Journal of Mathematical Economics and Finance, 2020
In these notes, we define and study some concepts from Special Relativistic Mechanics, in a diffe... more In these notes, we define and study some concepts from Special Relativistic Mechanics, in a differential geometric perspective. Our approach allows us to revisit and rethink some basic theoretical structures, in a way that reveals more feasible to developments in various directions, in particular in view of a better integration with Quantum Mechanics.
In this note, we examine critically some basic features of momentum operators, both in the case o... more In this note, we examine critically some basic features of momentum operators, both in the case of simple spatial context and in the case of spacetime. The natural time for the domain H of the momentum operator The Laurent Schwartz space Sn endowed with its own semimetric topology and with the Dirac inner product We emphasize that the right topology to consider is the standard Schwartz topology, not the topology induced by the above Dirac inner product which needs to provide probability issues and not continuity properties. The above choice for the space H satisfy at once some fundamental requirements of the theory:0. all the functions of the space H are both smooth and square integrable;1. the operator P reveals indeed a linear endomorphism everywhere defined uponH;2. the operator is continuous with respect to the Schwartz topology;3. the operator P is uniquely extensible to the entire space of tempered distributionsSn′ and this extension is continuous with respect to the standard ...
Statistical mechanics and quantum fields on fractals by E. Akkermans Spectral algebra of the Cher... more Statistical mechanics and quantum fields on fractals by E. Akkermans Spectral algebra of the Chernov and Bogoslovsky Finsler metric tensors by V. Balan Local multifractal analysis by J. Barral, A. Durand, S. Jaffard, and S. Seuret Extreme risk and fractal regularity in finance by L. E. Calvet and A. J. Fisher An algorithm for dynamical games with fractal-like trajectories by D. Carfi and A. Ricciardello The landscape of Anderson localization in a disordered medium by M. Filoche and S. Mayboroda Zeta functions for infinite graphs and functional equations by D. Guido and T. Isola Vector analysis on fractals and applications by M. Hinz and A. Teplyaev Non-regularly varying and nonperiodic oscillation of the on-diagonal heat kernels on self-similar fractals by N. Kajino Lattice effects in the scaling limit of the two-dimensional self-avoiding walk by T. Kennedy and G. F. Lawler The Casimir effect on Laakso spaces by R. Kesler and B. Steinhurst The decimation method for Laplacians on fra...
In this paper, we focus on some aspects of smooth manifolds, which appear of fundamental importan... more In this paper, we focus on some aspects of smooth manifolds, which appear of fundamental importance for the developments of differential geometry and its applications to Theoretical Physics, Special and General Relativity, Economics and Finance.
Journal of Mathematical Economics and Finance, 2020
In this paper, we provide two approximating functions for some dynamics associated with the first... more In this paper, we provide two approximating functions for some dynamics associated with the first wave of Covid-19 contagion in Italy. We consider also two particular cases of Sicily and Lombardy. We consider only the evolution of total infected cases and new daily cases. We show that the total infected cases need, in the time period considered, two different approximations. We approximate the daily infected curves by the first derivative of the above two functions. In the case of Lombardy, we consider a wider time interval to obtain an ultimate approximation.
Journal of Environmental Management and Tourism, 2018
In this paper, we face the problem of global feeding sustainability and related environmental iss... more In this paper, we face the problem of global feeding sustainability and related environmental issues, with a strong attention to possible public heath improvements. In particular, we consider food producers and sellers of vegan (or vegetarian) and non-vegan (or non-vegetarian) food and we build up feasible and measurable contracts between two different food producers, in order to construct a more sustainable and healthier diet for future generations. At this aim, we use co-opetitive approach by means of game theory. Our co-opetitive approach consists in a game theory structure, which could help small local producers of vegan food a simpler entry in the global market and free significant publicity. At the same time, our mathematical construction suggests how big global producers/sellers of non-vegetarian food could develop a smooth rapid transaction to a more sustainable and healthier production/supply. Specifically, our game constitutes an asymmetric R&D alliance between McDonald’s ...
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2012
Introductory notes on the Special Issue dedicated to the Permanent International Session of Resea... more Introductory notes on the Special Issue dedicated to the Permanent International Session of Research Seminars (PISRS) held in 2011 at the DESMaS Department of the University of Messina.
Journal of Mathematical Economics and Finance, 2018
General setting.1. This paper proposes an interaction model representing a global economy aiming ... more General setting.1. This paper proposes an interaction model representing a global economy aiming to become environmentally sustainable.2. The model looks at the production side and consumption side of the economies of two groups of countries.3. Regarding the production side, the suggested model considers aggregate common/coordinated investments in green technologies against climate change.4. On the side of consumptions, it considers economic and policy instruments to change the patterns of households’ consumptions, towards products respectful of the planet.5. The model follows a multi-dimensional game theory approach and applies a theoretical framework à la Cournot.
In this paper, we propose a new method of optimization based on genetic algorithms using the MATL... more In this paper, we propose a new method of optimization based on genetic algorithms using the MATLAB toolbox “Global Optimization”. The algorithm finds layers moduli of a flexible pavement through the measurement of pavement surface deflections under assigned load conditions. First, the algorithm for the forward calculation is validated, then the algorithm for the back-calculation is proposed, and the results are compared, in the case of airport pavements, with other software using different back-calculation techniques. The goodness of the procedure and the way of managing the algorithm operator is demonstrated by means of positive feedback obtained from the comparison of the results of ELMOD and BackGenetic3D. Moreover, the findings of the analysis prove that, in such an optimization procedure by GA, the best solution is always reached with a low number of generations, generally less than 10, allowing a reduction in the time of calculation and choosing a population big enough to sel...
In this paper, we deal with the renowned problem of plastic pollution caused by food consumption ... more In this paper, we deal with the renowned problem of plastic pollution caused by food consumption and its conservation. Specifically, we consider the producer/reseller decision problem of industrial organizations in conditions of perfect competition within small oligopoly clusters. Indeed, very often, one major sustainability problem is that the presence of direct competitors in the same market determines entrepreneurship choices which lower production costs and packaging costs at the expense of the environment and public health. For this purpose, in order to show economic scenarios in which the respect and preservation of the environment and natural resources are quantitatively compatible with profits and economic growth, we present a provisional coopetitive model of the strategic interaction of two food enterprises, in direct duopoly competition, through investments in sustainable-packaging technologies. The macroeconomic goal is to propose possible actions to reduce carbon footpri...
In this paper we start to construct some fundamental features of Dirac Calculus, specifically, we... more In this paper we start to construct some fundamental features of Dirac Calculus, specifically, we go inside the theory of Heisenberg continuous matrices, which, in our Schwartz Linear Algebra, are represented by Schwartz families. We distinguish the important subclass of transposable continuous matrices and give some basic and very important examples in Quantum Mechanics. So we define transposable Schwartz families and their transpose families, we prove the transposability of Dirac families and Fourier families. We find the transpose of regular-distribution families in a much general case. We define symmetric families, the analogous of symmetric ma- trices in the continuous case. We prove the symmetry of Dirac families and of Fourier families. We define Hermitian families, the analogous of Hermitian matrices in the continuous case. We prove the Hermitianity of Dirac families and of Fourier families. We define unitary families, the analogous of unitary matrices in the continuous case...
Journal of Mathematical Economics and Finance, 2020
In these notes, we define and study some concepts from Special Relativistic Mechanics, in a diffe... more In these notes, we define and study some concepts from Special Relativistic Mechanics, in a differential geometric perspective. Our approach allows us to revisit and rethink some basic theoretical structures, in a way that reveals more feasible to developments in various directions, in particular in view of a better integration with Quantum Mechanics.
In this note, we examine critically some basic features of momentum operators, both in the case o... more In this note, we examine critically some basic features of momentum operators, both in the case of simple spatial context and in the case of spacetime. The natural time for the domain H of the momentum operator The Laurent Schwartz space Sn endowed with its own semimetric topology and with the Dirac inner product We emphasize that the right topology to consider is the standard Schwartz topology, not the topology induced by the above Dirac inner product which needs to provide probability issues and not continuity properties. The above choice for the space H satisfy at once some fundamental requirements of the theory:0. all the functions of the space H are both smooth and square integrable;1. the operator P reveals indeed a linear endomorphism everywhere defined uponH;2. the operator is continuous with respect to the Schwartz topology;3. the operator P is uniquely extensible to the entire space of tempered distributionsSn′ and this extension is continuous with respect to the standard ...
Statistical mechanics and quantum fields on fractals by E. Akkermans Spectral algebra of the Cher... more Statistical mechanics and quantum fields on fractals by E. Akkermans Spectral algebra of the Chernov and Bogoslovsky Finsler metric tensors by V. Balan Local multifractal analysis by J. Barral, A. Durand, S. Jaffard, and S. Seuret Extreme risk and fractal regularity in finance by L. E. Calvet and A. J. Fisher An algorithm for dynamical games with fractal-like trajectories by D. Carfi and A. Ricciardello The landscape of Anderson localization in a disordered medium by M. Filoche and S. Mayboroda Zeta functions for infinite graphs and functional equations by D. Guido and T. Isola Vector analysis on fractals and applications by M. Hinz and A. Teplyaev Non-regularly varying and nonperiodic oscillation of the on-diagonal heat kernels on self-similar fractals by N. Kajino Lattice effects in the scaling limit of the two-dimensional self-avoiding walk by T. Kennedy and G. F. Lawler The Casimir effect on Laakso spaces by R. Kesler and B. Steinhurst The decimation method for Laplacians on fra...
In this paper, we focus on some aspects of smooth manifolds, which appear of fundamental importan... more In this paper, we focus on some aspects of smooth manifolds, which appear of fundamental importance for the developments of differential geometry and its applications to Theoretical Physics, Special and General Relativity, Economics and Finance.
Journal of Mathematical Economics and Finance, 2020
In this paper, we provide two approximating functions for some dynamics associated with the first... more In this paper, we provide two approximating functions for some dynamics associated with the first wave of Covid-19 contagion in Italy. We consider also two particular cases of Sicily and Lombardy. We consider only the evolution of total infected cases and new daily cases. We show that the total infected cases need, in the time period considered, two different approximations. We approximate the daily infected curves by the first derivative of the above two functions. In the case of Lombardy, we consider a wider time interval to obtain an ultimate approximation.
Journal of Environmental Management and Tourism, 2018
In this paper, we face the problem of global feeding sustainability and related environmental iss... more In this paper, we face the problem of global feeding sustainability and related environmental issues, with a strong attention to possible public heath improvements. In particular, we consider food producers and sellers of vegan (or vegetarian) and non-vegan (or non-vegetarian) food and we build up feasible and measurable contracts between two different food producers, in order to construct a more sustainable and healthier diet for future generations. At this aim, we use co-opetitive approach by means of game theory. Our co-opetitive approach consists in a game theory structure, which could help small local producers of vegan food a simpler entry in the global market and free significant publicity. At the same time, our mathematical construction suggests how big global producers/sellers of non-vegetarian food could develop a smooth rapid transaction to a more sustainable and healthier production/supply. Specifically, our game constitutes an asymmetric R&D alliance between McDonald’s ...
Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali, 2012
Introductory notes on the Special Issue dedicated to the Permanent International Session of Resea... more Introductory notes on the Special Issue dedicated to the Permanent International Session of Research Seminars (PISRS) held in 2011 at the DESMaS Department of the University of Messina.
Journal of Mathematical Economics and Finance, 2018
General setting.1. This paper proposes an interaction model representing a global economy aiming ... more General setting.1. This paper proposes an interaction model representing a global economy aiming to become environmentally sustainable.2. The model looks at the production side and consumption side of the economies of two groups of countries.3. Regarding the production side, the suggested model considers aggregate common/coordinated investments in green technologies against climate change.4. On the side of consumptions, it considers economic and policy instruments to change the patterns of households’ consumptions, towards products respectful of the planet.5. The model follows a multi-dimensional game theory approach and applies a theoretical framework à la Cournot.
In this paper, we propose a new method of optimization based on genetic algorithms using the MATL... more In this paper, we propose a new method of optimization based on genetic algorithms using the MATLAB toolbox “Global Optimization”. The algorithm finds layers moduli of a flexible pavement through the measurement of pavement surface deflections under assigned load conditions. First, the algorithm for the forward calculation is validated, then the algorithm for the back-calculation is proposed, and the results are compared, in the case of airport pavements, with other software using different back-calculation techniques. The goodness of the procedure and the way of managing the algorithm operator is demonstrated by means of positive feedback obtained from the comparison of the results of ELMOD and BackGenetic3D. Moreover, the findings of the analysis prove that, in such an optimization procedure by GA, the best solution is always reached with a low number of generations, generally less than 10, allowing a reduction in the time of calculation and choosing a population big enough to sel...
In this paper, we deal with the renowned problem of plastic pollution caused by food consumption ... more In this paper, we deal with the renowned problem of plastic pollution caused by food consumption and its conservation. Specifically, we consider the producer/reseller decision problem of industrial organizations in conditions of perfect competition within small oligopoly clusters. Indeed, very often, one major sustainability problem is that the presence of direct competitors in the same market determines entrepreneurship choices which lower production costs and packaging costs at the expense of the environment and public health. For this purpose, in order to show economic scenarios in which the respect and preservation of the environment and natural resources are quantitatively compatible with profits and economic growth, we present a provisional coopetitive model of the strategic interaction of two food enterprises, in direct duopoly competition, through investments in sustainable-packaging technologies. The macroeconomic goal is to propose possible actions to reduce carbon footpri...
In this paper we start to construct some fundamental features of Dirac Calculus, specifically, we... more In this paper we start to construct some fundamental features of Dirac Calculus, specifically, we go inside the theory of Heisenberg continuous matrices, which, in our Schwartz Linear Algebra, are represented by Schwartz families. We distinguish the important subclass of transposable continuous matrices and give some basic and very important examples in Quantum Mechanics. So we define transposable Schwartz families and their transpose families, we prove the transposability of Dirac families and Fourier families. We find the transpose of regular-distribution families in a much general case. We define symmetric families, the analogous of symmetric ma- trices in the continuous case. We prove the symmetry of Dirac families and of Fourier families. We define Hermitian families, the analogous of Hermitian matrices in the continuous case. We prove the Hermitianity of Dirac families and of Fourier families. We define unitary families, the analogous of unitary matrices in the continuous case...
In this book, we focus on some aspects of smooth manifolds, which appear of fundamental importanc... more In this book, we focus on some aspects of smooth manifolds, which appear of fundamental importance for the developments of differential geometry and its applications to Theoretical Physics, Special and General Relativity, Economics and Finance. In particular we touch basic topics, for instance definition of tangent vectors, change of coordinate system in the definition of tangent vectors, action of tangent vectors on coordinate systems, structure of tangent spaces, geometric interpretation of tangent vectors, canonical tangent vectors determined by local charts, tangent frames determined by local charts, change of local frames, tangent vectors and contravariant vectors, covariant vectors, the gradient of a real function, invariant scalars, tangent applications, local Jacobian matrices, basic properties of the tangent map, chain rule, diffeomorphisms and derivatives, transformation of tangent bases under derivatives, paths on a manifold, vector derivative of a path with respect to a re-parametrization, tangent derivative versus calculus derivative, vector derivative of a path in local coordinates, existence of a path with a given initial tangent vector and other topics.
In this work, we face the problem of quantizing the relativistic Hamiltonian of a free massive pa... more In this work, we face the problem of quantizing the relativistic Hamiltonian of a free massive particle (rest mass different from 0). In tempered distribution state spaces, we find the natural way to define the relativistic Hamiltonian operator and its associated Schrödinger equation. We, then, deduce the equivalent continuity equation for the Born probability density and study some its different (but equivalent) expressions. We determine the possible probability currents and flux velocity fields associated with the particle evolution. We provide the relativistic invariant expression for both Schrödinger equation and probability flux continuity equations.
In this work, we face the problem of quantizing the relativistic Hamil-tonian of a free massive p... more In this work, we face the problem of quantizing the relativistic Hamil-tonian of a free massive particle (rest mass different from 0). In tempered distribution state spaces, we find the natural way to define the relativistic Hamiltonian operator and its associated Schrödinger equation. We, then, deduce the equivalent continuity equation for the Born probability density and study some its different (but equivalent) expressions. We determine the possible probability currents and flux velocity fields associated with the particle evolution. We provide the relativistic invariant expression for both Schrödinger equation and probability flux continuity equations.
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Papers by David Carfi