A New Superconformal Mechanics

In this paper we propose a new supersymmetric extension of conformal mechanics. The Grassmannian variables that we introduce are the basis of the forms and of the vector-fields built over the symplectic space of the original system. Our supersymmetric Hamiltonian itself turns out to have a clear geometrical meaning being the Lie-derivative of the Hamiltonian flow of conformal mechanics. Using superfields we derive a constraint which gives the exact solution of the supersymmetric system in a way analogous to the constraint in configuration space which solved the original non-supersymmetric model. Besides the supersymmetric extension of the original Hamiltonian, we also provide the extension of the other conformal generators present in the original system. These extensions have also a supersymmetric character being the square of some Grassmannian charge. We build the whole superalgebra of these charges and analyze their closure. The representation of the even part of this superalgebra on the odd part turns out to be integer and not spinorial in character.Comment: Superfield re-define

Bulges

We model the evolution of the galactic bulge and of the bulges of a selected sample of external spiral galaxies, via the multiphase multizone evolution model. We address a few questions concerning the role of the bulges within galactic evolution schemes and the properties of bulge stellar populations. We provide solutions to the problems of chemical abundances and spectral indices, the two main observational constraints to bulge structure.Comment: 15 pages, 10 figures, to be published in MNRA

A New Look at the Schouten-Nijenhuis, Fr\"olicher-Nijenhuis and Nijenhuis-Richardson Brackets for Symplectic Spaces

In this paper we re-express the Schouten-Nijenhuis, the Fr\"olicher-Nijenhuis and the Nijenhuis-Richardson brackets on a symplectic space using the extended Poisson brackets structure present in the path-integral formulation of classical mechanics.Comment: 27+1 pages, Latex, no figure

Universal Hidden Supersymmetry in Classical Mechanics and its Local Extension

We review here a path-integral approach to classical mechanics and explore the geometrical meaning of this construction. In particular we bring to light a universal hidden BRS invariance and its geometrical relevance for the Cartan calculus on symplectic manifolds. Together with this BRS invariance we also show the presence of a universal hidden genuine non-relativistic supersymmetry. In an attempt to understand its geometry we make this susy local following the analogous construction done for the supersymmetric quantum mechanics of Witten.Comment: 6 pages, latex, Volkov Memorial Proceeding

A New Supersymmetric Extension of Conformal Mechanics

In this paper a new supersymmetric extension of conformal mechanics is put forward. The beauty of this extension is that all variables have a clear geometrical meaning and the super-Hamiltonian turns out to be the Lie-derivative of the Hamiltonian flow of standard conformal mechanics. In this paper we also provide a supersymmetric extension of the other conformal generators of the theory and find their "square-roots". The whole superalgebra of these charges is then analyzed in details. We conclude the paper by showing that, using superfields, a constraint can be built which provides the exact solution of the system.Comment: 11 pages, no figure

Non equilibrium statistical physics with fictitious time

Problems in non equilibrium statistical physics are characterized by the absence of a fluctuation dissipation theorem. The usual analytic route for treating these vast class of problems is to use response fields in addition to the real fields that are pertinent to a given problem. This line of argument was introduced by Martin, Siggia and Rose. We show that instead of using the response field, one can, following the stochastic quantization of Parisi and Wu, introduce a fictitious time. In this extra dimension a fluctuation dissipation theorem is built in and provides a different outlook to problems in non equilibrium statistical physics.Comment: 4 page

A simple planning problem for COVID-19 lockdown: a dynamic programming approach

A large number of recent studies consider a compartmental SIR model to study optimal control policies aimed at containing the diffusion of COVID-19 while minimizing the economic costs of preventive measures. Such problems are non-convex and standard results need not to hold. We use a Dynamic Programming approach and prove some continuity properties of the value function of the associated optimization problem. We study the corresponding Hamilton-Jacobi-Bellman equation and show that the value function solves it in the viscosity sense. Finally, we discuss some optimality conditions. Our paper represents a first contribution towards a complete analysis of non-convex dynamic optimization problems, within a Dynamic Programming approach

HJB Equations and Stochastic Control on Half-Spaces of Hilbert Spaces

In this paper, we study a first extension of the theory of mild solutions for Hamilton–Jacobi–Bellman (HJB) equations in Hilbert spaces to the case where the domain is not the whole space. More precisely, we consider a half-space as domain, and a semilinear HJB equation. Our main goal is to establish the existence and the uniqueness of solutions to such HJB equations, which are continuously differentiable in the space variable. We also provide an application of our results to an exit-time optimal control problem, and we show that the corresponding value function is the unique solution to a semilinear HJB equation, possessing sufficient regularity to express the optimal control in feedback form. Finally, we give an illustrative example

Exploitation of an olive oil industry by-product: olive pomace as a source of food aroma compounds

Italy is the second largest producer in the world of olive oil, preceded only by Spain. Although olive oil can be considered as a “green gold” all over the world, the treatment of its by-products is a critical aspect to cope with. Indeed, the polluting character of such by-product together with its high costs for an effective disposal strongly penalize the olive oil industry. In particular, 50 % of oil production costs depend on its waste disposal. In this context, the aim of this work was to evaluate a potential exploitation of olive pomace as a feedstock for the production of flavours of interest for the food industry