Search results for " MATHEMATICAL"
showing 10 items of 686 documents
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…
Greenhouse gas emissions from integrated urban drainage systems: where do we stand?
2017
Integrated urban drainage systems (IUDS) (i.e., sewer systems, wastewater treatment plants and receiving water bodies) contribute to climate change being sources of greenhouse gas emissions (GHG). This paper, produced by the International Working Group on Data and Models, which works under the IWA/IAHR Joint Committee on Urban Drainage, reviews the state-of-the-art and the recently developed modelling tools used to understand and manage GHG emissions from IUDS. Further, open problems and research gaps are discussed, while proposing a framework for handling GHG from IUDS. The literature review reveals that there is a need to strengthen and partially adequate already available mathematical mo…
THE IDENTIFIABILITY ANALYSIS FOR SETTING UP MEASURING CAMPAIGNS FOR INTEGRATED WATER QUALITY MODELLING
2010
Identifiability analysis enables one the quantification of the number of model parameters that can be assessed by calibration with respect to a data set. Such a methodology is based on the appraisal of sensitivity coefficients of the model parameters by means of Monte Carlo runs. By employing the Fisher Information Matrix, the methodology is able to gain insights with respect to the number of model parameters that can be reliably assessed. The paper presents a study where identifiability analysis is used as a tool for the setting up of measuring campaigns for integrated water quality modelling. The analysis has been applied to a real case study characterized by a partially urbanized catchme…
Urban Energy Hubs Economic Optimization and Environmental Comparison in Italy and Vietnam
2018
This paper aims to perform the minimization of the yearly energy supply cost from the main electricity and natural gas grids related to an energy district, considering the installation of different equipments. The case study refers to energy consumption of a medium density urban district and involves the exploitation of different energy sources and devices (photovoltaic systems, electrical energy storage, heat pumps and cogenerators). The analysis of the district energy supply is accomplished through an energy hub model. After a cost analysis related to the considered energy systems, a MILP algorithm was used for the optimization of a cost function and the simulation of various scenarios. M…