From Hermite to Humbert polynomials

We use the multivariable Hermite polynomials to derive integral representations of Chebyshev and Gegenbauer polynomials. It is shown that most of the properties of these classes of polynomials can be deduced in a fairly straightforward way from this representation, which proves a unifying framework for a large body of polynomial families, including forms of the Humbert and Bessel type, which are a natural consequence of the point of view developed in this paper

Some new classes of degenerated generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials

The aim of this paper is to study new classes of degenerated generalized Apostol-Bernoulli, Apostol-Euler and Apostol-Genocchi polynomials of order $\alpha$ and level $m$ in the variable $x$. Here the degenerate polynomials are a natural extension of the classic polynomials. In more detail, we derive their explicit expressions, recurrence relations and some identities involving those polynomials and numbers. Most of the results are proved by using generating function methods

Simple Semi-Analytical Expression of the Lightning Base Current in the FrequencyDomain

A simple procedure to express the lightning base current in the frequency domain is presented. The formula, based on a piecewise approximation of the lightning base current in time domain, allows obtaining an expression in the frequency domain in terms of elementary functions. The presented procedure is fast and general, since it can be used with any current waveshape

A Real-time Energy-Saving Mechanism in Internet of Vehicles Systems

Emerging technologies, such as self-driving cars and 5G communications, are raising new mobility and transportation possibilities in smart and sustainable cities, bringing to a new echo-system often referred to as Internet of Vehicles (IoV). In order to efficiently operate, an IoV system should take into account more stringent requirements with respect to traditional IoT systems, e.g., ultra-broadband connections, high-speed mobility, high-energy efficiency and requires efficient real-time algorithms. This paper proposes an energy and communication driven model for IoV scenarios, where roadside units (RSUs) need to be frequently assigned and re-assigned to the operating vehicles. The problem has been formulated as an Uncapacitated Facility Location Problem (UFLP) for jointly solving the RSU-to-vehicle allocation problem while managing the RSUs switch-on and -off processes. Differently from traditional UFLP approaches, based on static solutions, we propose here a fast-heuristic approach, based on a dynamic multi-period time scale mapping: the proposed algorithm is able to efficiently manage in real-time the RSUs, selecting at each period those to be activated and those to be switched off. The resulting methodology is tested against a set of benchmark instances, which allows us to illustrate its potential. Results, in terms of overall cost –mapping both energy consumption and transmission delays–, number of active RSUs, and convergence speed, are compared with static approaches, showing the effectiveness of the proposed dynamic solution. It is noticeable a gain of up to 11% in terms of overall cost with respect to the static approaches, with a moderate additional delay for finding the solution, around 0.8 s, while the overall number of RSUs to be switched on is sensibly reduced up to a fraction of 15% of the overall number of deployed RSUs, in the most convenient scenario

A Real-Time Energy-Saving Mechanism in Internet of Vehicles Systems

[EN] Emerging technologies, such as self-driving cars and 5G communications, are raising new mobility and transportation possibilities in smart and sustainable cities, bringing to a new echo-system often referred to as Internet of Vehicles (IoV). In order to efficiently operate, an IoV system should take into account more stringent requirements with respect to traditional IoT systems, e.g., ultra-broadband connections, high-speed mobility, high-energy efficiency and requires efficient real-time algorithms. This paper proposes an energy and communication driven model for IoV scenarios, where roadside units (RSUs) need to be frequently assigned and re-assigned to the operating vehicles. The problem has been formulated as an Uncapacitated Facility Location Problem (UFLP) for jointly solving the RSU-to-vehicle allocation problem while managing the RSUs switch-on and -off processes. Differently from traditional UFLP approaches, based on static solutions, we propose here a fast-heuristic approach, based on a dynamic multi-period time scale mapping: the proposed algorithm is able to efficiently manage in real-time the RSUs, selecting at each period those to be activated and those to be switched off. The resulting methodology is tested against a set of benchmark instances, which allows us to illustrate its potential. Results, in terms of overall cost-mapping both energy consumption and transmission delays-, number of active RSUs, and convergence speed, are compared with static approaches, showing the effectiveness of the proposed dynamic solution. It is noticeable a gain of up to 11% in terms of overall cost with respect to the static approaches, with a moderate additional delay for finding the solution, around 0.8 s, while the overall number of RSUs to be switched on is sensibly reduced up to a fraction of 15% of the overall number of deployed RSUs, in the most convenient scenario.The work of Luca Cesarano and Andrea Croce has been done during an abroad study period at Universitat Oberta de Catalunya, Spain, supported by Erasmus+ Study Programme of the European Union.Cesarano, L.; Croce, A.; Martins, LDC.; Tarchi, D.; Juan-Pérez, ÁA. (2021). A Real-Time Energy-Saving Mechanism in Internet of Vehicles Systems. IEEE Access. 9:157842-157858. https://doi.org/10.1109/ACCESS.2021.3130125157842157858

An efficient hybrid technique for the solution of fractional-order partial differential equations

In this paper, a hybrid technique called the homotopy analysis Sumudu transform method has been implemented solve fractional-order partial differential equations. This technique is the amalgamation of Sumudu transform method and the homotopy analysis method. Three examples are considered to validate and demonstrate the efficacy and accuracy of the present technique. It is also demonstrated that the results obtained from the suggested technique are in excellent agreement with the exact solution which shows that the proposed method is efficient, reliable and easy to implement for various related problems of science and engineering

Approximate symmetries and conservation laws for mechanical systems described by mixed derivative perturbed PDEs

This article focuses on developing and applying approximation techniques to derive conservation laws for the Timoshenko–Prescott mixed derivatives perturbed partial differential equations (PDEs). Central to our approach is employing approximate Noether-type symmetry operators linked to a conventional Lagrangian one. Within this framework, this paper highlights the creation of approximately conserved vectors for PDEs with mixed derivatives. A crucial observation is that the integration of these vectors resulted in the emergence of additional terms. These terms hinder the establishment of the conservation law, indicating a potential flaw in the initial approach. In response to this challenge, we embarked on the rectification process. By integrating these additional terms into our model, we could modify the conserved vectors, deriving new modified conserved vectors. Remarkably, these modified vectors successfully satisfy the conservation law. Our findings not only shed light on the intricate dynamics of fourth-order mechanical systems but also pave the way for refined analytical approaches to address similar challenges in PDE-driven systems