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pro vyhledávání: '"Borghi, Riccardo"'
Autor:
Borghi, Riccardo
The practical usefulness of Levin-type nonlinear sequence transformations as numerical tools for the summation of divergent series or for the convergence acceleration of slowly converging series, is nowadays beyond dispute. Weniger's transformation,
Externí odkaz:
http://arxiv.org/abs/2407.03344
Autor:
Borghi, Riccardo
The description of light diffraction using catastrophe optics is one of the most intriguing theoretical invention in the field of classical optics of the last four decades. Its practical implementation has faced some resistance over the years, mainly
Externí odkaz:
http://arxiv.org/abs/2404.11153
Autor:
Borghi, Riccardo
Publikováno v:
Mathematics, Vol. 12(1), pp. 154 (2024)
Since its introduction in 1650, Kepler's equation has never ceased to fascinate mathematicians, scientists, and engineers. Over the course of five centuries, a large number of different solution strategies have been devised and implemented. Among the
Externí odkaz:
http://arxiv.org/abs/2312.01437
Autor:
Borghi, Riccardo
Publikováno v:
Optics Letters Vol. 49 (3), pp. 730-733 (2024)
A semi-analytical computational algorithm to model the wavefield generated by paraxial diffraction of a class of Laguerre-Gauss beams by sharp-edge elliptic apertures is here developed. Thanks to such a powerful computational tool, some basic aspects
Externí odkaz:
http://arxiv.org/abs/2310.18298
Autor:
Borghi, Riccardo
Publikováno v:
Journal of the Optical Society of America A, 2023
A purely analytical extension of the flattened Gaussian beams [Opt. Commun. \textbf{107,} 335 (1994)] to any values of the beam order, is here proposed. Due to it, the paraxial propagation problem of axially symmetric, coherent flat-top beams through
Externí odkaz:
http://arxiv.org/abs/2301.04481
Autor:
Borghi, Riccardo
A general reformulation of classical sharp-edge diffraction theory is proposed within paraxial approximation. The, not so much known, Poincar\'e vector potential construction is employed directly inside Fresnel's 2D integral in order for it to be con
Externí odkaz:
http://arxiv.org/abs/2204.05685
Autor:
Borghi, Riccardo
Since more than three centuries Kepler's equation continues to represents an important benchmark for testing new computational techniques. In the present paper, the classical Kapteyn series solution of Kepler's equation originally conceived by Lagran
Externí odkaz:
http://arxiv.org/abs/2112.15154
Autor:
Borghi, Riccardo1 (AUTHOR) riccardo.borghi@uniroma3.it
Publikováno v:
Mathematics (2227-7390). Jan2024, Vol. 12 Issue 1, p154. 11p.
Autor:
Borghi, Riccardo
A pedagogical derivation of the Huygens cycloidal pendulum, suitable for high-school students, is here presented. Our derivation rests only on simple algebraic and geometrical tricks, without the need of any Calculus concept.
Externí odkaz:
http://arxiv.org/abs/2004.06401
Autor:
Borghi, Riccardo
An elementary derivation of the Newton "inverse square law" from the three Kepler laws is proposed. Our proof, thought essentially for first-year undergraduates, basically rests on Euclidean geometry. It could then be offered even to high-school stud
Externí odkaz:
http://arxiv.org/abs/2003.13405