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

Second order parabolic Hamilton–Jacobi–Bellman equations in Hilbert spaces and stochastic control: Lμ2 approach

AbstractWe study a Hamilton–Jacobi–Bellman equation related to the optimal control of a stochastic semilinear equation on a Hilbert space X. We show the existence and uniqueness of solutions to the HJB equation and prove the existence and uniqueness of feedback controls for the associated control problem via dynamic programming. The main novelty is that we look for solutions in the space L2(X,μ), where μ is an invariant measure for an associated uncontrolled process. This allows us to treat controlled systems with degenerate diffusion term that are not covered by the existing literature. In particular, we prove the existence and uniqueness of solutions and obtain the optimal feedbacks for controlled stochastic delay equations and for the first order stochastic PDE’s arising in economic and financial models

Endogenous growth and wave-like business fluctuations

This paper argues that observed long lags in innovation implementation rationalize Schumpeter's statement that “wave-like fluctuations in business ... are the form economic development takes in the era of capitalism.” Adding implementation delays to an otherwise standard endogenous growth model with expanding product variety, the equilibrium path admits a Hopf bifurcation where consumption, R&D and output permanently fluctuate. This mechanism is quantitatively consistent with the observed medium-term movements of US aggregate output. In this framework, an optimal allocation may be restored at equilibrium by the mean of a procyclical subsidy, needed to generate additional consumption smoothing. Finally, a procyclical R&D subsidy rate designed to half consumption fluctuations will increase the growth rate from 2.4% to 3.4% with a 9.6% (compensation equivalent) increase in welfare

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

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

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

Bilateral Severe Corneal Ulcer in a Patient with Lung Adenocarcinoma Treated with Gefitinib

We describe the case of Gefitinib-related bilateral corneal perforation. An 86-year-old female patient had bilateral painless and progressive vision loss due to neurotrophic corneal ulcer, following a 2-month treatment with Gefitinib, a selective epidermal growth factor receptor (EGFR) tyrosine kinase inhibitor for metastatic adenocarcinoma of the lung with confirmed EGFR gene mutation. She had no signs of ocular infection, inflammation, or lid problems to account for the development of corneal damage. Neurotrophic ulcer evolved into a frank perforation in one eye and an impending perforation on the other eye. EGFR inhibitors have been associated with dry eye, epithelial erosions, ulcerative keratitis, and corneal edema. However, to the best of our knowledge, this is the first case of bilateral severe corneal ulcer due to Gefitinib. The patient went on to have bilateral corneal graft surgery. This case aims to raise awareness among ophthalmologists and oncologists of the association between EGFR inhibitors, corneal neurotrophic ulcers, and possible evolution in corneal perforation

Optimal portfolio choice with path dependent labor income: the infinite horizon case

We consider an infinite horizon portfolio problem with borrowing constraints, in which an agentreceives labor income which adjusts to financial market shocks in a path dependent way. Thispath-dependency is the novelty of the model, and leads to an infinite dimensional stochasticoptimal control problem. We solve the problem completely, and find explicitly the optimalcontrols in feedback form. This is possible because we are able to find an explicit solutionto the associated infinite dimensional Hamilton-Jacobi-Bellman (HJB) equation, even if stateconstraints are present. To the best of our knowledge, this is the first infinite dimensionalgeneralization of Merton’s optimal portfolio problem for which explicit solutions can be found.The explicit solution allows us to study the properties of optimal strategies and discuss theirfinancial implications