Search results for: Francesco Caputo

Authors: Trilok Mathur, Shivi Agarwal

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This paper deals with the solutions of fuzzy-fractional-order Riccati equations under Caputo-type fuzzy fractional derivatives. The Caputo-type fuzzy fractional derivatives are defined based on Hukuhura difference and strongly generalized fuzzy differentiability. The Laplace-Adomian-Pade method is used for solving fractional Riccati-type initial value differential equations of fractional order. Moreover, we also displayed some examples to illustrate our methods.

Keywords: Caputo-type fuzzy fractional derivative, Fractional Riccati differential equations, Laplace-Adomian-Pade method, Mittag Leffler function

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Authors: Yacine Arioua

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In this paper, we investigate the existence and uniqueness of solutions for a coupled system of nonlinear Caputo-type Katugampola fractional differential equations with integral boundary conditions. Based upon a contraction mapping principle, Schauders fixed point theorems, some new existence and uniqueness results of solutions for the given problems are obtained. For application, some examples are given to illustrate the usefulness of our main results.

Keywords: fractional differential equations, coupled system, Caputo-Katugampola derivative, fixed point theorems, existence, uniqueness

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Authors: Hakiki Kheira, Belhamiti Omar

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In this paper, we propose a new compartmental fractional order model for the simulation of epidemic obesity dynamics. Using the Legendre wavelet method combined with the decoupling and quasi-linearization technique, we demonstrate the validity and applicability of our model. We also present some fractional differential illustrative examples to demonstrate the applicability and efficiency of the method. The fractional derivative is described in the Caputo sense.

Keywords: Caputo derivative, epidemiology, Legendre wavelet method, obesity

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Authors: Mario Calabrese, Francesca Iandolo, Pietro Vito, Raffaele D'Amore, Francesco Caputo

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This article presents a synopsis of Nature-Based Solutions (NBS), a fresh and emerging concept in mitigating and adapting to climate change. It outlines a classification of NBS, from the least intrusive to the most advanced engineering, and provides illustrations of each. Moreover, it gives an overview of the 'Life Metro Adapt' initiative, which dealt with the climatic challenges faced by the Milan Metropolitan City and encouraged the development of climate change adaptation methods using alternative, nature-focused solutions. Lastly, the article emphasizes the necessity of raising awareness about environmental issues to ensure that NBS becomes a regular practice today and can be refined in the future.

Keywords: nature-based solutions, urban resilience, climate change adaptation, life metro adapt initiative

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Authors: Jorge Olivares, Fernando Maass, Pablo Martin

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Fractional derivatives have been considered recently as a way to solve different problems in Engineering. In this way, second kind modified Bessel functions are considered here. The order α fractional differential equations of second kind Bessel functions, Kᵥ(x), are studied with simple initial conditions. The Laplace transform and Caputo definition of fractional derivatives are considered. Solutions have been found for ν=1/3, 1/2, 2/3, -1/3, -1/2 and (-2/3). In these cases, the solutions are the sum of two hypergeometric functions. The α fractional derivatives have been for α=1/3, 1/2 and 2/3, and the above values of ν. No convergence has been found for the integer values of ν Furthermore when α has been considered as a rational found m/p, no general solution has been found. Clearly, this case is more difficult to treat than those of first kind Bessel Function.

Keywords: Caputo, modified Bessel functions, hypergeometric, linear fractional differential equations, transform Laplace

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Authors: Fernando Maass, Pablo Martin, Jorge Olivares

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Fractional derivatives have become very important in several areas of Engineering, however, the solutions of simple differential equations are not known. Here we are considering the simplest first order nonhomogeneous differential equations with Bessel regular functions of the first kind, in this way the solutions have been found which are hypergeometric solutions for any fractional derivative of order α, where α is rational number α=m/p, between zero and one. The way to find this result is by using Laplace transform and the Caputo definitions of fractional derivatives. This method is for values longer than one. However for α entire number the hypergeometric functions are Kumer type, no integer values of alpha, the hypergeometric function is more complicated is type ₂F₃(a,b,c, t2/2). The argument of the hypergeometric changes sign when we go from the regular Bessel functions to the modified Bessel functions of the first kind, however it integer seems that using precise values of α and considering no integers values of α, a solution can be obtained in terms of two hypergeometric functions. Further research is required for future papers in order to obtain the general solution for any rational value of α.

Keywords: Caputo, fractional calculation, hypergeometric, linear differential equations

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Authors: Sadia Arshad

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The new coronavirus disease or COVID-19 still poses an alarming situation around the world. Modeling based on the derivative of fractional order is relatively important to capture real-world problems and to analyze the realistic situation of the proposed model. Weproposed a mathematical model for the investigation of COVID-19 dynamics in a generalized fractional framework. The new model is formulated in the Caputo sense and employs a nonlinear time-varying transmission rate. The existence and uniqueness solutions of the fractional order derivative have been studied using the fixed-point theory. The associated dynamical behaviors are discussed in terms of equilibrium, stability, and basic reproduction number. For the purpose of numerical implementation, an effcient approximation scheme is also employed to solve the fractional COVID-19 model. Numerical simulations are reported for various fractional orders, and simulation results are compared with a real case of COVID-19 pandemic. According to the comparative results with real data, we find the best value of fractional orderand justify the use of the fractional concept in the mathematical modelling, for the new fractional modelsimulates the reality more accurately than the other classical frameworks.

Keywords: fractional calculus, modeling, stability, numerical solution

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Authors: Patrizia Palumbo

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There are only two Italian films dealing with the Italian emigration to Germany: I magliari directed by Francesco Rosi and Itaker. Vietato agli italiani directed by Toni Trupia. Consequently, the analysis of these two films is essential to any study of the representation of the Italians’ experience in Germany, their hosting country. Francesco Rosi’s I magliari and Toni Trupia’s Itaker. Vietato agli italiani, released respectively in 1959 and in 2012, are both set in the second half of the twentieth century and deal with door to door Italian cloth sellers in German cities, con artists marketing rags as fine fabric to exclusively German customers. However, the perspective of the directors and screenwriters are, if not antithetical, profoundly different. Indeed, from 1959 to 2012, years in which the two films were released, Italy went from being a country of emigration to a country of both immigration (albeit now temporary) and emigration. The paper entitled ‘Representation of the Italian Emigration to Germany in the Films of Francesco Rosi and Toni Trupia’ will analyze, therefore, the two substantially different historical contingencies in which the two movies were produced and cast light on how the same historical reality, that of Italian cloth sellers in German cities, is portrayed by Rosi and Trupia’s films. In particular, it will show how in both films the female character is the site on which power (or the lack of it) is contested. More precisely, it will highlight how the German blond woman in Rosi’s film and the dark haired Albanian woman in Trupia’s film are a reflection of the changes Italy underwent in the last fifty years. Finally, this paper will comment on why Italian emigration to Germany has been overlooked by Italian scholars. Although these scholars are all familiar with many of the films directed by Francesco Rosi, one of the auteurs of Italian cinema, no real critical study of I magliari exists. Rosi’s film, it can be argued, may have aroused the uneasiness engendered by all works dealing with facts evoking shameful and humiliating times. The same is true for Trupia’s film. Even though his Itaker. Vietato agli italiani is set in the sixties, it cannot prescind from the reality of contemporary Italian emigration to Germany and Italy’s economic and political crisis. Bringing attention to Rosi and Trupia’s film seems to be a valid way to rekindle the interest in Italian emigration to Germany, a phenomenon that has contributed to the economic, social and cultural history of both Italy and Germany.

Keywords: film, Germany, history, Italian emigration

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Authors: Asma Hanif, A. I. K. Butt, Shabir Ahmad, Rahim Ud Din, Mustafa Inc

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This paper is devoted to a study of the fuzzy fractional mathematical model reviewing the transmission dynamics of the infectious disease Covid-19. The proposed dynamical model consists of susceptible, exposed, symptomatic, asymptomatic, quarantine, hospitalized and recovered compartments. In this study, we deal with the fuzzy fractional model defined in Caputo’s sense. We show the positivity of state variables that all the state variables that represent different compartments of the model are positive. Using Gronwall inequality, we show that the solution of the model is bounded. Using the notion of the next-generation matrix, we find the basic reproduction number of the model. We demonstrate the local and global stability of the equilibrium point by using the concept of Castillo-Chavez and Lyapunov theory with the Lasalle invariant principle, respectively. We present the results that reveal the existence and uniqueness of the solution of the considered model through the fixed point theorem of Schauder and Banach. Using the fuzzy hybrid Laplace method, we acquire the approximate solution of the proposed model. The results are graphically presented via MATLAB-17.

Keywords: Caputo fractional derivative, existence and uniqueness, gronwall inequality, Lyapunov theory

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Authors: Ezio Bassi, Francesco Vercesi, Francesco Benzi

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The aim of this study is to evaluate the potentiality of synchronous reluctance motors for lift systems by also evaluating the vibroacoustic behaviour of the motor. Two types of synchronous machines are designed, analysed, and compared with an equivalent induction motor, which is the more common solution in such gearbox applications. The machines' performance are further improved with optimization procedures based on multiobjective optimization genetic algorithm (MOGA). The difference between the two synchronous motors consists in the rotor geometry; a symmetric and an asymmetric rotor design were investigated. The evaluation of the vibroacoustic performance has been conducted with a multi-variable model and finite element software taking into account electromagnetic, mechanical, and thermal features of the motor, therefore carrying out a multi-physics analysis of the electrical machine.

Keywords: synchronous reluctance motor, vibro-acoustic, lift systems, genetic algorithm

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Authors: Jorge Gonzalez Camus, Carlos Lizama

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In this work is proved the existence of at least one globally attractive mild solution to the Cauchy problem, for fractional evolution equation of neutral type, involving the fractional derivate in Caputo sense. An almost sectorial operator on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Hausdorff measure of noncompactness and fixed point theorems, specifically Darbo-type. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the analytic integral resolvent operator, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, each mild solution is globally attractive, a property that is desired in asymptotic behavior for that solution.

Keywords: attractive mild solutions, integral Volterra equations, neutral type equations, non-local in time equations

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Authors: Mohammed Abdulhameed, Sagir M. Abdullahi

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In this paper, based on the applications of nanoparticle, the blood flow along with nanoparticles through stenosed artery is studied. The blood is acted by periodic body acceleration, an oscillating pressure gradient and an external magnetic field. The mathematical formulation is based on Caputo-Fabrizio fractional derivative without singular kernel. The model of ordinary blood, corresponding to time-derivatives of integer order, is obtained as a limiting case. Analytical solutions of the blood velocity and temperature distribution are obtained by means of the Hankel and Laplace transforms. Effects of the order of Caputo-Fabrizio time-fractional derivatives and three different nanoparticles i.e. Fe3O4, TiO4 and Cu are studied. The results highlights that, models with fractional derivatives bring significant differences compared to the ordinary model. It is observed that the addition of Fe3O4 nanoparticle reduced the resistance impedance of the blood flow and temperature distribution through bell shape stenosed arteries as compared to TiO4 and Cu nanoparticles. On entering in the stenosed area, blood temperature increases slightly, but, increases considerably and reaches its maximum value in the stenosis throat. The shears stress has variation from a constant in the area without stenosis and higher in the layers located far to the longitudinal axis of the artery. This fact can be an important for some clinical applications in therapeutic procedures.

Keywords: nanoparticles, blood flow, stenosed artery, mathematical models

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Authors: A. Guezane-Lakoud, S. Bensebaa

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In this paper, we study a boundary value problem of nonlinear fractional differential equation. Existence and positivity results of solutions are obtained.

Keywords: positive solution, fractional caputo derivative, Banach contraction principle, Avery and Peterson fixed point theorem

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Authors: Jorge Gonzalez-Camus

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In this work is proved the existence of at least one minimal and maximal mild solutions to the Cauchy problem, for fractional evolution equation of neutral type, involving a general kernel. An operator A generating a resolvent family and integral resolvent family on a Banach space X and a kernel belonging to a large class appears in the equation, which covers many relevant cases from physics applications, in particular, the important case of time - fractional evolution equations of neutral type. The main tool used in this work was the Kuratowski measure of noncompactness and fixed point theorems, specifically Darbo-type, and an iterative method of lower and upper solutions, based in an order in X induced by a normal cone P. Initially, the equation is a Cauchy problem, involving a fractional derivate in Caputo sense. Then, is formulated the equivalent integral version, and defining a convenient functional, using the theory of resolvent families, and verifying the hypothesis of the fixed point theorem of Darbo type, give us the existence of mild solution for the initial problem. Furthermore, the existence of minimal and maximal mild solutions was proved through in an iterative method of lower and upper solutions, using the Azcoli-Arzela Theorem, and the Gronwall’s inequality. Finally, we recovered the case derivate in Caputo sense.

Keywords: fractional evolution equations, Volterra integral equations, minimal and maximal mild solutions, neutral type equations, non-local in time equations

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Authors: Mohamed Houas, Maamar Benbachir

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In this paper, under weak assumptions, we study the existence and uniqueness of solutions for a nonlinear fractional boundary value problem. New existence and uniqueness results are established using Banach contraction principle. Other existence results are obtained using scheafer and krasnoselskii's fixed point theorem. At the end, some illustrative examples are presented.

Keywords: caputo derivative, boundary value problem, fixed point theorem, local conditions

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Authors: Tsegahun Manyazewal, Francesco Marinucci, Getachew Belay, Abraham Tesfaye, Gonfa Ayana, Amaha Kebede, Tsegahun Manyazewal, Francesco Marinucci, Getachew Belay, Abraham Tesfaye, Gonfa Ayana, Amaha Kebede, Yewondwossen Tadesse, Susan Lehman, Zelalem Temesgen

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In-service health trainings in Sub-Saharan Africa are mostly content-centered with higher disconnection with the real practice in the facility. This study intended to evaluate in-service training approach aimed to strengthen health care human resources. A combined web-based and face-to-face training was designed and piloted in Ethiopia with the diagnosis of tuberculosis. During the first part, which lasted 43 days, trainees accessed web-based material and read without leaving their work; while the second part comprised a one-day hands-on evaluation. Trainee’s competency was measured using multiple-choice questions, written-assignments, exercises and hands-on evaluation. Of 108 participants invited, 81 (75%) attended the course and 71 (88%) of them successfully completed. Of those completed, 73 (90%) scored a grade from A to C. The approach was effective to transfer knowledge and turn it into practical skills. In-service health training should transform from a passive one-time-event to a continuous behavioral change of participants and improvements on their actual work.

Keywords: Ethiopia, health care, Mycobacterium tuberculosis, training

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Authors: A. Zahra, G. de Cesare, D. Caputo, A. Nascetti

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PDMS (Polydimethylsiloxane) polymer is a suitable material for biological and MEMS (Microelectromechanical systems) designers, because of its biocompatibility, transparency and high resistance under plasma treatment. PDMS round channel is always been of great interest due to its ability to confine the liquid with membrane type micro valves. In this paper we are presenting a very simple way to form round shape microfluidic channel, which is based on reflow of positive photoresist AZ® 40 XT. With this method, it is possible to obtain channel of different height simply by varying the spin coating parameters of photoresist.

Keywords: lab-on-chip, PDMS, reflow, round microfluidic channel

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Authors: Yildiray Keskin, Omer Acan, Murat Akkus

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In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations.

Keywords: fractional diffusion equations, Caputo fractional derivative, reduced differential transform method, partial

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Authors: Pablo Martin, Jorge Olivares, Fernando Maass

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The use of fractional derivatives to different problems in Engineering and Physics has been increasing in the last decade. For this reason, we have here considered partial derivatives when the integral is a spherical Bessel function of the first kind in both regular and modified ones simple initial conditions have been also considered. In this way, the solution has been found as a combination of hypergeometric functions. The case of a general rational value for α of the fractional derivative α has been solved in a general way for alpha between zero and two. The modified spherical Bessel functions of the first kind have been also considered and how to go from the regular case to the modified one will be also shown.

Keywords: caputo fractional derivatives, hypergeometric functions, linear differential equations, spherical Bessel functions

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Authors: Francesco Marotti de Sciarra, Raffaele Barretta

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Starting from nonlocal continuum mechanics, a thermodynamically new nonlocal model of Euler-Bernoulli nanobeams is provided. The nonlocal variational formulation is consistently provided and the governing differential equation for transverse displacement are presented. Higher-order boundary conditions are then consistently derived. An example is contributed in order to show the effectiveness of the proposed model.

Keywords: Bernoulli-Euler beams, nanobeams, nonlocal elasticity, closed-form solutions

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Authors: Kamel Al-Khaled

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Reaction-diffusion equations are commonly used in population biology to model the spread of biological species. In this paper, we propose a fractional reaction-diffusion equation, where the classical second derivative diffusion term is replaced by a fractional derivative of order less than two. Based on the symbolic computation system Mathematica, Adomian decomposition method, developed for fractional differential equations, is directly extended to derive explicit and numerical solutions of space fractional reaction-diffusion equations. The fractional derivative is described in the Caputo sense. Finally, the recent appearance of fractional reaction-diffusion equations as models in some fields such as cell biology, chemistry, physics, and finance, makes it necessary to apply the results reported here to some numerical examples.

Keywords: fractional partial differential equations, reaction-diffusion equations, adomian decomposition, biological species

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Authors: Sachin Kumar

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Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy.

Keywords: fractional PDE, fuzzy valued function, diffusion equation, Legendre polynomial, spectral method

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Authors: M. Capocelli, A. Caputo, M. De Falco, D. Mazzei, V. Piemonte

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This paper presents the experimental results and the related modeling of a thermal energy storage (TES) facility, ideated and realized by ENEA and realizing the thermocline with an innovative geometry. Firstly, the thermal energy exchange model of an equivalent shell & tube heat exchanger is described and tested to reproduce the performance of the spiral exchanger installed in the TES. Through the regression of the experimental data, a first-order thermocline model was also validated to provide an analytical function of the thermocline, useful for the performance evaluation and the comparison with other systems and implementation in simulations of integrated systems (e.g. power plants). The experimental data obtained from the plant start-up and the short-cut modeling of the system can be useful for the process analysis, for the scale-up of the thermal storage system and to investigate the feasibility of its implementation in actual case-studies.

Keywords: CSP plants, thermal energy storage, thermocline, mathematical modelling, experimental data

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Authors: Francesco Pinci

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This research investigates the significance of product packaging as an effective marketing tool. By using commercially available pasta as an example, the study specifically examines the visual components of packaging, including color, shape, packaging material, and logo. The insights gained from studies like this are particularly valuable to food and beverage companies as they provide marketers with a deeper understanding of the factors influencing consumer purchasing decisions. The research analyzes data collected through surveys conducted via Google Forms and visual data obtained using iMotions eye-tracker software. The results affirm the importance of packaging design elements, such as color and product information, in shaping consumer buying behavior.

Keywords: consumer behaviour, eyetracker, food marketing, neuromarketing

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Authors: Agnese Natali, Francesco Morelli, Walter Salvatore

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Automated Rack Supported Warehouses (ARSWs) are structures currently designed as steel racks. Even if there are common characteristics, there are differences that don’t allow to adopt the same design approach. Aiming to highlight the factors influencing the design and the behavior of ARSWs, a set of 5 structures designed by 5 European companies specialized in this field is used to perform both a critical analysis of the design approaches and the assessment of the seismic performance, which is used to point out the criticalities and the necessity of new design philosophy.

Keywords: steel racks, automated rack supported warehouse, thin walled cold-formed elements, seismic assessment

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Authors: Riccardo Loggia, Francesca Pizzimenti, Francesco Lelli, Luigi Martirano

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Recent air emission regulations point toward the complete electrification of road vehicles. An increasing number of users are beginning to prefer full electric or hybrid, plug-in vehicle solutions, incentivized by government subsidies and the lower cost of electricity compared to gasoline or diesel. However, it is necessary to optimize charging stations so that they can simultaneously satisfy as many users as possible. The purpose of this paper is to present optimization algorithms that enable simultaneous charging of multiple electric vehicles while ensuring maximum performance in relation to the type of charging station.

Keywords: electric vehicles, charging stations, sharing model, fast charging, car park, power profiles

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Authors: Agnese Natali, Francesco Morelli, Walter Salvatore

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Automated Rack Supported Warehouses (ARSWs) are storage buildings whose structure is made of the same racks where goods are placed. The possibility of designing dissipative seismic-resistant ARSWs is investigated. Diagonals are the dissipative elements, arranged as tense-only X bracings. Local optimization is numerically performed to satisfy the over-resistant connection request for the dissipative element, that is hard to be reached due the geometrical limits of the thin-walled diagonals and must be balanced with resistance, the limit of slenderness, and ductility requests.

Keywords: steel racks, thin-walled cold-formed elements, structural optimization, hierarchy rules, dog-bone philosophy

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Authors: Francesco Venuti, Simona Alfiero

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The aim of this paper is to develop an empirical research on the nature and consequences of corporate governance on Eurozone Insurance Industry risk taking attitude. More particularly, we analyzed the effect of public ownership on risk taking with respect to privately held Insurance Companies. We also analyzed the effects on risk taking attitude of different degrees of ownership concentration, directors compensation, and the dimension/diversity of the Board of Directors. Our results provide quite strong evidence that, coherently with the Agency Theory, publicly traded insurance companies with more concentrated ownership are less risky than the corresponding privately held.

Keywords: agency theory, corporate governance, insurance companies, risk taking

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Authors: Alò Roberta, Bottiglione Francesco, Mantriota Giacomo

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The efficiency of the actuation system of lower limb exoskeletons and of active orthoses is a significant aspect of the design of such devices because it affects their efficacy. F-IVT is an innovative actuation system to power artificial knee joint with energy recovery capabilities. Its key and non-conventional elements are a flywheel, that acts as a mechanical energy storage system, and an Infinitely Variable Transmission (IVT). The design of the F-IVT can be optimized for a certain walking condition, resulting in a heavy reduction of both the electric energy consumption and of the electric peak power. In this work, by means of simulations of level ground walking at different speeds, it is demonstrated how F-IVT is still an advantageous actuator, even when it does not work in nominal conditions.

Keywords: active orthoses, actuators, lower extremity exoskeletons, knee joint

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Authors: Bochen Jia, Francesco Zhu

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People are constantly surprised at how real and immersive virtual reality (VR) is, even though the technology is still rudimentary, and we are only scratching the surface of its possibilities. Therefore, this literature review built a body of knowledge of existing technology that can be used to improve immersiveness in VR. For this paper, "Sense of Presence (SoP)" was chosen as the terminology to describe immersiveness in VR. Eight studies that tested VR technologies were identified. Many other studies were included to back up the incentives behind these technologies. VR technologies include vibration, airflow, thermal components, EMS, and quadcopters. Study results from selected papers were analyzed, compared, and generally positive. Seven studies had positive results, and only one had negative results. Vibration is the most effective option to improve SoP.

Keywords: virtual reality, sense of presence, self-awareness, literature review

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