Publications and preprints

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The page is organized into two sections, reflecting the “dual nature” of my academic education:

• the first section is about my work in the area of pure mathematics;
• the second section is about results at the frontier between applied mathematics and computational electromagnetics.

Note. Some journals are now making their archives accessible for free. Yet, many links on this page lead to articles behind a paywall. In all cases, I can provide a copy of my publications on request (just send me an e-mail at the address salvo.tringali (at) gmail.com).

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Work in pure mathematics

• Publications and preprints (in reverse chronological order)

• An Abstract Factorization Theorem and Some Applications
  submitted (arXiv:2102.01598)
• On the density of sumsets (with Paolo Leonetti)
  submitted (arXiv:2001.10413)
• On half-factoriality of transfer Krull monoids (with Weidong Gao, Chao Liu, and Qinghai Zhong)
  Communications in Algebra, Vol. 49 (2021), No. 1, pp. 409-420 (DOI – arXiv:1911.04267)
• A generalization to number fields of Euler's theorem on the series of reciprocals of primes
  submitted (arXiv:1911.03732)
• Strongly primary monoids, with a focus on Puiseux monoids (with Alfred Geroldinger and Felix Gotti)
  Journal of Algebra, Vol. 567 (2021), pp. 310-345 (DOI – arXiv:1910.10270)
• On Small Sets of Integers (with Paolo Leonetti)
  to appear in The Ramanujan Journal (2021) (DOI – PDF – arXiv:1905.08075)
• Structural properties of subadditive sequences with applications to factorization theory and additive combinatorics
  submitted (PDF)
• On the Arithmetic of Power Monoids and Sumsets in Cyclic Groups (with Austin A. Antoniou)
  to appear in Pacific Journal of Mathematics (arXiv:1804.10913)
• Structural properties of subadditive families with applications to factorization theory
  Israel Journal of Mathematics, Vol. 234 (2019), No. 1, 1-35 (DOI – arXiv:1706.03525)
• Commutativity of integral quasi-arithmetic means on measure spaces (with Dorota Głazowska, Paolo Leonetti, and Janusz Matkowski)
  Acta Mathematica Hungarica, Vol. 153 (2017), No. 2, 350-355 (DOI – arXiv:1703.03938)
• Power monoids: A bridge between Factorization Theory and Arithmetic Combinatorics (with Yushuang Fan)
  Journal of Algebra, Vol. 512 (Oct 2018), 252-294 (DOI – arXiv:1701.09152)
• Arithmetic of commutative semigroups with a focus on semigroups of ideals and modules (with Yushuang Fan, Alfred Geroldinger, and Florian Kainrath)
  Journal of Algebra and Its Applications, Vol. 16 (2017), No. 11, 42 pp. (DOI – arXiv:1612.03116)
• Multivariate Delta Goncarov and Abel Polynomials (with Rudolph Lorentz and Catherine H. Yan)
  Journal of Mathematical Analysis and Applications, Vol. 446 (Feb 2017), No. 1, pp. 663-680 (DOI – arXiv:1608.05836)
• On the number of distinct prime factors of a sum of super-powers (with Paolo Leonetti)
  Journal of Number Theory, Vol. 186 (2018), pp. 226-237 (DOI – arXiv:1511.08784)
• Generalized Goncarov polynomials (with Rudolph Lorentz and Catherine H. Yan), pp. 56-85 in
  S. Butler, J. Cooper, and G. Hurlbert (eds.), Connections in Discrete Mathematics: A Celebration of the Work of Ron Graham
  Cambridge University Press, 2018 (arXiv:1511.04039)
• Upper and lower densities have the strong Darboux property (with Paolo Leonetti)
  Journal of Number Theory, Vol. 174 (2017), pp. 445-455 (DOI – arXiv:1510.07473)
• On the notions of upper and lower density (with Paolo Leonetti)
  Proceedings of the Edinburgh Mathematical Society, Vol. 63 (Feb 2020), No. 1, pp. 139-167 (DOI – arXiv:1506.04664)
• On the commutation of generalized means on probability spaces (with Paolo Leonetti and Janusz Matkowski)
  Indagationes Mathematicae, Vol. 27 (2016), No. 4, pp. 945-953 (DOI – arXiv:1503.01139)
• The Davenport constant of a box (with Alain Plagne)
  Acta Arithmetica, Vol. 171 (2015), No. 3, pp. 197-219 (DOI – arXiv:1405.4363)
• Sums of dilates in ordered groups (with Alain Plagne)
  Communications in Algebra, Vol. 44 (2016), No. 12, pp. 5223-5236 (DOI – arXiv:1403.0934)
• Cauchy-Davenport type theorems for semigroups
  Mathematika, Vol. 62 (2016), No. 1, pp. 1-12 (DOI – arXiv:1307.8396)
• On the divisibility of $a^n \pm b^n$ by powers of $n$
  Integers, Vol. 13 (Nov. 2013), pp. 993-998 (PDF – arXiv:1301.0131)
• On a system of equations with primes (with Paolo Leonetti)
  Journal de Théorie des Nombres de Bordeaux, Vol. 26 (2014), No. 2, pp. 399-413 (DOI – PDF – arXiv:1212.0802)
• A Cauchy-Davenport theorem for semigroups
  Uniform Distribution Theory, Vol. 9 (2014), No. 1, pp. 27-42 (PDF – arXiv:1210.4203)
• Small doubling in ordered semigroups
  Semigroup Forum, Vol. 90 (2015), No. 1, pp. 135-148 (DOI – PDF – arXiv:1208.3233)

PhD thesis (Université de Lyon, campus ``Jean Monnet'', France)
Speciality: mathematics - Subspecialities: additive combinatorics and number theory

Title:	Some Questions in Combinatorial and Elementary Number Theory
	(PDF copy of the thesis, in English for the most part; slides of the presentation, in French)
Date of defense:	26 November 2013

Thesis directors:	François Hennecart (Université de Lyon, campus ``Jean Monnet'')
	Alain Plagne (École polytechnique, Centre de mathématiques Laurent Schwartz)

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Work at the frontier between computational electromagnetics and applied mathematics

• Publications in peer-reviewed journals

• Modeling Realistic Contrast Maps from MRI Images for Microwave Breast Cancer Detection (with Giovanni Angiulli and Tommaso Isernia), IEEE AP Magazine, Vol. 53, No. 1 (2011), pp. 113-122 (published version)
• Classing and extracting information from radar images (with Giovanni Angiulli, Vincenzo Barrile, Giuseppe Meduri and Raffaele Pucinotti), PIERS Online, Vol. 4, No. 6 (2008), pp. 621-624
• Stabilizing the $E$-Field Integral Equation at the internal resonances through the computation of its numerical null space (with Giovanni Angiulli), International Journal of Applied Electromagnetics and Mechanics, Vol. 32, No. 2 (2010), pp. 63-72
• Automatic design of circular SIW resonators by a hybrid approach based on polynomial fitting and SVRMs (with Domenico De Carlo), Journal of Electromagnetic Waves and Applications, Vol. 24, Nos 5-6 (2010), pp. 735-744
• Convergence of Krylov solvers and the choice of basis and weighting functions in the MoM solution of the Electrical Field Integral Equation (with Giovanni Angiulli), PIERS Online, Vol. 4, No. 7 (2008), pp. 771-774

• Publications in the proceedings of peer-reviewed international conferences

• Guidelines for effective microwave breast imaging: a numerical assessment against 3D anthropomorphic phantoms (with Ilaria Catapano, Lorenzo Crocco, Loreto Di Donato, Giovanni Angiulli, Tommaso Isernia and Ovidio Mario Bucci), 4th European Conference on Antennas and Propagation (EuCAP 2010), Barcelona (ES), 12-16 Apr. 2010 (PDF)
• Modelling SIW resonators using support vector regression machines (with Giovanni Angiulli, Domenico De Carlo, Giandomenico Amendola and Emilio Arnieri), 24th Progress In Electromagnetics Research Symposium (24th PIERS), pp. 406-409, Cambridge, MA (US), 2-6 July 2008
• Accurate Tools for Convergence Prediction of Series Solutions of Contrast Source Integral Equations (with Giovanni Angiulli, Michele D'Urso and Tommaso Isernia), 13th International Conference on Ground Penetrating Radar (GPR 2010), Lecce (IT), 21-25 June 2010 (published version)
• An algebraic preconditioner based on properties of the skew-Hermitian part of the linear systems arising from the discretization of the $E$-field integral equation (with Giovanni Angiulli and Paolo Quattrone), 11th International Conference on Electromagnetics in Advanced Applications (ICEAA '09), pp. 632-635, Turin (IT), 14-18 Sept. 2009
• On the preconditioning of algebraic linear systems arising from the discretization of the EFIE (with Giovanni Angiulli and Paolo Quattrone), 26th Progress in Electromagnetic Research Symposium (26th PIERS), pp. 577-579, Moscow (RU), 18-21 Aug. 2009
• On the relationship between non-uniqueness of electromagnetic scattering integral equations and Krylov subspace methods (with Giovanni Angiulli and Paolo Quattrone), 26th Progress in Electromagnetic Research Symposium (26th PIERS), pp. 599-603, Moscow (RU), 18-21 Aug. 2009
• Convergence of Krylov solvers and choice of basis and weighting set of functions in the Moment Method solution of Electrical Field Integral Equation (with Giovanni Angiulli), 24th Progress In Electromagnetics Research Symposium (24th PIERS), pp. 73-76, Cambridge, MA (US), 2-6 July 2008
• EFIE stabilization at internal resonances computing its numerical null space (with Giovanni Angiulli), 13th Biennial IEEE Conference On Electromagnetic Field Computation (CEFC 2008), Athens (GR), 11-15 Maj 2008
• Equivalent real formulations for solving complex linear systems in computational electromagnetics, (with Giovanni Angiulli and Giuseppe Di Massa), 5th European Conference on Numerical Methods in Electromagnetism (NUMELEC), Lille (FR), 29 Nov.-1 Dec. 2006

• Publications in the proceedings of peer-reviewed national (Italian) conferences

• Sviluppo ed analisi di strategie efficienti per la diagnostica a microonde del tumore al seno (with Ilaria Catapano, Lorenzo Crocco, Loreto Di Donato, Francesco Soldovieri, Ovidio Mario Bucci, Giovanni Angiulli and Tommaso Isernia), 18th Riunione Nazionale di ElettroMagnetismo (RiNEM 2010), Benevento (IT), 6-10 Sept. 2010
• Un precondizionatore per l'EFIE basato sull'impiego della sua componente antihermitiana (with Giovanni Angiulli), 17th Riunione Nazionale di ElettroMagnetismo (RiNEM 2008), Lecce (IT), 15-19 Sept. 2008
• Formulazioni reali equivalenti per la soluzione di sistemi lineari complessi in elettromagnetismo computazionale (with Giovanni Angiulli and Giuseppe Di Massa), 16th Riunione Nazionale di ElettroMagnetismo (RiNEM 2006), Genoa (IT), 18-21 Sept. 2006

• PhD thesis (Università di Reggio Calabria, Italy)
  Speciality: electronics engineering - Subspeciality: computational electromagnetics

Title:	Stable solutions of the electric-field integral equation by a method of regularization and preconditioning based on Krylov subspaces (in Italian)
Date of defense:	19 February 2009
Thesis director:	Giovanni Angiulli (Università di Reggio Calabria)

• Laurea thesis (Università di Reggio Calabria, Italy)
  Speciality: electronics engineering - Subspeciality: computational electromagnetics

Title:	Diagonalization of non-self-adjoint operators resulting from the study of the scattering of electromagnetic fields by ideal cylindrical conductors (in Italian)
Date of defense:	25 January 2005
Thesis directors:	Giovanni Angiulli (Università di Reggio Calabria)
	Mario Versaci (Università di Reggio Calabria)


Note. In Italy, the ``laurea'' was the main academic degree until the reforms following the Bologna process. A laurea was, actually, a long university degree (5 years for engineers), which concluded with the presentation of a thesis (usually based on experimental work) in front of a jury.

Last update: Feb 10, 2021