Federico Zullo
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View article: Nonlinear Evolution Equations of the Soliton Type: Old and New Results
Nonlinear Evolution Equations of the Soliton Type: Old and New Results Open
View article: The N-species integrable Volterra system as a maximally superintegrable Hamiltonian system
The N-species integrable Volterra system as a maximally superintegrable Hamiltonian system Open
The results presented in this paper are a natural development of those described in the paper {\it The Volterra Integrable case. Novel analytical and numerical results} (OCNMP Vol.4 (2024) pp 188-211), where the authors reconsidered the in…
View article: Unified structures for solutions of Painlevé equation II
Unified structures for solutions of Painlevé equation II Open
We present certain general structures related to the solutions of Painlevé equation II and to the solutions of the differential equation satisfied by the corresponding Hamiltonian equations, together with the tau functions. By taking advan…
View article: Lommel functions, Padé approximants and hypergeometric functions
Lommel functions, Padé approximants and hypergeometric functions Open
View article: The Volterra Integrable case. Novel analytical and numerical results
The Volterra Integrable case. Novel analytical and numerical results Open
In the present paper we reconsider the integrable case of the Hamiltonian $N$-species Volterra system, as it has been introduced by Vito Volterra in 1937 and significantly enrich the results already published in the ArXiv in 2019 by two of…
View article: Integral Representations and Zeros of the Lommel Function and the Hypergeometric $$_1F_2$$ Function
Integral Representations and Zeros of the Lommel Function and the Hypergeometric $$_1F_2$$ Function Open
View article: The Volterra Integrable case. Novel analytical and numerical results
The Volterra Integrable case. Novel analytical and numerical results Open
In the present paper we reconsider the integrable case of the Hamiltonian $N$-species Volterra system, as it has been introduced by Vito Volterra in 1937 and significantly enrich the results already published in the ArXiv in 2019 by two of…
View article: Lommel functions, Padé approximants and hypergeometric functions
Lommel functions, Padé approximants and hypergeometric functions Open
We consider the Lommel functions $s_{μ,ν}(z)$ for different values of the parameters $(μ,ν)$. We show that if $(μ,ν)$ are half integers, then it is possible to describe these functions with an explicit combination of polynomials and trigon…
View article: Modeling of heat conduction through rate equations
Modeling of heat conduction through rate equations Open
Starting from a classical thermodynamic approach, we derive rate-type equations to describe the behavior of heat flow in deformable media. Constitutive equations are defined in the material (Lagrangian) description where the standard time …
View article: Integrable maps in 4D and modified Volterra lattices
Integrable maps in 4D and modified Volterra lattices Open
In recent work, we presented the construction of a family of difference equations associated with the Stieltjes continued fraction expansion of a certain function on a hyperelliptic curve of genus $g$. As well as proving that each such dis…
View article: Modeling of heat conduction through rate equations
Modeling of heat conduction through rate equations Open
Starting from a classical thermodynamic approach, we derive rate-type equations to describe the behavior of heat flow in deformable media. Constitutive equations are defined in the material (Lagrangian) description where the standard time …
View article: Nonlinear and nonlocal models of heat conduction in continuum thermodynamics
Nonlinear and nonlocal models of heat conduction in continuum thermodynamics Open
The aim of this paper is to develop a general constitutive scheme within continuum thermodynamics to describe the behavior of heat flow in deformable media. Starting from a classical thermodynamic approach, the rate-type constitutive equat…
View article: Integral representations and zeros of the Lommel function and the hypergeometric $_1F_2$ function
Integral representations and zeros of the Lommel function and the hypergeometric $_1F_2$ function Open
We give different integral representations of the Lommel function $s_{μ,ν}(z)$ involving trigonometric and hypergeometric $_2F_1$ functions. By using classical results of Polya, we give the distribution of the zeros of $s_{μ,ν}(z)$ for cer…
View article: Integrable maps in 4D and modified Volterra lattices
Integrable maps in 4D and modified Volterra lattices Open
In recent work, we presented the construction of a family of difference equations associated with the Stieltjes continued fraction expansion of a certain function on a hyperelliptic curve of genus $g$. As well as proving that each such dis…
View article: Schwarzian derivative, Painlevé XXV–Ermakov equation, and Bäcklund transformations
Schwarzian derivative, Painlevé XXV–Ermakov equation, and Bäcklund transformations Open
The role of Schwarzian derivative in the study of nonlinear ordinary differential equations is revisited. Solutions and invariances admitted by Painlevé XXV–Ermakov equation, Ermakov equation, and third‐order linear equation in a normal fo…
View article: On the Optimal Shape and Efficiency Improvement of Fin Heat Sinks
On the Optimal Shape and Efficiency Improvement of Fin Heat Sinks Open
In this paper, we analyze the values of the entropic efficiency of longitudinal fins by investigating the coupling between the function describing the fin profile and the corresponding steady-state temperature distribution along the fin. B…
View article: Schwarzian derivative, Painlevé XXV-Ermakov equation and Bäcklund transformations
Schwarzian derivative, Painlevé XXV-Ermakov equation and Bäcklund transformations Open
The role of Schwarzian derivative in the study of nonlinear ordinary differential equations is revisited. Solutions and invariances admitted by Painlevé XXV-Ermakov equation, Ermakov equation and third order linear equation in a normal for…
View article: ON A REGULARISATION OF A NONLINEAR DIFFERENTIAL EQUATION RELATED TO THE NON-HOMOGENEOUS AIRY EQUATION
ON A REGULARISATION OF A NONLINEAR DIFFERENTIAL EQUATION RELATED TO THE NON-HOMOGENEOUS AIRY EQUATION Open
In this paper we study a nonlinear differential equation related to a non-homogeneous Airy equation. The linear equation has two families of solutions. We apply a procedure of resolution of points of indeterminacy to a system of first orde…
View article: Non-Rectification of Heat in Graded Si-Ge Alloys
Non-Rectification of Heat in Graded Si-Ge Alloys Open
View article: Entropy Rates and Efficiency of Convecting-Radiating Fins
Entropy Rates and Efficiency of Convecting-Radiating Fins Open
We present a novel indicator for the effectiveness of longitudinal, convecting-radiating fins to dissipate heat. Starting from an analysis of the properties of the entropy rate of the steady state, we show how it is possible to assess the …
View article: Notes on the zeros of the solutions of the non-homogeneous Airy's equation
Notes on the zeros of the solutions of the non-homogeneous Airy's equation Open
We present some observations on the distribution of the zeros of solutions of the nonhomogeneous Airy's equation. We show the existence of a principal family of solutions, with simple zeros, and particular solutions, characterized by a dou…
View article: Non rectification of heat in graded Si-Ge alloys
Non rectification of heat in graded Si-Ge alloys Open
We investigate the possibility to obtain a thermal diode with functionally graded Si-Ge alloys. A wire with variable section is considered. After the introduction of a formula giving the thermal conductivity of the wire as a function of th…
View article: Entropy Production and Efficiency in Longitudinal Convecting–Radiating Fins
Entropy Production and Efficiency in Longitudinal Convecting–Radiating Fins Open
The properties of the entropy production in convecting-radiating fins are analyzed. By taking advantage of the explicit expression for the distribution of heat along the fin, we investigate the possibility to assess the efficiency of these…
View article: A numerical method to estimate the peak of new infected and the SARS-CoV-2 outbreak in Italy
A numerical method to estimate the peak of new infected and the SARS-CoV-2 outbreak in Italy Open
We give some numerical observations on the total number of infected by the SARS-CoV-2 in Italy. The analysis is based on a tanh formula involving two parameters. A polynomial correlation between the parameters gives an upper bound for the …
View article: Convecting–radiating fins: Explicit solutions, efficiency and optimization
Convecting–radiating fins: Explicit solutions, efficiency and optimization Open
View article: Some numerical observations about the COVID-19 epidemic in Italy
Some numerical observations about the COVID-19 epidemic in Italy Open
We give some numerical observations on the total number of infected by the SARS-CoV-2 in Italy. The analysis is based on a tanh formula involving two parameters. A polynomial correlation between the parameters gives an upper bound for the …
View article: On the dynamics of the zeros of solutions of the Airy equation
On the dynamics of the zeros of solutions of the Airy equation Open
View article: On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation
On the quantification of non-equilibrium exergy for thermodynamic systems evolving according to Cattaneo’s equation Open
This paper is a follow-up of previous work aimed at the identification and quantification of the exergy of macroscopic non-equilibrium systems. Assuming that both energy and exergy are a priori concepts, it is possible to show that a syste…
View article: Уравнения Ермакова-Пинни и Эмдена-Фаулера: новые решения на основе преобразований Беклунда нового типа
Уравнения Ермакова-Пинни и Эмдена-Фаулера: новые решения на основе преобразований Беклунда нового типа Open
Изучается класс нелинейных обыкновенных дифференциальных уравнений вида $y"y=F(z,y^2)$, где $F$ - гладкая функция. К этому классу нелинейных обыкновенных дифференциальных уравнений относятся различные обыкновенные дифференциальные уравнени…
View article: The Gross-Pitaevskii equation: Bäcklund transformations and admitted solutions
The Gross-Pitaevskii equation: Bäcklund transformations and admitted solutions Open
Bäcklund transformations are applied to study the Gross-Pitaevskii equation. Supported by previous results, a class of Bäcklund transformations admitted by this equation are constructed. Schwartzian derivative as well as its invariance pro…