Search results for " Euclidean"
showing 8 items of 8 documents
Characterisation of upper gradients on the weighted Euclidean space and applications
2020
In the context of Euclidean spaces equipped with an arbitrary Radon measure, we prove the equivalence among several different notions of Sobolev space present in the literature and we characterise the minimal weak upper gradient of all Lipschitz functions.
Hadronic light-by-light contribution to $(g-2)_\mu$ from lattice QCD with SU(3) flavor symmetry
2020
We perform a lattice QCD calculation of the hadronic light-by-light contribution to $(g-2)_\mu$ at the SU(3) flavor-symmetric point $m_\pi=m_K\simeq 420\,$MeV. The representation used is based on coordinate-space perturbation theory, with all QED elements of the relevant Feynman diagrams implemented in continuum, infinite Euclidean space. As a consequence, the effect of using finite lattices to evaluate the QCD four-point function of the electromagnetic current is exponentially suppressed. Thanks to the SU(3)-flavor symmetry, only two topologies of diagrams contribute, the fully connected and the leading disconnected. We show the equivalence in the continuum limit of two methods of computin…
Genesi geometrica delle volte centriche
1996
Un'analisi completa degli organismi voltati comporta lo studio delle molteplici componenti necessarie alla loro definizione: configurazione geometrica, sistema costruttivo, area storico-geografica di appartenenza, interpretazioni Stilistiche. L’obiettivo di questo studio è indirizzato all' analisi delle volte continue su pianta centrica definibili attraverso le leggi della geometria euclidea. L’indagine si pone all'interno dei confini relativi alla loro configurazione geometrica e il criterio adottato, svincolato da classificazioni di carattere tipologico o stilistico, propone l'identificazione di famiglie geometriche in base alla figura del poligono di base dell'impianto. Si può identifica…
Wilson Loop Form Factors: A New Duality
2017
We find a new duality for form factors of lightlike Wilson loops in planar $\mathcal N=4$ super-Yang-Mills theory. The duality maps a form factor involving an $n$-sided lightlike polygonal super-Wilson loop together with $m$ external on-shell states, to the same type of object but with the edges of the Wilson loop and the external states swapping roles. This relation can essentially be seen graphically in Lorentz harmonic chiral (LHC) superspace where it is equivalent to planar graph duality. However there are some crucial subtleties with the cancellation of spurious poles due to the gauge fixing. They are resolved by finding the correct formulation of the Wilson loop and by careful analyti…
Hadronic light-by-light scattering contribution to the muon $g-2$ from lattice QCD: semi-analytical calculation of the QED kernel
2023
Hadronic light-by-light scattering is one of the virtual processes that causes the gyromagnetic factor $g$ of the muon to deviate from the value of two predicted by Dirac's theory. This process makes one of the largest contributions to the uncertainty of the Standard Model prediction for the muon $(g-2)$. Lattice QCD allows for a first-principles approach to computing this non-perturbative effect. In order to avoid power-law finite-size artifacts generated by virtual photons in lattice simulations, we follow a coordinate-space approach involving a weighted integral over the vertices of the QCD four-point function of the electromagnetic current carried by the quarks. Here we present in detai…
On the Choice of the Most Suitable Period to Map Hill Lakes via Spectral Separability and Object-Based Image Analyses
2023
Technological advances in Earth observation made images characterized by high spatial and temporal resolutions available, nevertheless bringing with them the radiometric heterogeneity of small geographical entities, often also changing in time. Among small geographical entities, hill lakes exhibit a widespread distribution, and their census is sometimes partial or shows unreliable data. High resolution and heterogeneity have boosted the development of geographic object-based image analysis algorithms. This research analyzes which is the most suitable period for acquiring satellite images to identify and delimitate hill lakes. This is achieved by analyzing the spectral separability of the su…
Projector operators in clustering
2016
In a recent paper the notion of {\em quantum perceptron} has been introduced in connection with projection operators. Here we extend this idea, using these kind of operators to produce a {\em clustering machine}, i.e. a framework which generates different clusters from a set of input data. Also, we consider what happens when the orthonormal bases first used in the definition of the projectors are replaced by frames, and how these can be useful when trying to connect some noised signal to a given cluster.
I poligoni stellati: origini storiche ed implicazioni didattiche
2019
The genesis of mathematical concepts in the evolutionary line of human thought in the long story and the genesis in individual optics possess evident analogies. Starting from this assumption, we describe an activity presented to 15-year-old students; the aim was to consolidate fundamental concepts of Euclidean geometry related to regular polygons. The experimentation has used a didactic approach based on the historical evolution of the formal definition of regular star polygon through the centuries. The activity and the results obtained in terms of internalization of the concepts in the students are showed.