Period polynomials and Ihara brackets

Schneps [J. Lie Theory 16 (2006), 19--37] has found surprising links between Ihara brackets and even period polynomials. These results can be recovered and generalized by considering some identities relating Ihara brackets and classical Lie brackets. The period polynomials generated by this method are found to be essentially the Kohnen-Zagier polynomials.Comment: 12 pages, LaTE

Survival probability of the branching random walk killed below a linear boundary

We give an alternative proof of a result by N. Gantert, Y. Hu and Z. Shi on the asymptotic behavior of the survival probability of the branching random walk killed below a linear boundary, in the special case of deterministic binary branching and bounded random walk steps. Connections with the Brunet-Derrida theory of stochastic fronts are discussed

Convex Sobolev inequalities and spectral gap

This note is devoted to the proof of convex Sobolev (or generalized Poincar\'{e}) inequalities which interpolate between spectral gap (or Poincar\'{e}) inequalities and logarithmic Sobolev inequalities. We extend to the whole family of convex Sobolev inequalities results which have recently been obtained by Cattiaux and Carlen and Loss for logarithmic Sobolev inequalities. Under local conditions on the density of the measure with respect to a reference measure, we prove that spectral gap inequalities imply all convex Sobolev inequalities with constants which are uniformly bounded in the limit approaching the logarithmic Sobolev inequalities. We recover the case of the logarithmic Sobolev inequalities as a special case

Towards a pivotal-based approach for business process alignment.

This article focuses on business process engineering, especially on alignment between business analysis and implementation. Through a business process management approach, different transformations interfere with process models in order to make them executable. To keep the consistency of process model from business model to IT model, we propose a pivotal metamodel-centric methodology. It aims at keeping or giving all requisite structural and semantic data needed to perform such transformations without loss of information. Through this we can ensure the alignment between business and IT. This article describes the concept of pivotal metamodel and proposes a methodology using such an approach. In addition, we present an example and the resulting benefits

Must-Take Cards: Merchant Discounts and Avoided Costs

Antitrust authorities often argue that merchants cannot reasonably turn down payment cards and therefore must accept excessively high merchant discounts. The paper attempts to shed light on this “must-take cards” view from two angles. First, the paper gives some operational content to the notion of “must-take card” through the “avoided-cost test” or “tourist test”: would the merchant want to refuse a card payment when a non-repeat customer with enough cash in her pocket is about to pay at the cash register? It analyzes its relevance as an indicator of excessive interchange fees. Second, it identifies four key sources of potential social biases in the payment card systems’ determination of interchange fees: internalization by merchants of a fraction of cardholder surplus, issuers’ per-transaction markup, merchant heterogeneity, and extent of cardholder multi-homing. It compares the industry and social optima both in the short term (fixed number of issuers) and the long term (in which issuer offerings and entry respond to profitability)