Confluentes Mathematici最新文献

{"title":"TIME-HARMONIC MAXWELL EQUATIONS IN BIOLOGICAL CELLS — THE DIFFERENTIAL FORM FORMALISM TO TREAT THE THIN LAYER","authors":"M. Duruflé, V. Péron, C. Poignard","doi":"10.1142/S1793744211000345","DOIUrl":"https://doi.org/10.1142/S1793744211000345","url":null,"abstract":"We study the behavior of the electromagnetic field in a biological cell modelled by a medium surrounded by a thin layer and embedded in an ambient medium. We derive approximate transmission conditions in order to replace the membrane by these conditions on the boundary of the interior domain. Our approach is essentially geometric and based on a suitable change of variables in the thin layer. Few notions of differential calculus are given in order to obtain the first order conditions in a simple way, and numerical simulations validate the theoretical results. Asymptotic transmission conditions at any order are given in the last section of the paper.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"11 1","pages":"325-357"},"PeriodicalIF":0.0,"publicationDate":"2011-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91262812","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"THREE-DIMENSIONAL INTERACTION OF SHOCKS IN IRROTATIONAL FLOWS","authors":"D. Serre","doi":"10.1142/S1793744211000394","DOIUrl":"https://doi.org/10.1142/S1793744211000394","url":null,"abstract":"The general d-dimensional Riemann problem raises naturally the question of resolving the interaction of d planar shocks merging at a point. In gas dynamics, we may consider only standing shocks. This problem has received a satisfactory answer in dimension d = 2 (see [3, 4]). We investigate the 3-dimensional case. We restrict to the irrotational case, in order to keep the complexity of the solution within reasonable bounds. We show that a new kind of waves appears downstream, which we call a conical wave. When the equation of state is that of Chaplygin/von Karman, we give a complete mathematical answer to this problem. This involves the existence and uniqueness of a complete minimal surface in a hyperbolic space, with prescribed asymptotics.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"119 1","pages":"543-576"},"PeriodicalIF":0.0,"publicationDate":"2011-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78559048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"TRANSFORMATION DU PROBLÈME DE RÉSOLUTION DE SYSTÈMES DE TOEPLITZ BINIVEAUX À UN PROBLÈME POLYNOMIAL","authors":"Houssam Khalil, Bernard Mourrain, M. Schatzman","doi":"10.1142/S1793744211000357","DOIUrl":"https://doi.org/10.1142/S1793744211000357","url":null,"abstract":"On presente une relation entre la solution d'un systeme de Toeplitz biniveaux, Tu = g, et les syzygies de polynomes a deux variables ou hyperplans mobiles. Cette approche nous donne la possibilite de definir les generateurs pour les matrices de Toeplitz biniveaux en utilisant les generateurs du module de syzygie correspondant. On demontre que ce module est generalise par 8 elements et que la solution de Tu = g peut etre interpretee comme le reste de la division d'un vecteur, dependant de g, par ces generateurs. Ce nouveau point de vu de resolution peut etre interprete comme une decomposition de Gohberg–Semencul [3, 5] pour les matrices de Toeplitz biniveaux. La difficulte de generaliser la notion de structure de deplacement [2, 4, 3] du cas scalaire (de niveau un) au cas par blocs, et l'absence de notion de generateurs pour les matrices de Toeplitz biniveaux sont a la base de l'absence d'une telle decomposition jusqu'a present. L'utilisation de cette idee pour resoudre les systemes de Toeplitz scalaires nous permet de donner un algorithme de resolution ultra rapide. L'absence de la notion de μ-base pour les modules de syzygies en plusieurs variables complique la situation pour les systemes de Toeplitz biniveaux, et l'obtention d'un algorithme de resolution ultra rapide utilisant cette approche reste un probleme ouvert.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"47 1","pages":"253-262"},"PeriodicalIF":0.0,"publicationDate":"2011-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82587326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A POSITION-BASED TIME-STEPPING ALGORITHM FOR VIBRO-IMPACT PROBLEMS WITH A MOVING SET OF CONSTRAINTS","authors":"L. Paoli","doi":"10.1142/S179374421100031X","DOIUrl":"https://doi.org/10.1142/S179374421100031X","url":null,"abstract":"We consider a second-order measure differential inclusion describing the dynamics of a mechanical system subjected to time-dependent frictionless unilateral constraints and we assume inelastic collisions when the contraints are saturated. For this model of impact, we propose a time-stepping algorithm formulated at the position level and we establish its convergence to a solution of the Cauchy problem.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"36 1","pages":"263-290"},"PeriodicalIF":0.0,"publicationDate":"2011-11-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87469728","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Quantifier elimination in ordered abelian groups","authors":"R. Cluckers, Immanuel Halupczok","doi":"10.1142/S1793744211000473","DOIUrl":"https://doi.org/10.1142/S1793744211000473","url":null,"abstract":"We give a new proof of quantifier elimination in the theory of all ordered abelian groups in a suitable language. More precisely, this is only \"quantifier elimination relative to ordered sets\" in the following sense. Each definable set in the group is a union of a family of quantifier free definable sets, where the parameter of the family runs over a set definable (with quantifiers) in a sort which carries the structure of an ordered set with some additional unary predicates. As a corollary, we find that all definable functions in ordered abelian groups are piecewise linear on finitely many definable pieces.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"31 1","pages":"587-615"},"PeriodicalIF":0.0,"publicationDate":"2011-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74306859","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the gradient flow of a one-homogeneous functional","authors":"A. Briani, A. Chambolle, M. Novaga, G. Orlandi","doi":"10.1142/S1793744211000461","DOIUrl":"https://doi.org/10.1142/S1793744211000461","url":null,"abstract":"We consider the gradient flow of a one-homogeneous functional, whose dual involves the derivative of a constrained scalar function. We show in this case that the gradient flow is related to a weak, generalized formulation of a Hele–Shaw flow. The equivalence follows from a variational representation, which is a variant of well-known variational representations for the Hele–Shaw problem. As a consequence we get existence and uniqueness of a weak solution to the Hele–Shaw flow. We also obtain an explicit representation for the Total Variation flow in dimension 1, and easily deduce basic qualitative properties, concerning in particular the \"staircasing effect\".","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"284 1","pages":"617-635"},"PeriodicalIF":0.0,"publicationDate":"2011-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73049768","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Adaptive time splitting method for multi-scale evolutionary partial differential equations","authors":"S. Descombes, Max Duarte, T. Dumont, V. Louvet, M. Massot","doi":"10.1142/S1793744211000412","DOIUrl":"https://doi.org/10.1142/S1793744211000412","url":null,"abstract":"This paper introduces an adaptive time splitting technique for the solution of stiff evolutionary PDEs that guarantees an effective error control of the simulation, independent of the fastest physical time scale for highly unsteady problems. The strategy considers a second-order Strang method and another lower order embedded splitting scheme that takes into account potential loss of order due to the stiffness featured by time-space multi-scale phenomena. The scheme is then built upon a precise numerical analysis of the method and a complementary numerical procedure, conceived to overcome classical restrictions of adaptive time stepping schemes based on lower order embedded methods, whenever asymptotic estimates fail to predict the dynamics of the problem. The performance of the method in terms of control of integration errors is evaluated by numerical simulations of stiff propagating waves coming from nonlinear chemical dynamics models as well as highly multi-scale nanosecond repetitively pulsed gas discharges, which allow to illustrate the method capabilities to consistently describe a broad spectrum of time scales and different physical scenarios for consecutive discharge/post-discharge phases.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"34 1","pages":"1-31"},"PeriodicalIF":0.0,"publicationDate":"2011-04-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81495433","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A GENERAL WAVELET-BASED PROFILE DECOMPOSITION IN THE CRITICAL EMBEDDING OF FUNCTION SPACES","authors":"H. Bahouri, A. Cohen, G. Koch","doi":"10.1142/S1793744211000370","DOIUrl":"https://doi.org/10.1142/S1793744211000370","url":null,"abstract":"We characterize the lack of compactness in the critical embedding of functions spaces X ⊂ Y having similar scaling properties in the following terms: a sequence (un)n≥0 bounded in X has a subsequence that can be expressed as a finite sum of translations and dilations of functions (ϕl)l>0 such that the remainder converges to zero in Y as the number of functions in the sum and n tend to +∞. Such a decomposition was established by Gerard in [13] for the embedding of the homogeneous Sobolev space X = Ḣs into the Y = Lp in d dimensions with 0 < s = d/2 - d/p, and then generalized by Jaffard in [15] to the case where X is a Riesz potential space, using wavelet expansions. In this paper, we revisit the wavelet-based profile decomposition, in order to treat a larger range of examples of critical embedding in a hopefully simplified way. In particular, we identify two generic properties on the spaces X and Y that are of key use in building the profile decomposition. These properties may then easily be checked for typical choices of X and Y satisfying critical embedding properties. These includes Sobolev, Besov, Triebel-Lizorkin, Lorentz, Holder and BMO spaces.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"48 1","pages":"387-411"},"PeriodicalIF":0.0,"publicationDate":"2011-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76259515","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"RACINES CARRÉES D'OPÉRATEURS ELLIPTIQUES ET ESPACES DE HARDY","authors":"Emmanuel Russ","doi":"10.1142/S1793744211000278","DOIUrl":"https://doi.org/10.1142/S1793744211000278","url":null,"abstract":"Il est bien connu que, pour tout 1 0 tel que pour toute fonction . Lorsque p = 1, (0.1) est fausse pour L1(ℝn) mais devient ou H1(ℝn) est l'espace de Hardy reel classique. Dans cette vue d'ensemble, nous rassemblons des resultats qui etendent (0.1) et (0.2) dans deux directions. D'une part, nous nous placons dans un ouvert fortement lipschitzien de ℝn, ou dans un cadre geometrique non euclidien (variete riemannienne complete ou graphe). D'autre part, nous remplacons Δ par un operateur elliptique d'ordre 2 plus general (operateur sous forme divergence dans un ouvert de ℝn, laplacien de Hodge dans une variete riemannienne, laplacien discret sur un graphe). Dans le cas des domaines fortement lipschitziens de ℝn, ces questions conduisent a introduire des espaces de Hardy–Sobolev et a en donner des proprietes analogues a celles des espaces de Sobolev usuels. Dans le cas des varietes riemanniennes, nous introduisons des espaces de Hardy de formes differentielles exactes. Ces espaces sont adaptes au laplacien de Hodge et possedent des proprietes analogues a l'espace de Hardy H1(ℝn). Le laplacien de Hodge possede un calcul fonctionnel holomorphe sur ces espaces, et en particulier la transformee de Riesz est continue. Sous des hypotheses geometriques convenables, nous comparons ces espaces de Hardy aux espaces de Hardy usuels (dans le cas d'espaces de fonctions) ou aux espaces Lp. Enfin, sur un graphe verifiant certaines proprietes geometriques, nous obtenons des versions discretes de la plupart des resultats correspondants pour les transformees de Riesz et inegalites reliees obtenues dans des varietes riemanniennes. Nous donnons egalement des resultats concernant les puissances fractionnaires d'operateurs elliptiques d'ordre 2. Il s'agit de proprietes d'algebre pour des espaces de Bessel fractionnaires sur des groupes de Lie unimodulaires, generalisant les resultats euclidiens. Nous utilisons egalement des estimations de la norme L2 de puissances fractionnaires de certains operateurs pour montrer une inegalite de Poincare fractionnaire pour certaines mesures de probabilite dans ℝn ou des groupes de Lie a croissance polynomiale.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"21 1","pages":"1-119"},"PeriodicalIF":0.0,"publicationDate":"2011-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73664361","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"ON BIALGEBRAS AND HOPF ALGEBRAS OF ORIENTED GRAPHS","authors":"D. Manchon","doi":"10.1142/S1793744212400038","DOIUrl":"https://doi.org/10.1142/S1793744212400038","url":null,"abstract":"We define two coproducts for cycle-free oriented graphs, thus building up two commutative connected graded Hopf algebras, such that one is a comodule-coalgebra on the other, thus generalizing the result obtained in [2] for Hopf algebras of rooted trees.","PeriodicalId":52130,"journal":{"name":"Confluentes Mathematici","volume":"4 1","pages":"1240003"},"PeriodicalIF":0.0,"publicationDate":"2010-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75931071","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}