Search results for "MATHEMATICS"
showing 10 items of 22031 documents
Highly occupied gauge theories in 2 + 1 dimensions : a self-similar attractor
2019
Motivated by the boost-invariant Glasma state in the initial stages in heavy-ion collisions, we perform classical-statistical simulations of SU(2) gauge theory in 2+1 dimensional space-time both with and without a scalar field in the adjoint representation. We show that irrespective of the details of the initial condition, the far-from-equilibrium evolution of these highly occupied systems approaches a unique universal attractor at high momenta that is the same for the gauge and scalar sectors. We extract the scaling exponents and the form of the distribution function close to this non-thermal fixed point. We find that the dynamics are governed by an energy cascade to higher momenta with sc…
Jeu de Taquin and Diamond Cone for so(2n+1, C)
2020
International audience; The diamond cone is a combinatorial description for a basis of a natural indecomposable n-module, where n is the nilpotent factor of a complex semisimple Lie algebra g. After N. J. Wildberger who introduced this notion, this description was achieved for g = sl(n) , the rank 2 semisimple Lie algebras and g = sp (2n).In this work, we generalize these constructions to the Lie algebra g = so(2n + 1). The orthogonal semistandard Young tableaux were defined by M. Kashiwara and T. Nakashima, they index a basis for the shape algebra of so(2n + 1). Defining the notion of orthogonal quasistandard Young tableaux, we prove that these tableaux describe a basis for a quotient of t…
Weighted Hardy Spaces of Quasiconformal Mappings
2019
We establish a weighted version of the $H^p$-theory of quasiconformal mappings.
Radial symmetry of p-harmonic minimizers
2017
"It is still not known if the radial cavitating minimizers obtained by Ball [J.M. Ball, Discontinuous equilibrium solutions and cavitation in nonlinear elasticity, Phil. Trans. R. Soc. Lond. A 306 (1982) 557--611] (and subsequently by many others) are global minimizers of any physically reasonable nonlinearly elastic energy". The quotation is from [J. Sivaloganathan and S. J. Spector, Necessary conditions for a minimum at a radial cavitating singularity in nonlinear elasticity, Ann. Inst. H. Poincare Anal. Non Lineaire 25 (2008), no. 1, 201--213] and seems to be still accurate. The model case of the $p$-harmonic energy is considered here. We prove that the planar radial minimizers are indee…
Applications of Microlocal Analysis in Inverse Problems
2020
This note reviews certain classical applications of microlocal analysis in inverse problems. The text is based on lecture notes for a postgraduate level minicourse on applications of microlocal analysis in inverse problems, given in Helsinki and Shanghai in June 2019.
Generalized wave propagation problems and discrete exterior calculus
2018
We introduce a general class of second-order boundary value problems unifying application areas such as acoustics, electromagnetism, elastodynamics, quantum mechanics, and so on, into a single framework. This also enables us to solve wave propagation problems very efficiently with a single software system. The solution method precisely follows the conservation laws in finite-dimensional systems, whereas the constitutive relations are imposed approximately. We employ discrete exterior calculus for the spatial discretization, use natural crystal structures for three-dimensional meshing, and derive a “discrete Hodge” adapted to harmonic wave. The numerical experiments indicate that the cumulat…
Mi descrivi il tuo disegno del Mattoncino Lego? Un’esperienza didattica di matematica nella scuola dell’infanzia
2018
La consapevolezza dell’importanza di guardare, attraverso una lente di tipo matematico, i disegni prodotti dai bambini, considerandoli come strumento diagnostico per quello che D’Amore et al. (2004) chiamano come il “Campo di Esperienza” Spazio, Ordine e Misura, ha dato spunto a questo contributo che discute una sperimentazione didattica condotta in una sezione di scuola dell’infanzia (5 anni). All’interno della stessa è stato chiesto ai bambini di rappresentare dei mattoncini Lego con un disegno, e di descrivere successivamente i propri elaborati rintracciando e argomentando in essi eventuali segni di scarto numerico-spaziali rispetto al mattoncino osservato/manipolato, attraverso visioni …
First observation and study of the K± → π±π0e+e− decay
2018
The NA48/2 experiment at CERN reports the first observation of the K-+/- -> pi(+/-)pi(0)e(+)e(-) decay from an exposure of 1.7 x 10(11) charged kaon decays recorded in 2003-2004. A sample of 4919 candidates with 4.9% background contamination allows the determination of the branching ratio in the full kinematic region, BR(K-+/- -> pi(+/-)pi(0)e(+)e(-)) = (4.24 +/- 0.14) x 10(-6). The study of the kinematic space shows evidence for a structure dependent contribution in agreement with predictions based on chiral perturbation theory. Several P- and CP-violating asymmetries are also evaluated.
Topological canal foliations
2019
Regular canal surfaces of $\mathbb{R}^3$ or $\mathbb{S}^3$ admit foliations by circles: the characteristic circles of the envelope. In order to build a foliation of $\mathbb{S}^3$ with leaves being canal surfaces, one has to relax the condition “canal” a little (“weak canal condition”) in order to accept isolated umbilics. Here, we define a topological condition which generalizes this “weak canal” condition imposed on leaves, and classify the foliations of compact orientable 3-manifolds we can obtain this way.
Il ruolo della comprensione del testo nel processo di matematizzazione e modellizzazione
2017
In questo articolo vengono analizzate le risposte fornite a un interessante item relativo alla Prova standardizzata di matematica somministrata nel maggio 2015 a tutti gli allievi di quinta elementare del Canton Ticino. A partire dai risultati statistici emersi da un campione di 508 protocolli selezionati, viene presentata un’analisi qualitativa effettuata su un campione più ristretto di 174 studenti di prima media, allo scopo di rintracciare le cause delle difficoltà emerse nella risoluzione. Da questa analisi si rileva come le risposte sbagliate di diversi studenti siano legate a difficoltà nella comprensione del testo dell’item, in particolare a difficoltà di interpretazione linguistica.…