Search results for " Mathematica"
showing 10 items of 689 documents
Bed scouring downstream of hydraulic structures under steady flow conditions: Experimental analysis of space and time scales and implications for mat…
2011
Abstract Sediment transport and bed deformation in alluvial rivers are space and time dependent. The knowledge of the space and time scales can be helpful for the definition of predictive procedures of an alluvial reach response to changing boundary conditions. In this work, attention is paid to scouring process occurring downstream of the rigid basement of a hydraulic structure. The analysis is focused on transient bed profiles which are determined, under steady flow conditions, by a decrease of the upstream sediment transport rate. In particular, the paper is aimed at improving understanding of the space and time scales required by the alluvial system to reach the equilibrium conditions. …
Importance des récentes variations pluviométriques à Djibouti et besoins de quantification de leurs impacts
2014
Ces dernières décennies, l’Afrique de l’Est souffre d’une longue et lente détérioration pluviométrique. De 2007 à 2011, la ville de Djibouti a enregistré un déficit de 73% des précipitations moyennes annuelles par rapport à la moyenne de 30 ans (1981-2010). Pour caractériser la sécheresse actuelle, nous analysons une série pluviométrique reconstruite pour Djibouti-Ville de 1901 à 2013, les données de terrain permettant d’illustrer les impacts de ces variations pluviométriques. Les précipitations enregistrées à Djibouti ne présentent aucune tendance sur le long terme (1901-2013). Par contre, ces dernières années montrent une très grande variabilité: le suivi de la moyenne pluviométrique sur …
New techniques for classification of multigerms
2018
Abstract The goal of these notes is to give an overview of the state of the art in classification of multigerms. We have tried to make them self-contained but certainly not extensive. The results included here scope most of the research on classification of multigerms carried out in the last 15 years with special emphasis on recent results by the authors of these notes and their collaborators.
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.
An Extension of Weyl’s Equidistribution Theorem to Generalized Polynomials and Applications
2020
Author's accepted manuscript. This is a pre-copyedited, author-produced version of an article accepted for publication in International Mathematics Research Notices following peer review. The version of record Bergelson, V., Knutson, I. J. H. & Son, Y. (2020). An Extension of Weyl’s Equidistribution Theorem to Generalized Polynomials and Applications. International Mathematics Research Notices, 2021(19), 14965-15018 is available online at: https://academic.oup.com/imrn/article/2021/19/14965/5775499 and https://doi.org/10.1093/imrn/rnaa035. Generalized polynomials are mappings obtained from the conventional polynomials by the use of the operations of addition and multiplication and taking th…
Space of signatures as inverse limits of Carnot groups
2021
We formalize the notion of limit of an inverse system of metric spaces with 1-Lipschitz projections having unbounded fibers. The construction is applied to the sequence of free Carnot groups of fixed rank n and increasing step. In this case, the limit space is in correspondence with the space of signatures of rectifiable paths in ℝn, as introduced by Chen. Hambly-Lyons’s result on the uniqueness of signature implies that this space is a geodesic metric tree. As a particular consequence we deduce that every path in ℝn can be approximated by projections of some geodesics in some Carnot group of rank n, giving an evidence that the complexity of sub-Riemannian geodesics increases with the step.
Degrees of characters in the principal block
2021
Abstract Let G be a finite group. We prove that if the set of degrees of characters in the principal p-block of G has size at most 2 then G is p-solvable, and G / O p ′ ( G ) has a metabelian normal Sylow p-subgroup. The general question of proving that if an arbitrary p-block has two degrees then their defect groups are metabelian remains open.
Algebrability of the set of hypercyclic vectors for backward shift operators
2020
Abstract We study the existence of algebras of hypercyclic vectors for weighted backward shifts on Frechet sequence spaces that are algebras when endowed with coordinatewise multiplication or with the Cauchy product. As a particular case, we obtain that the sets of hypercyclic vectors for Rolewicz's and MacLane's operators are algebrable.
MATHEMATICS AS A QUASI-EMPIRICAL SCIENCE
2006
The present paper aims at showing that there are times when set theoretical knowledge increases in a non-cumulative way. In other words, what we call ‘set theory’ is not one theory which grows by simple addition of a theorem after the other, but a finite sequence of theories T1, ..., T n in which Ti+1, for 1 ≤ i < n, supersedes T i . This thesis has a great philosophical significance because it implies that there is a sense in which mathematical theories, like the theories belonging to the empirical sciences, are fallible and that, consequently, mathematical knowledge has a quasi-empirical nature. The way I have chosen to provide evidence in favour of the correctness of the main thesis of t…
Global sensitivity analysis for micropollutant modeling by means of an urban integrated approach
2015
The paper presents the sensitivity analysis of an integrated urban water quality system by means of the global sensitivity analysis (GSA). Specifically, an home-made integrated model developed in previous studies has been modified in order to include the micropollutant assessment (namely, sulfamethoxazole - SMX). The model is able to estimate also the interactions between the three components of the system: sewer system (SS), wastewater treatment plant (WWTP) and the receiving water body (RWB). The analysis has been applied to an experimental catchment nearby Palermo (Italy): the Nocella catchment. Five scenarios each characterized by different combinations of sub-systems (i.e., SS, WWTP an…