Search

In this paper we consider the multidimensional binary vector assignment problem. An input of this problem is defined by m disjoint multisets $$V^1, V^2, \ldots , V^m$$ , each composed of n binary vectors of size p. An output is a set of n disjoint m-tuples of vectors, where each m-tuple is obtained by picking one vector from each multiset $$V^i$$ . To each m-tuple we associate a p dimensional vector by applying the bit-wise AND operation on the m vectors of the tuple. The objective is to minimize the total number of zeros in these n vectors. We denote this problem by , and the restriction of this problem where every vector has at most c zeros by . was only known to be -hard, even for . We show that, assuming the unique games conjecture, it is -hard to -approximate for any fixed and . This result is tight as any solution is a -approximation. We also prove without assuming UGC that is -hard even for . Finally, we show that is polynomial-time solvable for fixed (which cannot be extended to ).

According to the real $\tau$-conjecture, the number of real roots of a sum of products of sparse univariate polynomials should be polynomially bounded in the size of such an expression. It is known that this conjecture implies a superpolynomial lower bound on the arithmetic circuit complexity of the permanent. In this paper, we use the Wronksian determinant to give an upper bound on the number of real roots of sums of products of sparse polynomials of a special form. We focus on the case where the number of distinct sparse polynomials is small, but each polynomial may be repeated several times. We also give a deterministic polynomial identity testing algorithm for the same class of polynomials. Our proof techniques are quite versatile; they can in particular be applied to some sparse geometric problems that do not originate from arithmetic circuit complexity. The paper should therefore be of interest to researchers from these two communities (complexity theory and sparse polynomial systems).

Dans un r\'ecent article, Lagarias et Soundararajan \'etudient les solutions friables \`a l'\'equation a+b=c. Sous l'hypoth\`ese de Riemann g\'en\'eralis\'ees aux fonctions L de Dirichlet, ils obtiennent une estimation pour le nombre de solutions pond\'er\'ees par un poids lisse et une minoration pour le nombre de solutions non pond\'er\'ees. Le but de cet article est de pr\'esenter des arguments qui permettent d'une part de pr\'eciser les termes d'erreur et d'\'etendre les domaines de validit\'e de ces estimations afin de faire le lien avec un travail de la Bret\`eche et Granville, d'autre part d'obtenir le comportement asymptotique exact du nombre de solutions non pond\'er\'ees. In a recent paper, Lagarias and Soundararajan study the y-smooth solutions to the equation a+b=c. Under the Generalised Riemann Hypothesis, they obtain an estimate for the number of those solutions weighted by a compactly supported smooth function, as well as a lower bound for the number of bounded unweighted solutions. In this paper, we aim to prove a more precise estimate for the number of weighted solutions that is valid when y is relatively large with respect to x, so as to connect our estimate with the one obtained by La Bret\`eche and Granville in a recent work. We also prove the conjectured upper bound for the number of bounded unweighted solutions, thus obtaining its exact asymptotic behaviour., Comment: 20 pages

In this paper, we try to enumerate the results dealing with the combinatorial and algorithmic aspects of the median orders and Slater orders of tournaments. Most of the quoted results may be found in the different papers devoted to these topics ; some others are new ones. Dans cet article, nous essayons de faire le point sur les résultats concernant les aspects combinatoires et algorithmiques des ordres médians et des ordres de Slater des tournois. La plupart des résultats recensés sont tirés de différentes publications ; plusieurs sont originaux.

Customer complaint handling is very important for the service industry. This paper presents the justice theory (with its distributive, procedural and interactional dimensions) through a literature review and a content analysis of service experiences. This paper aims to show the relevance of the justice theory frameworks to manage complaints and to develop a grid of analysis. Then, some managerial propositions are made in order to help companies to improve their customer complaint management., La gestion des réclamations revêt une importance toute particulière dans le secteur des services. Cet article se propose de présenter les apports des théories de la justice pour la gestion des réclamations dans le cadre d'expériences de services. A partir d'une revue de la littérature et d'une enquête, les auteurs illustrent l'ensemble des règles de justice contenues dans la théorie de la justice (dimensions distributive, procédurale et interactionnelle) et proposent une grille de lecture pour la gestion des réclamations. Un certain nombre de propositions managériales sont formulées pour permettre aux entreprises de mieux gérer leurs réclamations.

Motivated by the fact that circular or spherical data are often much concentrated around a location $\pmb\theta$, we consider inference about $\pmb\theta$ under "high concentration" asymptotic scenarios for which the probability of any fixed spherical cap centered at $\pmb\theta$ converges to one as the sample size $n$ diverges to infinity. Rather than restricting to Fisher-von Mises-Langevin distributions, we consider a much broader, semiparametric, class of rotationally symmetric distributions indexed by the location parameter $\pmb\theta$, a scalar concentration parameter $\kappa$ and a functional nuisance $f$. We determine the class of distributions for which high concentration is obtained as $\kappa$ diverges to infinity. For such distributions, we then consider inference (point estimation, confidence zone estimation, hypothesis testing) on $\pmb\theta$ in asymptotic scenarios where $\kappa_n$ diverges to infinity at an arbitrary rate with the sample size $n$. Our asymptotic investigation reveals that, interestingly, optimal inference procedures on $\pmb\theta$ show consistency rates that depend on $f$. Using asymptotics "\`a la Le Cam", we show that the spherical mean is, at any $f$, a parametrically super-efficient estimator of $\pmb\theta$ and that the Watson and Wald tests for $\mathcal{H}_0:{\pmb\theta}={\pmb\theta}_0$ enjoy similar, non-standard, optimality properties. We illustrate our results through simulations and treat a real data example. On a technical point of view, our asymptotic derivations require challenging expansions of rotationally symmetric functionals for large arguments of $f$., Comment: 51 pages, 5 figures

International audience; This paper focuses on the use of interactive mediation tools during the museum visit. What are the dimensions of the museum visit experience? Is it specific to the nature of the interactive tool (audioguide, tablet, interactive kiosk, multi-user digital table) used during the visit ? First, a state of the art of the researches which focused on the influence of interactive mediation tools on the museum visit is presented. Second, the results from the qualitative method are analysed. On a managerial level, the goal is to help museum professionnals to choose interactive mediation tools in order to enrich the visit experience and broaden their audiences.; La nature de l’outil interactif utilisé (audioguide, tablette tactile, borne interactive, table tactile multi-usagers) lors de la visite induit-elle une expérience muséale spécifique ? Tout d’abord une synthèse de la revue de la littérature est présentée portant sur l’influence des outils interactifs de médiation sur l’expérience de visite muséale. Puis, les résultats issus d’une démarche qualitative sont analysés. La finalité managériale est d’aider les professionnels dans leur processus de choix des outils interactifs de médiation afin d’enrichir l’expérience de visite muséale vécue par les publics, dans un objectif de leur élargissement et de leur diversification.

In a previous paper we proved that a necessary and sufficient condition for all martingales of a given filtration $(\mathscr{F}_t)$ to be continuous is that, for every stopping time $T$ and every $\mathscr{F}_T$-measurable random variable $X$, there exists a continuous local martingale $M$ with $M_T = X$ a.s. The aim of this paper is to study the following question: Can we choose $M \geq 0$ whenever $X \geq 0$? We also give a negative answer to Conjecture 7.1 of Harrison and Pliska.

Pre-print of a publication in "Annales math\'ematiques du Qu{\'e}bec". Let $k$ be a totally real number field and let $k_\infty$ be its cyclotomic $\mathbb{Z}_p$-extension for $p$ totally split in $k$. This text completes our article entitled: "Approche $p$-adique de la conjecture de Greenberg pour les corps totalement r\'eels" (Annales Math\'ematiques Blaise Pascal 2017), by means of heuristics on the $p$-adic behavior of the norms, in $k_n/k$, of the ideals in $k_\infty$ ; indeed, this conjecture (on the nullity of the invariants $\lambda$ et $\mu$ of Iwasawa) depends of images in the torsion group ${\mathcal T}_k$ of the Galois group of the maximal abelian $p$-ramified pro-$p$-extension of $k$, thus of Artin symbols in a finite extension $F/k$ obtained by Galois descent of ${\mathcal T}_k$. An assumption of distribution of these norms implies $\lambda=\mu=0$. Several statistics and numerical examples in the quadratic case confirm the probable exactness of such properties which constitute the fundamental obstruction for a proof of Greenberg's conjecture in the sole context of Iwasawa's theory., Comment: in French, Completes with numerical computations and heuristics our previous paper arXiv:1611.09592 on Greenberg's conjecture. Annales math{\'e}matiques du Quebec, A para{\^i}tre

Let $F$ be a family of graphs. Then for every graph $G$ the maximum number of disjoint subgraphs of $G$, each isomorphic to a member of $F$, is at most the minimum size of a set of vertices that intersects every subgraph of $G$ isomorphic to a member of $F$. We say that $F$ packs if equality holds for every graph $G$. Only very few families pack. As the next best weakening we say that $F$ has the Erdős-Posa property if there exists a function $f$ such that for every graph $G$ and integer $k>0$ the graph $G$ has either $k$ disjoint subgraphs each isomorphic to a member of $F$ or a set of at most $f(k)$ vertices that intersects every subgraph of $G$ isomorphic to a member of $F$. The name is motivated by a [classical 1965 result of Erdős and Posa](https://en.wikipedia.org/wiki/Erd%C5%91s%E2%80%93P%C3%B3sa_theorem) stating that for every graph $G$ and integer $k>0$ the graph $G$ has either $k$ disjoint cycles or a set of $O(k\log k)$ vertices that intersects every cycle. Thus the family of all cycles has the Erdős-Posa property with $f(k)=O(k\log k)$. In contrast, the family of odd cycles fails to have the Erdős-Posa property. For every integer $\ell$, a sufficiently large Escher Wall is a non-bipartite graph that has an embedding in the projective plane such that every face is even and every homotopically non-trivial closed curve intersects the graph at least $\ell$ times. In particular, it contains no set of strictly less than $\ell$ vertices such that each odd cycle contains at least one them, yet it has no two disjoint odd cycles. By now there is a large body of literature proving that various families $F$ have the Erdős-Posa property. A very general theorem of Robertson and Seymour says that for every planar graph $H$ the family $F(H)$ of all graphs with a minor isomorphic to $H$ has the Erdős-Posa property. (When $H$ is non-planar, $F(H)$ does not have the Erdős-Posa property.) The present paper proves that for every planar graph $H$ the family $F(H)$ has the Erdős-Posa property with $f(k)=O(k\log k)$, which is asymptotically best possible for every graph $H$ with at least one cycle.

The paper studies compactness properties of the affine Sobolev inequality of Lutwak et al. (J Differ Geom 62:17–38, 2002) and Zhang (J Differ Geom 53:183–202, 1999) in the case $$p=2$$ , and existence and regularity of related minimizers, in particular, solutions to the nonlocal Dirichlet problems $$\begin{aligned} -\sum _{i,j=1}^{N}(A^{-1}[u])_{ij}\frac{\partial ^2u}{\partial x_i\partial x_j}=f \text{ in } \Omega \subset {\mathbb {R}}^N, \end{aligned}$$ and $$\begin{aligned} -\sum _{i,j=1}^{N}(A^{-1}[u])_{ij}\frac{\partial ^2u}{\partial x_i\partial x_j}=u^{q-1},\quad u>0, \text{ in } \Omega \subset {\mathbb {R}}^N, \end{aligned}$$ where $$A_{ij}[u]=\int _\Omega \frac{\partial u}{\partial x_i}\frac{\partial u}{\partial x_j}{\mathrm {d}}{x}$$ and $$q\in (2,\frac{2N}{N-2})$$ .

International audience; A better understanding of the link between consumption and life satisfaction has become a major stake for economists, who seek to find ways to improve the subjective well-being of people. But research results on the link between product and service consumption and life satisfaction are contradictory and depend on the kind of product, the country and time. The aim of this paper is to show the benefit of taking several moderators of the relationship between product satisfaction and life satisfaction into account: "product centrality", which can be defined as the importance and the impact of the product consumption on everyday life, "self congruity" and "lifestyle congruity". The results of three studies, one qualitative and two quantitative, show the effect of these three variables. Moreover, the influence of time on this relationship is studied.; Mieux comprendre le lien entre la consommation et la satisfaction dans la vie est devenu un enjeu pour les économistes du bonheur qui tentent de trouver des leviers pour améliorer le bien-être subjectif des populations. Or, les travaux portant sur l'influence de la consommation de produits ou de services sur la satisfaction dans la vie divergent selon le produit, le pays et le temps. L'objectif de cet article est de montrer l'intérêt d'intégrer plusieurs modérateurs de la relation entre la satisfaction à l'égard du produit et la satisfaction dans la vie : la « centralité du produit », qui peut être définie comme l'importance et l'impact de la consommation d'un produit ou service dans la vie quotidienne, la « congruence entre le produit et le soi » et la « congruence entre le produit et le style de vie ». Trois études, l'une qualitative, les deux autres quantitatives, ont permis de montrer l'influence de ces variables. Par ailleurs, l'effet de la dimension temporelle sur la relation est étudié.

Let $P^+(n)$ denote the largest prime factor of the integer $n$ and $P_y^+(n)$ denote the largest prime factor $p$ of $n$ which satisfies $p\leqslant y$. In this paper, firstly we show that the triple consecutive integers with the two patterns $P^+(n-1)>P^+(n)P^+(n+1)$ have a positive proportion respectively. More generally, with the same methods we can prove that for any $J\in \mathbb{Z}, J\geqslant3$, the $J-$tuple consecutive integers with the two patterns $P^+(n+j_0)= \min\limits_{0\leqslant j\leqslant J-1}P^+(n+j)$ and $P^+(n+j_0)= \max\limits_{0\leqslant j\leqslant J-1}P^+(n+j)$ also have a positive proportion respectively. Secondly for $y=x^{\theta}$ with $0, Comment: in French

International audience; , Une lecture socio-technique des effets des systèmes d'encaissement automatique : quand la technologie reconfigure les relations sur le point de vente, Décisions Marketing, 82, 109-124. Résumé Les systèmes d'encaissement automatique (caisses libre-service dites self-check out et systèmes de self-scanning) connaissent un développement accéléré en France depuis une dizaine d'années. Au travers d'une étude qualitative menée auprès de clients de la grande distribution, cet article permet de mieux comprendre les effets de ces nouveaux dispositifs sur les relations entre les acteurs sur le point de vente. Loin de déshumaniser le point de vente, ils reconfigurent les relations du client avec son entourage, avec les autres clients, ainsi qu'avec les hô-tesses de caisse. Plus largement, à l'échelle de la société, ils suscitent des questionnements sur la transformation des liens et le partage du travail. Des recommandations sont proposées aux managers pour faciliter l'intégration de ces dispositifs dans le point de vente. Abstract A socio-technical analysis of the impact of self-check outs: when technologies redesign customer relationship at the point of sale Self-checkout technologies (self-checkout and self-scanning systems) have seen an accelerated expansion over the last decade. Through qualitative interviews with retailers' clients, this paper adopts a relational perspective by revealing these new devices' impact on clients' identity as well as on their relationships at three levels: the relationships with the check-out assistants, with family members and other clients. At a societal level, these devices raise new questions for clients about human relationships and work organization. Guidelines are proposed to managers in order to facilitate self-checkout devices' integration in the point of sales' environment.

International audience; Integrity, benefits and self-brand connections: three critical consumer brand engagement drivers on socialnetworksThis paper focuses on the antecedents of consumer brand engagement on social networks and on its effectson loyalty intention. It highlights that engagement is not only directed towards the brand (and encompasses3 dimensions: cognitive, affective and behavioral) but also towards social networks members’ interconnections(social brand engagement). 245 fans were surveyed about their favorite brand on Facebook. The results showthat perceived benefits and self-brand connections impact social engagement and that, in turn, social engagementinfluences brand engagement. Furthermore, the results highlight that consumer brand engagement mediates theeffects of brand integrity, perceived benefits and self-brand connections on loyalty intentions.; Cet article s’intéresse aux déterminants de l’engagement du consommateur envers la marque sur les réseauxsociaux et à ses effets sur l’intention de fidélité. Il souligne que cet engagement est dirigé non seulement vers lamarque (et comporte trois dimensions : cognitive, affective et comportementale) mais aussi vers les membres duréseau social (engagement social). Une étude quantitative auprès de 245 fans interrogés sur leur marque préféréesur Facebook montre que les bénéfices perçus ainsi que les connexions du soi à la marque impactent l’engage-ment social via la page de la marque et que ce dernier influence l’engagement envers la marque via la page de lamarque. En outre, elle met en évidence que l’engagement envers la marque via la page de la marque est média-teur des effets de l’intégrité de la marque, des bénéfices perçus ainsi que des connexions du soi à la marque surl’intention de fidélité à la marque.

An integer is said to be $y$-friable if its greatest prime factor is less than $y$. In this paper, we obtain estimates for exponential sums over $y$-friable numbers up to $x$ which are non-trivial when $y \geq \exp\{c \sqrt{\log x} \log \log x\}$. As a consequence, we obtain an asymptotic formula for the number of $y$-friable solutions to the equation $a+b=c$ which is valid unconditionnally under the same assumption. We use a contour integration argument based on the saddle point method, as developped in the context of friable numbers by Hildebrand & Tenenbaum, and used by Lagarias, Soundararajan and Harper to study exponential and character sums over friable numbers., 31 pages, in French

In this paper, we generalize Mauduit and Rivat's theorem on the Rudin-Shapiro sequence. Weakening the hypothesis needed in their theorem, we prove a prime number theorem for a large class of functions defined on the digits. Our result covers the case of generalized Rudin-Shapiro sequences as well as bloc-additive sequences on finite and infinite expansions. We also give a partial answer to a question posed by Kalai., Comment: in French

International audience; “Fed up with messages about ecology!”: towards an understanding of consumer contestation of ecological messagesThough ecology is seen as a major concern for French consumers, several studies show that it can also becriticized. Indeed some individuals knowingly challenge and even reject ecological messages from firms andauthorities. Through different qualitative methodologies this paper identifies the causes and manifestations ofthe contestation of ecological messages in order to have a better understanding of this phenomenon. It showsthe coexistence of a negative evaluation of the messages with negative emotional reactions leading to a state ofcontestation that may vary from skepticism to resistance. Recommendations for environmental communicationcampaigns are provided to companies and authorities.; Bien que l’écologie semble être un sujet important pour les Français, des études récentes font état de réserves etcritiques à son égard. En effet, certains individus contestent sciemment les discours écologiques des entrepriseset des pouvoirs publics, voire les rejettent. A l’aide de méthodes qualitatives mobilisant ce type d’individus, cetarticle identifie les déterminants et manifestations du phénomène de contestation des discours écologiques pourmieux le caractériser. Il souligne la coexistence d’une évaluation négative des discours et de réactions émotion-nelles négatives faisant émerger un état de contestation variable suivant les individus, allant du scepticisme à larésistance. Des recommandations en termes de communication environnementale sont finalement proposées auxentreprises et pouvoirs publics concernés.

An integer n is said to be y-friable if its largest prime factor $P^+(n)$ is less than y. In this paper, it is shown that the y-friable integers less than x have a weak exponent of distribution at least $3/5-\varepsilon$ when $(\log x)^c\leq y\leq x^{1/c}$ for some $c=c(\varepsilon)\geq 1$, that is, they are well distributed in the residue classes of a fixed integer $a$, on average over moduli $\leq x^{3/5-\varepsilon}$ for each fixed $a\neq 0$ and $\varepsilon>0$. We present an application to the estimation of the sum $\sum_{2\leq n\leq x, P^+(n)\leq y}\tau(n-1)$ when $(\log x)^c\leq y$. This follows and improves on previous work of Fouvry and Tenenbaum. Our proof combines the dispersion method of Linnik in the setting of Bombieri, Fouvry, Friedlander and Iwaniec, and recent work of Harper on friable integers in arithmetic progressions., Comment: 27 pages, in French, English abstract

International audience; Consumer participation in the different steps of products or services' production process is developing following many directions, from the most ordinary to the most creative ones. In this context, the present paper tries to clarify the definition of consumer participation and proposes a typology of consumer participation practices based on two dimensions: consumer resources needed and motivations. This matrix offers a framework for managers to analyze their current and future devices, as well as those of their competitors, through the prism of the role assigned to the customer. Finally, implications and guidelines are addressed to firms willing to develop the participatory dimension of their customer relationship management.; La participation du consommateur aux différentes phases du processus de production d'un produit ou service se développe aujourd'hui sous des formes variées, des plus ordinaires aux plus créatives. Dans ce contexte, cet article tente de clarifier la définition de la participation du consommateur, puis propose une classification des pratiques de participation fondée sur deux dimensions : les ressources à mobiliser et la motivation à participer. Cette matrice offre aux managers une grille d'analyse de leurs dispositifs de participation, ainsi que ceux de leurs concurrents, au travers du prisme du rôle attribué au client. Des pistes de réflexion sont ensuite adressées aux enseignes souhaitant développer la dimension participative de leurs dispositifs de gestion de la relation client.

International audience; Customer roles in the physical distribution of productsThe paper discusses the roles that firms can assign to their customers within the physical distributionof their products. First, the article shows that four strategies of customers empowerment are pos-sible, depending on their involvement within the handling of products out of the stores and/or theirhome delivery. Then it shows that several strategies coexist today in retail, with on one hand firmsthat force customers to play one role and on the other hand firms that let them free on this plan.Finally, the article highlights five success factors of such strategies.; L’article traite des rôles que les firmes peuvent faire jouer à leurs clients dans la logistique de dis-tribution de leurs produits. Il montre tout d’abord que quatre stratégies d’utilisation du client sontpossibles, selon que la firme implique les clients dans la sortie des produits des magasins et/ou leurtransport à domicile. L’article souligne ensuite que deux stratégies coexistent, avec d’un côté desfirmes qui contraignent les clients à tenir un seul rôle et de l’autre celles qui les laissent libre sur ceplan. Enfin, cinq facteurs permettant de faire un succès des stratégies axées sur le rôle logistique desclients sont mis en exergue.

International audience; We give a more building-oriented and somewhat simpler proof of the `saturation' theorem of Kapovich and Millson for any complex semisimple group. The main difference with their approach lies in the combinatorial part of the proof. We state a theorem of folding/unfolding triangles in the affine building, only in combinatorial terms. For the analytical part, we gather materials that appear in distinct papers of Kapovich, Leeb and Millson to complete the proof

International audience; Multichannel Marketing: How to get the commitment of store employeesThis paper studies employees’ commitment to multichannel distribution defined as the employees’ acceptance ofthe multichannel customer and of multichannel marketing actions. The first study reveals the existence of “coo-petition” between store and e-commerce staff. The coexistence of competition and coordination leads the authorsto define the concept of a “coopetitive” market. The second study develops a cluster analysis of employees basedon their perception of this strategic orientation and examines differences in commitment between the groups.Perceptions of the coopetitive market orientation, of the degree of centralisation and of the independence ofwage systems are explored. The contributions are related, firstly, to the typological perspective, secondly, to theidentification of similarities and differences between sales personnel in contact with the customer. The effects ofother factors are also studied and implications are discussed in order to improve commitment to a multichannelsales policy.; Cet article analyse l’adhésion du personnel des magasins au multicanal définie comme l’acceptation du clientmulticanal et des actions marketing multicanal. Une première recherche montre une « coopétition interne » entremagasins et e-commerce qui conduit à la notion d’orientation marché coopétitive. Une seconde recherche réaliseune typologie du personnel d’une enseigne de distribution spécialisée fondée sur leurs perceptions de cette orien-tation et compare les niveaux d’adhésion des groupes au multicanal. Les perceptions de l’orientation marché coo-pétitive, du degré de centralisation, de l’indépendance des systèmes de rémunération sont examinées. Les apportsse situent dans la perspective typologique et le repérage des similarités et des différences au sein du personnelde l’enseigne en contact avec les clients. Les influences d’autres facteurs sont aussi étudiées et des implicationsmanagériales et des voies de recherche sont proposées pour améliorer l’adhésion au multicanal.

Let p be an odd prime number and K be a p-adic field. In this paper, we develop an analogue of Fontaine's theory of (phi,Gamma)-modules replacing the p-cyclotomic extension by the extension K_infty obtained by adding to K a compatible system of p^n-th roots of a fixed uniformizer pi of K. As a result, we obtain a new classification of p-adic representations of G_K = Gal(Kbar/K) by some (phi, \tau)-modules. We then make a link between the theory of (phi,tau)-modules discussed above and the so-called theory of (phi,N_nabla)$-modules developped by Kisin. As a corollary, we answer a question of Tong Liu: we prove that, if K is a finite extension of Q_p, every representation of G_K of E(u)-finite height is potentially semi-stable., Comment: 51 pages serious problem in Section 3 fixed; 2010-65

International audience; The development of e-commerce raises some challenges in the case of franchise networks, above all when franchise contracts contain territorial exclusivity clauses, which are jeopardized by the possibility to sell online. The European Commission generally allows transactional websites to be created upon the initiative of the franchisor or one of its franchisees. This policy raises legal and marketing challenges that are explored in this paper through a bi-disciplinary approach. It focuses on the practices of franchisors (first part) and franchisees (second part) regarding e-commerce as well as on the mechanisms used to pre-empt potential conflicts arising from territorial exclusivity clauses contained in franchise contracts.; Le développement du e-commerce soulève des difficultés dans les réseaux de franchise, surtout lorsque le contrat de franchise contient une clause d'exclusivité territoriale. Ces stipulations contractuelles sont mises à mal par la possibilité de vendre en ligne. La Commission européenne autorise par principe la création d'un site Internet marchand à l'initiative du franchiseur ou de l'un des franchisés du réseau. Ce choix soulève des enjeux juridiques et marketing que se propose d'explorer cet article dans une approche bi-disciplinaire. Il s'intéressera aux pratiques des franchiseurs (première partie) et des franchisés (seconde partie) en termes de e-commerce ainsi qu'aux moyens d'anticiper les conflits potentiels liés à la présence de clauses d'exclusivité territoriale dans les contrats de franchise.

International audience; This paper has several aims: firstly to identify the representative actions of resistance toward advertising and their underlying motivations; secondly to check if this resistance results in particular behaviors. In order to reach these objectives, cluster and factorial analyses were conducted. They highlight the diversity of resistant profiles according to their resistant level and their motives: the most resistant consumers prefer ads which detail products characteristics; non-resistants prefer less realistic ads. By linking these profiles to the buying criteria and the information’s sources used by resistant consumers managerial implications are proposed to face their behaviours. For example, the choice of communication modes perceived as less discordant could be a solution.; Cet article a plusieurs objectifs : identifier des actions représentatives de la résistance à la publicité et leurs motivations sous-jacentes ; vérifier si cette résistance se traduit par des comportements particuliers. Pour atteindre ces objectifs, des analyses typologiques et factorielles ont été menées. Elles mettent en évidence la diversité des profils de résistants selon leur degré de résistance et leurs motivations : les consommateurs les plus résistants préfèrent les publicités valorisant les caractéristiques des produits, au contraire des non-résistants, qui préfèrent les publicités moins réalistes. En reliant ces profils aux critères d’achat et aux sources d’informations utilisées par les consommateurs résistants, des implications managériales sont suggérées pour s’adapter à ces comportements. Par exemple, le choix de modes de communication perçus comme moins dissonants pourrait être un axe possible.

International audience; The aim of this paper is to propose a typology of consumerswith regard to fair trade. A survey (n = 825) was performedon the basis of the theory of planned behavior increasedby scepticism. The sample is close to the structure of theFrench population in terms of age and gender. The resultsshow that the scepticism variable takes a significant partof the theoretical model. Largely based on this model, 5classes of consumers are identified, 3 with high scepticism.Each class of consumer is detailed based on model and so-cio-demographics variables. Managerial actions are pro-posed to stakeholders.; Nous dressons une typologie des consommateurs face auxproduits du commerce équitable. Pour cela une enquête (n= 825) a été réalisée sur la base de la théorie du comporte-ment planifié, augmentée du scepticisme. L’échantillon estproche de la structure de la population française en termesd’âge et de genre. Les résultats montrent que le scepticismeprend une part significative dans le modèle théorique. En sebasant principalement sur ce modèle, 5 classes de consom-mateurs sont identifiées dont 3 qui se caractérisent par unscepticisme élevé. Chaque classe est détaillée en fonctiondes variables du modèle et des données sociodémogra-phiques. Des pistes d’actions pour les acteurs du secteursont proposées.

Within the current context of the Grenelle Environment Round Table, French government advocates source reduction strategies for over-packaging. But, companies wonder about their impact on consumers. Thanks to video recorded observations and interviews with consumers, this paper aims at examining their practices of purchase, storage and destruction of overpackaging and their beliefs towards them. The findings reveal that over-packaging, which can be unnoticed, is questioned by some consumers. The results allow us to evaluate overpackaging’s perceived usefulness according to six criteria for four profiles of consumers and to propose managerial recommendations in terms of over-packaging removal by adapting products, communication as well as distribution., Dans le cadre du Grenelle de l’Environnement, le gouvernement français prône une suppression des suremballages par les entreprises, qui s’interrogent sur son impact sur les consommateurs. A l’aide d’observations filmées et d’entretiens de consommateurs, cet article examine les pratiques d’achat, de manipulation et de destruction des suremballages ainsi que les croyances à leur égard. Ces enseignements révèlent que la présence de suremballages, qui peut passer inaperçue, est discutée par les consommateurs. Les résultats permettent d’évaluer l’utilité perçue des suremballages en fonction de six critères pour quatre profils de consommateurs puis de fournir des recommandations aux managers envisageant leur retrait, en termes d’adaptation des produits, de la communication et des modes de distribution.

International audience; The management of store design is still a topic of greatconcern for retail chains. Research on the impact of thephysical environment has mainly dealt with the impact ofstore atmospherics and its components. This paper aimsat enlarging the scope of store design research by takinginto account the ergonomics of the store and its impact onshoppers. We show that the impact of store ergonomics isas important as the impact of store atmospherics. Thus, thepaper contributes to the understanding of the role of storeenvironment in shopper behavior.; La gestion du design des espaces de vente reste un sujetde préoccupation majeur pour les enseignes de distribution.Toutefois, les travaux sur l’impact de l’environnement aupoint de vente se sont limités à l’atmosphère et ses compo-santes. Cet article se propose d’élargir cette perspective àla dimension ergonomique du design et à son impact sur lesconsommateurs. Nous montrons que l’effet de l’ergonomieest d’une importance comparable à celle de l’atmosphère,enrichissant de fait le rôle de l’aménagement de l’espacede vente dans le comportement d’achat du consommateur.

Soit E une courbe elliptique définie sur un corps de nombres K. On dit qu'un nombre premier p est réductible pour le couple (E, K) si E admet une p-isogénie définie sur K. L'ensemble de tous ces nombres premiers est fini si et seulement si E n'a pas de multiplication complexe définie sur K. Dans cet article, on montre que l'ensemble des nombres premiers réductibles pour le couple (E, K) est contenu dans l'ensemble des diviseurs premiers d'une liste explicite d'entiers (dépendant de E et de K) dont une infinité d'entre eux est non nulle. Cela fournit un algorithme efficace de calcul dans le cas fini. D'autres critères moins généraux, mais néanmoins utiles sont donnés ainsi que de nombreux exemples numériques. Let E be an elliptic curve defined over a number field K. We say that a prime number p is reducible for (E, K) if E admits a p-isogeny defined over K. The so-called reducible set of all such prime numbers is finite if and only if E does not have complex multiplication over K. In this paper, we prove that the reducible set is included in the set of prime divisors of an explicit list of integers (depending on E and K), infinitely many of them being non-zero. It provides an efficient algorithm for computing it in the finite case. Other less general but rather useful criteria are given, as well as many numerical examples.

In this paper, we focus on a q-analogue of the Riemann zeta function at positive integers, which can be written for s\in\N^* by \zeta_q(s)=\sum_{k\geq 1}q^k\sum_{d|k}d^{s-1}. We give a new lower bound for the dimension of the vector space over \Q spanned, for 1/q\in\Z\setminus\{-1;1\} and an even integer A, by 1,\zeta_q(3),\zeta_q(5),...,\zeta_q(A-1). This improves a recent result of Krattenthaler, Rivoal and Zudilin (\emph{S\'eries hyperg\'eom\'etriques basiques, q-analogues des valeurs de la fonction zeta et s\'eries d'Eisenstein}, J. Inst. Jussieu {\bf 5}.1 (2006), 53-79). In particular, a consequence of our result is that for 1/q\in\Z\setminus\{-1;1\}, at least one of the numbers \zeta_q(3),\zeta_q(5),\zeta_q(7),\zeta_q(9) is irrational., Comment: 33 pages

A proof of the transcendence of a real number ! based on the Thue‐Siegel‐Roth‐Schmidt method involves generally a sequence (" n)n! 1 of algebraic numbers of bounded degree or a sequence (xn)n! 1 of integer r-tuples. In the present paper, we show how such a proof can produce a transcendence measure for ! , if one is able to quantify the growth of the heights of the algebraic numbers " n or of the points xn. Our method rests on the quantitative Schmidt subspace theorem. We further give several applications, including to certain normal numbers and to the extremal numbers introduced by Roy.

In this paper, we propose a trajectory tracking control of timed event graphs on a sliding horizon. The approach uses a specific algebraic model whose form is Ax · b. Concepts of componentwise order, lattice and monotone inequality prove the existence of a unique minimum or maximum trajectory and allow its calculation.

Let S be a finite set of primes, p in S, and Q_S a maximal algebraic extension of Q unramified outside S and infinity. Assume that |S|>=2. We show that the natural maps Gal(Q_p^bar/Q_p) --> Gal(Q_S/Q) are injective. Much of the paper is devoted to the problem of constructing selfdual automorphic cuspidal representations of GL(2n,A_Q) with prescribed properties at all places, that we study via the twisted trace formula of J. Arthur. The techniques we develop shed also some lights on the orthogonal/symplectic alternative for selfdual representations of GL(2n)., 50 pages, french. Section 4.18 has been extended : let F be a totally real field and \pi a selfdual cuspidal automorphic representation of GL(2n,A_F) which is cohomological at all the archimedean places and discrete at a finite place at least, we show that for each place v the L-parameter of \pi_v preserves a non-degenerate symplectic pairing

Let $n$ be an integer $\geqslant 2$. A group $G$ is called generalized $n$-abelian if it admits a {\em positive polynomial} endomorphism of degree $n$, that is if there exist $n$ elements $a_1, a_2, \dots, a_n$ of $G$ such that the function $\varphi: x\mapsto x^{a_1}x^{a_2}\cdots x^{a_n}$ is an endomorphism of $G$. In this paper we give some sufficient conditions for a generalized $n$-abelian group to be abelian. In particular, we show that every group admitting a positive polynomial monomorphism of degree 3 is abelian.

We present a generalization of minimal separation in an undirected graph, and show how the maximal rectangles of the adjacency matrix describe such separators, and form an ortholattice, which we call the Separability Lattice. Furthermore, for any given ortholattice L, we show that there does not exist a unique minimal graph of which L is the Separability Lattice. We establish a necessary and sufficient condition for the existence of such a graph. The end of the paper deals with algorithmic considerations on the class of orthocom-plemented lattices. Nous présentons une généralisation de la notion de séparateur minimal dans un graphe non orienté, et nous montrons que ces séparateurs sont représentés par les rectangles maximaux de la matrice d'adjacence, structurés en un orthotreillis, que nous appelons treillis de séparabilité. Réciproquement, tant donné un orthotreillis, nous montrons qu'il n'existe pas en général un unique graphe minimal dont il serait treillis de séparabilité. Nous donnons une condition nécessaire et suffisante pour que cette dernière propriété soit vérifiée. Le dernier paragraphe de l'article contient des considérations algorithmiques relatives aux treillis orthocomplémentés.

Multiway dissimilarities naturally generalize the usual two-way dissimilarities. In this paper, particular classes of multiway dissimilarities are studied as well as some models for deriving from a dissimilarity of a given number of ways, one of a greater or a lower number of ways. An application to clustering systems specification has led to a one-to-one correspondence between a class of multiway dissimilarities and a family of stratified clustering systems. Les dissimilarités multivoies sont une généralisation naturelle des dissimilarités usuelles deux voies. Dans ce papier, des classes de dissimilarités multivoies sont étudiées, ainsi que des modèles de passage d'un nombre de voies donné à un autre nombre de voies. Une application à la spécification de systèmes classifiants a conduit à une bijection entre une classe de dissimilarités multivoies et une famille de systèmes stratifiés de classification.

Admettant l'hypoth\`ese de Schinzel et la finitude des groupes de Tate-Shafarevich des courbes elliptiques sur les corps de nombres, toute intersection lisse de deux quadriques dans l'espace projectif de dimension n satisfait au principe de Hasse si n>4. Le m\^eme r\'esultat vaut pour n=4, c'est-\`a-dire pour les surfaces de del Pezzo de degr\'e 4, lorsque le groupe de Brauer est r\'eduit aux constantes et que la surface est suffisamment g\'en\'erale. ----- Assuming Schinzel's hypothesis and the finiteness of Tate-Shafarevich groups of elliptic curves over number fields, smooth intersections of two quadrics in n-dimensional projective space satisfy the Hasse principle if n>4. The same result holds for n=4, i.e., for del Pezzo surfaces of degree 4, provided the Brauer group is reduced to constants and the surface is sufficiently general., Comment: 6 pages, in French, with abridged English version; old paper (2005), posted for archival purposes

21 pages; Let $\wh K$ be the field of formal Laurent series in $X^{-1}$ over the finite field $k$, and let $A$ be the ring of polynomials in $X$ over $k$. One of the main results of the paper is to give a particularly nice coding of the geodesic flow on the quotient of the Bruhat-Tits tree $\TT$ of ${\rm PGL}_2(\wh K)$ by ${\rm PGL}_2(A)$, by using the continued fraction expansion of the endpoints of the geodesic lines in $\TT$ (the space of ends of $\TT$ identifies with $\PP_1(\wh K)$). This allows in particular to prove in a dynamical way the invariance of the Haar measure by the Artin map.

In this paper, we study the cohomological dimen- sion of groups GS := Gal(KS/K), where KS is the maximal pro-p-extension of a number field K, unramified outside a finite set S of places of K. This dimension is well-understood only when S contains all places above p; in the case where only some of the places above p are contained in S, one can still obtain some results if KS/K contains at least one Zp-extension K1/K. Indeed, in that case, the study of the Zp((Gal(K1/K)))-module Gal(KS/K1) ab allows one to give sucient

Netnography is a qualitative research method which uses Internet as a source of data in leaning against the virtual communities of consumption. It analyses consumers’ communicational acts from the community in order to generate insights about consumption object which is the center of the community. In this article, netnography is positioned and defined; its data collection and analysis methods are then presented. The aim of this paper is to draw the attention of the marketers to the potential of this approach, on the one hand, by giving it a rigorous theoretical framework, and on the other hand, by proposing some helps for its implementation., La netnographie est une méthode d’enquête qualitative qui utilise Internet comme source de données en s’appuyant sur les communautés virtuelles de consommation. Elle analyse les actes communicationnels des membres d’une communauté virtuelle de consommation dans le but de produire une connaissance nouvelle relative à l’objet de consommation autour duquel gravite la communauté. Après avoir positionné et défini la netnographie, l’article en présente les techniques de collecte et d’analyse des données. L’objectif est d’attirer l’attention des marketers sur le potentiel de cette approche, d’une part, en lui donnant un cadre théorique rigoureux, et d’autre part, en fournissant des pistes utiles à sa mise en œuvre.

International audience; An integer n is called friable when its prime number factorization consists exclusively of (relatively) small factors. Let P(n) be the largest prime factor occurring in this factorization, and let S(x,y) denote the set {n? x,P(n)? y}. This work investigates the asymptotic behaviour of the summatory function Psi_f(x, y):=\sum_{n\in S(x,y)}f(n) when f is a multiplicative arithmetical function satisfying some simple and general conditions concerning its mean behaviour on primes and on powers of primes. One such condition is |\sum_{p? z}f(p)\log p-\kappa z|? Cz/R(z) (z>1), where C is a constant and \kappa>0; requirements on R are technical conditions too long to state here, but satisfied by any "reasonable" positive increasing function. By setting R(z)=(\log z)^\delta in the very general Théorème 2.1, the authors obtain a more general as well as more precise estimate on \Psi_f(x, y) (Corollaire 2.2) than that recently obtained by J. M. Song [Acta Arith. 102 (2002), no. 2, 105--129; MR1889623 (2003a:11123)]. Their next result (Corollaire 2.3) offers a general estimate in the case where f(p) is on average very close to a constant, and contains without loss of precision estimates of the literature for particular functions f, such as the so-called Piltz functions \tau_k, or the function µ^2 where µ is the Möbius function. Then, as a further application of their first result, they establish an Erdös-Wintner theorem on friable integers (Théorème 2.4). They finally mention an application to the case where f(n) is the characteristic function of the integers that can be represented as a sum of two squares of integers (Théorème 2.5); their estimate is uniformly valid for x ? 3, exp((\log x)^{2/5+\epsilon})? y? x. The paper begins with an historical introduction, and is followed by an extensive bibliography on the subject.

Article dans revue scientifique avec comité de lecture.; Nous présentons dans ce travail une méthode, issue de travaux de Bilu et de Bilu et Hanrot, qui permet, sous certaines conditions, de borner de façon bien plus précise que par la méthode de Baker les solutions d'équations diophantiennes superelliptiques. Cette méthode s'applique en particulier à l'équation de Catalan $|x^p -y^q| = 1$, où $q > p$ sont deux premiers, et nous permet de prouver que cette dernière n'a pas de solution non triviale quand $q$ ne divise pas $h^-(\Q(\zeta_p))$. || In this paper we present a method coming from work by Bilu and Bilu and Hanrot which, under certain assumptions, allows one to obtain bounds for the solutions of superelliptic equations that are much sharper than usual bound derived through the use of

The aim of this paper is to build a categories typology from a square contingency table containing variables using the same nomenclature. Our assumption is that it exists categories groups according to attractions between categories and sequence of attractions among them. We use a modelling based on graphs and a decomposition method of connected (strong) component. L'objectif est de mettre en évidence, à partir d'un tableau de contingence croisant 2 variables utilisant la même nomenclature, une typologie des catégories de cette nomenclature. La recherche de cette typologie est basée sur l'hypothèse selon laquelle il existe des groupes de catégories en fonction des attractions entretenues entre elles ainsi que de leurs enchaînements. On s'appuie sur une modélisation sous forme de graphes et sur une méthode de décomposition des composantes (fortement) connexes.

International audience; A numeral system is a sequence of an infinite different closed normal $\lambda$-terms which has closed $\lambda$-terms for successor and zero test. A numeral system is said adequate iff it has a closed $\lambda$-term for predecessor. A storage operator for a numeral system is a closed $\lambda$-term which simulate ``call-by-value'' in the context of a ``call-by-name'' strategy. E. Tronci conjectured the following result : a numeral system is adequate if it has a storage operator. This paper gives a negative answer to this conjecture for the numeral systems typable in the J.-Y. Girard type system F. The E. Tronci's conjecture remains open in pure $\lambda$-calculus.

Nous r esolvons dans cet article la question de la d ecidabilit e de la th eorie monadique du second ordre du monode inversif libre. Nous d enissons a cette n la notion de th eorie monadique du second ordre d'un monode donn e et la contrepartie combinatoire de cette notion, les ensembles reconnaissables de mots g en eralis es sur un monode donn e. Nous rappelons alors la d enition du monode inversif libre ainsi que la caract erisation de ce monode due a Scheiblich. En utilisant cette caract erisation et les syst emes de pavages de Wang, nous montrons que la th eorie monadique du second ordre du monode inversif libre sur un singleton est ind ecidable, ce qui entra^ ne la propri et e pour le monode inversif libre sur un ensemble de plus d'un el ement. Abstract We solve in this paper the question of the decidability of the monadic second order theory of the free inverse monoid. To this aim, we dene the notion of monadic second order theory of a given monoid, and the combinat- oric counterpart of this notion, the recognizable sets of generalized words on a given monoid. Then we recall the denition of the free inverse monoid and the characterization of this monoid that has been given by Scheiblich. Using this characterisation and the Wang tiling systems, we show that the second order theory of the free inverse monoid on a singleton is undecidable, which entails the property for the free inverse monoid on a set which may contain more than one element.

In this paper we consider the problem of separating by a polynomial function two open disjoint semi-algebraic subsets A and B of a real affine variety M under the assumption that the subsets are already polynomially separated up to a proper algebraic subset. First of all some elementary results in small dimensions are given. When M is non-singular, a hypothesis on the behaviour of the boundaries of A and B is sufficient to obtain the separation. The problem is also analysed if M is singular, and some positive results are obtained in the compact case.

This paper deals with predictable representation and time changed processes. Let $(M^i)_{i\geq 0}$ be a sequence of independent local martingales. Suppose that each $M^i$ has the property of predictable representation with respect to its natural filtration. Suppose also that $(A^i)_{i\geq 1}$ is a sequence of continuous, increasing, $(\mathscr{F}^{M^0}_t)$ adapted processes. We study sufficient conditions in order that $M = M^0 + \sum M^i_{A^i}$ be a local martingale and $M$ have the property of predictable representation with respect to the filtration $(\mathscr{F}^{M^0}_t) \vee (\mathscr{F}^{M^1_{A^1}}_t \vee (\mathscr{F}^{M^2_{A^2}}_t \vee \cdots$. Such problems arise in the modeling of a security market with continuous trading [1].