaternion algebra , we describe this involution quite explicitly in terms of the norm form for Q and the corresponding involution for B
  
  
• 308 - séminaire - A. CORTELLA - J.-P. TIGNOL - The asymmetry of an anti-automorphism (29/09/1900) - DVI  - PS 
  
  The asymmetry of a nonsingular pairing on a vector space is an endomorphism of the space on which the classification of arbitrary pairings (not necessarily symmetric or skew-symmetric) is based. A general notion of asymmetry is defined for arbitrary anti-automorphisms on a central simple algebra, and conditions are given to characterize the elements which are the asymmetries of some anti-automorphism. The asymmetry is used to define the determinant of an anti-automorphism
  
  
• 309 - séminaire - M.A. ELOMARY - J.-P. TIGNOL - Classification of quadratic forms over skew fields of characteristic 2 (3/10/1900) - DVI  - PS 
  
  Quadratic forms over division algebras over local or global fields of characteristic~2 are classified by an invariant derived from the Clifford algebra construction.
  
  
• 310 - séminaire - R. ANGUELOV - J. M-S LUBUMA - Contributions to the mathematics of the nonstandard finite difference method with applications to certain discrete schemes (2/11/1900) - DVI  - PS 
  
  We formalise the transfer of essential properties of the solution of adifferential equation to the solution of a discrete scheme as qualitativestability with respect to the properties. This permits to motivate somerules (viz. on the order of the difference equation, on the renormalisationof the denominator of the discrete derivative and on nonlocal approximationof nonlinear terms) used in the design of nonstandard finite differenceschemes. Extensions of some models are considered and numerical examples confirming the efficiency of the nonstandard approach areprovided
  
  
• 311 - séminaire - P. ROSELLI - M. WILLEM - A convexity inequality (7/12/1900) - DVI  - PS 
  
  
  
  
• 312 - séminaire - D. SMETS - J. SU - M. WILLEM - Non radial ground states for the Hénon equation (5/01/1901) - DVI  - PS 
  
  We analyse symmetry breakinf for ground states of the Hénon equation [5] in a ball. Asymptotic estimates of the transition are also given when p is close to either 2 or 2*
  
  
• 313 - séminaire - D. CHATAUR - Formes différentielles généralisées sur une opérade et modèles algébriques des fibrations (30/01/1901) - DVI  - PS 
  
  
  
  
• 314 - séminaire - C. FABRY - Some aspects of resonance in nonlinear oscillators (31/01/1901) - DVI  - PS 
  
  
  
  
• 315 - séminaire - M. CHERPION - P. HABETS - R.L. POUSO - Extremal solutions for first order singular problems with discontinuous nonlinearities (2/03/1901) - DVI  - PS 
  
  We derive sufficient conditions for the existence of extremal solutions for first order ordinary differential equations whose right--hand side may be discontinuous and singular. Furthermore, the initial conditions that we consider may be located exactly over one of the singularities
  
  
• 316 - séminaire - L. HAINE - The Bochner-Krall problem: some new perspectives (23/03/1901) - DVI  - PS 
  
  The Bochner-Krall problem asks for the classification of all families of orthogonal polynomials that are also eigenfunctions of a differential operator. We survey some recent work on this problem. An important issue is to extend the problem by allowing for a doubly infinite three-term recursion relation, instead of a semi-infinite one. In this way, the problem gets connected with the associated classical orthogonal polynomials, the Darboux factorization method and the Burchnall-Chaundy theory of commutative rings of difference operators
  
  
• 317 - séminaire - M.GRAN - Exact completion and Protomodularity (20/06/1901) - DVI  - PS 
  
  We characterize those categories which are projective coversof regular protomodular categories. Our result gives in particular a characterization of those categories with weak finite limits with the property that their exact completions are semi-abelian categories
  
  
• 318 - séminaire - V. RADULESCU - D. SMETS - Critical singular problems on infinite cones (12/10/2001) - DVI  - PS 
  
  
  
  
• 319 - séminaire - D. BONHEURE - C.FABRY - Littlewood’s problem for isochronous oscillators (29/01/1902) - DVI  - PS 
  
  
  
  
• 320 - séminaire - D. BONHEURE - C. DE COSTER - Forced singular oscillators and the method of lower and upper solutions (31/01/1902) - DVI  - PS 
  
  
  
  
• 321 - séminaire - L. HAINE - P. ILIEV - Askey-Wilson type functions, with bound states (16/03/1902) - DVI  - PS 
  
  The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in cite{IR}, are slightly modified so as to make it transparent that these functions satisfy a beautiful symmetry property. It essentially means that the geometric and the spectral parameters are interchangeable in these functions. We call the resulting functions the Askey-Wilson functions. Then, we show that by adding bound states (with arbitrary weights) at specific points outside of the continuous spectrum of someinstances of the Askey-Wilson difference operator, we can generatefunctions that satisfy a doubly infinite three-term recursion relation and are also eigenfunctions of $q$-difference operators of arbitrary orders.Our result provides a discrete analogue of the solutions of the purely differential version of the bispectral problem that were discovered in the pioneering work cite{DG} of Duistermaat and Gr"unbaum
  
  
• 322 - séminaire - D. BONHEURE - L. SANCHEZ - M. TARALLO - S.TERRACINI - Heteroclinic connections between nonconsecutive equilibria of a fourth order differential equation (19/03/2002) - DVI  - PS 
  
  Assuming that $f$ is a potential having three minima at the samelevel of energy, we study for the conservative equationbegin{equation}label{abs}u^{iv}-g(u)u''-frac{1}{2}g'(u)u'^2+f'(u)?end{equation}the existence of a heteroclinic connection between the extremalequilibria. Our method consists in minimizing the functional$$int_{-infty}^{+infty}[frac{1}{2}[(u''{}^2)+g(u)u'{}^2]+f(u)],dx$$whose Euler-Lagrange equation is given by (ref{abs}), in asuitable space of functions
  
  
• 323 - séminaire - D. Bonheure, C. Fabry, D. Ruiz - Equations with periodic nonlinearities (19/09/2002) - DVI  - PS 
  
  We study differential equations with periodic nonlinearities. Inparticular, we prove that for $|a|$ small, the equation $ -u'' -u+ g(u) ?t) +a sin(t-phi), $ where $g$ is a $C^1$ periodicfunction with zero mean value and $h$ is orthogonal to $cos t$and $ sin t,$ has $2pi$-periodic solutions. The proof relies onan abstract result based on variational arguments; its applicationmakes use of integral estimates by the stationary phase method. Wealso study the existence of multiple solutions
  
  
• 324 - séminaire - D. Bonheure - Multitransition kinks and pulses (9/10/2002) - DVI  - PS 
  
  We study the existence of stationary solutions of a class ofdiffusion equations related to the so-called extendedFisher-Kolmogo-rov equation and the Swift-Hohenberg equation. Weprove the existence of multitransition kinks and pulses. Thesesolutions are obtained as local minima of the associatedfunctional. For the Swift-Hohenberg equation, our result partiallyproves a numerical conjecture
  
  
• 325 - séminaire - Andre Ronveaux - Jean Mawhin - Rediscovering the contributions of Rodrigues on therepresentation of special functions (6/03/2004) - DVI  - PDF 
  
  
  
  
• 326 - séminaire - Jean Van Schaftingen - Estimates for $mathrm{L}^1$ vector fields with a second order condition (25/05/2004) - DVI  - PDF 
  
  An estimate on the integral of the product of a vector field $f in mathrm{L}^1(R^N;R^{2N-1})$ and a function $uin mathrm{W}^{1,N}(R^N)$ when $f$ satisfies a condition involving the sum of some second-order derivatives. This generalizes a previous result concerning vector fields whose divergence is a summable function cite{BourgainBrezis2004DivCurl,VanSchaftingen2004Divf}. A relationship between this inequality and a Korn--Sobolev inequality of Strauss cite{Strauss1973KornSobolev} is established
  
  
• 327 - séminaire - Thierry De Pauw - Autour du Th'eor`eme de la divergence (16/06/2004) - DVI  - PDF 
  
  
  
  
• 328 - séminaire - Luc Haine - The spectral matrices of Toda solitonsand the fundamental solution of some discrete heat equations (12/09/2004) - DVI  - PDF 
  
  The Stieltjes spectral matrix measure of the doublyinfinite Jacobi matrix associated with a Toda $g$-soliton iscomputed, using Sato theory. The result is used togive an explicit expansion of the fundamental solution of some discreteheat equations, in a series of Jackson's $q$-Bessel functions. ForAskey-Wilson type solitons cite{H,HI3},this expansion reduces to a finite sum. This generalizes a resultin cite{GI}, which corresponds to the limit $qto 1$
  
  
• 329 - séminaire - J. Goblet - A Selection Theory for Multiple-valued Functions In The Sense Of Almgren (29/01/2005) - DVI 
  
  
  
  

Pour les prépublications à partir de 2005, veuillez vous référer à la page Séminaires de mathématique (prépublications).