A5014238743- Mathematical functions and polynomials
- Advanced Mathematical Identities
- Fractional Differential Equations Solutions
- Iterative Methods for Nonlinear Equations
- Advanced Mathematical Theories and Applications
- History and Theory of Mathematics
- Algebraic and Geometric Analysis
- Particle Accelerators and Free-Electron Lasers
- Polynomial and algebraic computation
- Matrix Theory and Algorithms
- Mathematical and Theoretical Analysis
- Quantum Mechanics and Non-Hermitian Physics
- Particle accelerators and beam dynamics
- Advanced X-ray Imaging Techniques
- Mathematics and Applications
- Advanced Combinatorial Mathematics
- Nonlinear Waves and Solitons
- Numerical methods in inverse problems
- Control Systems and Identification
- Advanced Numerical Analysis Techniques
- Analytic Number Theory Research
- Statistical Mechanics and Entropy
- Numerical methods for differential equations
- Random Matrices and Applications
- COVID-19 epidemiological studies
University of Palermo
2015-2025
Italian University Line
2024
ENEA Frascati Research Centre
2013-2023
National Agency for New Technologies, Energy and Sustainable Economic Development
2013-2023
Istituto Nazionale di Fisica Nucleare, Laboratori Nazionali di Frascati
2020-2022
University of Catania
2013-2017
On the wake of results obtained so far at SPARC_LAB test-facility Laboratori Nazionali di Frascati (Italy), we are currently investigating possibility to design and build a new multi-disciplinary user-facility, equipped with soft X-ray Free Electron Laser (FEL) driven by ∼1 GeV high brightness linac based on plasma accelerator modules. This study is performed in synergy EuPRAXIA study. In this paper report about recent progresses going facility.
The monomiality principle is based on an abstract definition of the concept derivative and multiplicative operators. This allows to treat different families special polynomials as ordinary monomials. procedure underlines a generalization Heisenberg–Weyl group, along with relevant technicalities symmetry properties. In this article, we go deeply into formulation meaning employ it study properties set polynomials, which, asymptotically, reduce two-variable Kampè dè Fèrièt family. We derive...
This study focuses on Vehicle-Integrated Photovoltaic (VIPV) strategy adopted as an energy supply vector in disaster scenarios. As a matter of fact, may be very critical issue context, when grid networks damaged. Emergency vehicles, including ambulances and trucks, well mobile units such containers operating rooms, can equipped with photovoltaic modules serve emergency sources, supporting both vehicle operations relief efforts. A methodology was developed to estimate production under...
The fourth generation of synchrotron radiation sources, commonly referred to as the Free Electron Laser (FEL), provides an intense source brilliant X-ray beams enabling investigation matter at atomic scale with unprecedented time resolution. These sources require use conventional linear accelerators providing high electron beam performance. achievement chirped pulse amplification allowing lasers be operated Terawatt range, opened way for Plasma Acceleration (LPA) technique where energy...
This thesis is intended to provide an account of the theory and applications Operational Methods that allow "translation" special functions polynomials into a "different" mathematical language. The language we are referring symbolic methods, largely based on formalism umbral type which provides tremendous simplification derivation associated properties. strategy will follow establishing rules replace higher trascendental in terms elementary take advantage from such recasting.
In this paper, we introduce higher-order harmonic numbers and derive their relevant properties generating functions by using an umbral-type method. We discuss the link with recent works on subject, show that combinations of umbral other techniques (such as Laplace types integral transforms) yield a very efficient tool to explore these numbers.
Differintegral methods, namely those techniques using differential and integral operators on the same footing, currently exploited in calculus, provide a fairly unexhausted source of tools to be applied wide class problems involving theory special functions not only. The use transforms Borel type associated formalism will shown an effective means, allowing link between umbral operational methods. We merge these two points view get new efficient method obtain integrals summation generating as well.
The FEL integral equation is reviewed here and studied under different contexts, accounting for diverse physical regimes. We include higher order harmonics saturation effects, explain the origin of scaling relations, widely exploited to describe either dynamics or nonnlinear harmonic generation.
The development of innovative materials, based on the modern technologies and processes, is key factor to improve energetic sustainability reduce environmental impact electrical equipment. In particular, modeling magnetic hysteresis crucial for design construction electronic devices. recent years, additive manufacturing techniques are playing a decisive role in project production elements circuits applications various engineering fields. To this aim, use deep learning paradigm, integrated...
Special polynomials, ascribed to the family of Gegenbauer, Legendre, and Jacobi their associated forms, can be expressed in an operational way, which allows a high degree flexibility for formulation relevant theory.We develop point view based on umbral type formalism, exploited past, study some aspects theory special functions, general, particular those Bessel functions.We propose fairly general analysis, allowing transparent link between different forms polynomials .
A common environment in which to place Bessel and circular functions is envisaged. We show, by the use of operational methods, that Gaussian provides umbral image these functions. emphasize role spherical a family associated auxiliary polynomials, as transition elements between families The consequences this point view relevant impact on study properties special carefully discussed.
Dual numbers and their higher-order version are important tools for numerical computations, in particular finite difference calculus. Based on the relevant algebraic rules matrix realizations of dual numbers, we present a novel point view, embedding within formalism reminiscent operational umbral
We employ methods largely exploited in Physics, the analysis of evolution dynamical systems, to study pattern Covid-19 infection Italy. The techniques we are based on use logistic function and its derivative, namely Hubbert function. latter is give a prediction number infected per day. also mention possibility taking advantage from other mathematical tools e.g. Gompertz equation make some comparison different predictive capabilities.
Inspired by ideas from umbral calculus and based on the two types of integrals occurring in defining equations for gamma reciprocal functions, respectively, we develop a multi-variate version so-called image technique. Besides providing class new formulae generalized hypergeometric functions an implementation series manipulations computing lacunary generating our main application these techniques is study Sobolev-Jacobi polynomials. Motivated applications to theoretical chemistry, moreover...
The theory of harmonic-based functions is discussed here within the framework umbral operational methods. We derive a number results based on elementary notions relying properties Gaussian integrals.
The high gain free electron laser (FEL) equation is a Volterra type integro-differential amenable for analytical solutions in limited number of cases. In this note, novel technique, based on an expansion employing family two variable Hermite polynomials, shown to provide straightforward cases hardly solvable with conventional means. possibility extending the method by use using different polynomials (two Legendre like) also discussed.
In a previous note we made an analysis of the spreading COVID disease in Italy. We used model based on logistic and Hubbert functions, exploited has shown limited usefulness terms predictions failed fixing fundamental indications like point inflection growth. this elaborate model, using multi-logistic models attempt more realistic analysis.