Search results for "102"
showing 10 items of 2892 documents
Sharp estimates and saturation phenomena for a nonlocal eigenvalue problem
2011
Abstract We determine the shape which minimizes, among domains with given measure, the first eigenvalue of a nonlocal operator consisting of a perturbation of the standard Dirichlet Laplacian by an integral of the unknown function. We show that this problem displays a saturation behaviour in that the corresponding value of the minimal eigenvalue increases with the weight affecting the average up to a (finite) critical value of this weight, and then remains constant. This critical point corresponds to a transition between optimal shapes, from one ball as in the Faber–Krahn inequality to two equal balls.
Tracing 2000 Years at the Source of the Douix, Côte-d’Or, France: Water, Offerings, and Recurrence
2019
The Source of the Douix in Châtillon-sur-Seine, France, has been visited by local inhabitants for over 2000 years and served as a watery focal point for the ritual deposition of various types of offerings. While water deposits are by no means uncommon across Europe, the continued use of a single space over multiple millennia is. An examination of the preserved offerings at the Douix indicate there are three phases of depositional activity: late Hallstatt to early La Tène periods, late La Tène to Gallo-Roman periods, and the early modern period. Despite being separated by hundreds of years there are similarities across depositional phases including the importance of modified metallic objects…
Module categories of finite Hopf algebroids, and self-duality
2017
International audience; We characterize the module categories of suitably finite Hopf algebroids (more precisely, $X_R$-bialgebras in the sense of Takeuchi (1977) that are Hopf and finite in the sense of a work by the author (2000)) as those $k$-linear abelian monoidal categories that are module categories of some algebra, and admit dual objects for "sufficiently many" of their objects. Then we proceed to show that in many situations the Hopf algebroid can be chosen to be self-dual, in a sense to be made precise. This generalizes a result of Pfeiffer for pivotal fusion categories and the weak Hopf algebras associated to them.
Self-efficacy and approaches to learning mathematics among engineering students : empirical evidence for potential causal relations
2020
Theories of self-efficacy and approaches to learning are well-established in the psychology of learning. However, studies on relationships between the primary constructs on which these theories are...
Sesquilinear forms associated to sequences on Hilbert spaces
2019
The possibility of defining sesquilinear forms starting from one or two sequences of elements of a Hilbert space is investigated. One can associate operators to these forms and in particular look for conditions to apply representation theorems of sesquilinear forms, such as Kato's theorems. The associated operators correspond to classical frame operators or weakly-defined multipliers in the bounded context. In general some properties of them, such as the invertibility and the resolvent set, are related to properties of the sesquilinear forms. As an upshot of this approach new features of sequences (or pairs of sequences) which are semi-frames (or reproducing pairs) are obtained.
Elliptic 1-Laplacian equations with dynamical boundary conditions
2018
Abstract This paper is concerned with an evolution problem having an elliptic equation involving the 1-Laplacian operator and a dynamical boundary condition. We apply nonlinear semigroup theory to obtain existence and uniqueness results as well as a comparison principle. Our main theorem shows that the solution we found is actually a strong solution. We also compare solutions with different data.
Sensory preconditioning in newborn rabbits: from common to distinct odor memories.
2013
Brief Communication; International audience; This study evaluated whether olfactory preconditioning is functional in newborn rabbits and based on joined or independent memory of odorants. First, after exposure to odorants A+B, the conditioning of A led to high responsiveness to odorant B. Second, responsiveness to B persisted after amnesia of A. Third, preconditioning was also functional with two overlapping pairs of odorants (A+B and B+C) and amnesia of one odorant did not affect memory of the others. Thus, incidental pairing of odorants allows reinforcement of one odorant to implicitly reinforce the others, the bond then vanishes, and the memory of each element becomes independent.
L∞ estimates in optimal mass transportation
2016
We show that in any complete metric space the probability measures μ with compact and connected support are the ones having the property that the optimal transportation distance to any other probability measure ν living on the support of μ is bounded below by a positive function of the L∞ transportation distance between μ and ν. The function giving the lower bound depends only on the lower bound of the μ-measures of balls centered at the support of μ and on the cost function used in the optimal transport. We obtain an essentially sharp form of this function. In the case of strictly convex cost functions we show that a similar estimate holds on the level of optimal transport plans if and onl…
Banach spaces of general Dirichlet series
2018
Abstract We study when the spaces of general Dirichlet series bounded on a half plane are Banach spaces, and show that some of those classes are isometrically isomorphic between themselves. In a precise way, let { λ n } be a strictly increasing sequence of positive real numbers such that lim n → ∞ λ n = ∞ . We denote by H ∞ ( λ n ) the complex normed space of all Dirichlet series D ( s ) = ∑ n b n λ n − s , which are convergent and bounded on the half plane [ Re s > 0 ] , endowed with the norm ‖ D ‖ ∞ = sup Re s > 0 | D ( s ) | . If (⁎) there exists q > 0 such that inf n ( λ n + 1 q − λ n q ) > 0 , then H ∞ ( λ n ) is a Banach space. Further, if there exists a strictly increasing sequ…
Godbillon–Vey sequence and Françoise algorithm
2019
Abstract We consider foliations given by deformations d F + ϵ ω of exact forms dF in C 2 in a neighborhood of a family of cycles γ ( t ) ⊂ F − 1 ( t ) . In 1996 Francoise gave an algorithm for calculating the first nonzero term of the displacement function Δ along γ of such deformations. This algorithm recalls the well-known Godbillon–Vey sequences discovered in 1971 for investigation of integrability of a form ω. In this paper, we establish the correspondence between the two approaches and translate some results by Casale relating types of integrability for finite Godbillon–Vey sequences to the Francoise algorithm settings.