On the number of limit cycles bifurcating from a non-global degenerated center

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Semidiscretization and long-time asymptotics of nonlinear diffusion equations

We review several results concerning the long time asymptotics of nonlinear diffusion models based on entropy and mass transport methods. Semidiscretization of these nonlinear diffusion models are proposed and their numerical properties analysed. We demonstrate the long time asymptotic results by numerical simulation and we discuss several open problems based on these numerical results. We show that for general nonlinear diffusion equations the long-time asymptotics can be characterized in terms of fixed points of certain maps which are contractions for the euclidean Wasserstein distance. In fact, we propose a new scaling for which we can prove that this family of fixed points converges to the Barenblatt solution for perturbations of homogeneous nonlinearities for values close to zero.

Intermediate asymptotics beyond homogeneity and self-similarity: long time behavior for [formula]

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The optimal behaviour of firms facing stochastic costs

This paper aims at assessing the optimal behavior of a firm facing stochastic costs of production. In an imperfectly competitive setting, we evaluate to what extent a firm may decide to locate part of its production in other markets different from which it is actually settled. This decision is taken in a stochastic environment. Portfolio theory is used to derive the optimal solution for the intertemporal profit maximization problem. In such a framework, splitting production between different locations may be optimal when a firm is able to charge different prices in the different local markets.

Sources of Competitiveness in Tourist Local Systems

At the end of the XIX Century, Marshall described the existence of some concentrations of small and medium enterprises specialised in a specific production activity in certain districts of some industrial English cities. Starting from his contribute, Italian scholars have paid particular attention to this local system of production coined by Marshall under the term industrial district. In other countries, different but related territorial models have played a central role as the milieu or the geographical industrial clusters. Recently, these models have been extended to non-industrial fields like culture, rural activities and tourism. In this text, we explore the extension of these territorial models to the study of tourist activities in Italy, using a framework that can be easily applied to other countries or regions. The paper is divided in five sections. In the first one, we propose a review of the territorial models applied to tourism industry. In the second part, we construct a tourist filiere and we apply a methodology for the identification of local systems through GIS tools. Thus, taxonomy of the Italian Tourist Local Systems is presented. In the third part, we discuss about the sources of competitiveness of these Tourist Local Systems. In the forth section, we test a spatial econometrics model regarding different kinds of Italian Tourist Local Systems (rural systems, arts cities, tourist districts) in order to measure external economies and territorial networks. Finally, conclusions and policy implications are exposed.

Reduction, Linearization and stability of relative equilibria for mechanical systems on riemannian manifolds

Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability of relative equilibria. In particular, for mechanical control systems, an explicit characterization is given for the manner in which reduction by an infinitesimal isometry, and linearization along a controlled trajectory "commute." As part of the development, relationships are derived between the Jacobi equation of geodesic variation and concepts from reduction theory, such as the curvature of the mechanical connection and the effective potential. As an application of our techniques, fiber and base stability of relative equilibria are studied. The paper also serves as a tutorial of Riemannian geometric methods applicable in the intersection of mechanics and control theory.

Numerical schemes of diffusion asymptotics and moment closures for kinetic equations

We investigate different models that are intended to describe the small mean free path regime of a kinetic equation, a particular attention being paid to the moment closure by entropy minimization. We introduce a specific asymptotic-induced numerical strategy which is able to treat the stiff terms of the asymptotic diffusive regime. We evaluate on numerics the performances of the method and the abilities of the reduced models to capture the main features of the full kinetic equation.

Do creative industries cluster? mapping creative local production systems in Italy

An important debate on the role of creativity and culture as factors of local economic development is distinctly emerging. Despite the emphasis put on the theoretical definition of these concepts, it is necessary to strengthen comparative research for the identification and analysis of the kind of creativity embedded in the territory as well as its determinants. Creative local production systems are identified in Italy and Spain departing from local labour markets as territorial units, and focusing on two different kinds of creative

Conjugacy in Thompson's groups

We give a unified solution the conjugacy problem in Thompson’s groups F, V , and T using strand diagrams, and we analyze the complexity of the resulting algorithms.

Dynamics in Thompson's group F

We describe an explicit relationship between strand diagrams and piecewise-linear functions for elements of Thompson’s group F. Using this correspondence, we investigate the dynamics of elements of F, and we show that conjugacy of one-bump functions can be described by a Mather-type invariant.

Mather invariants in groups of piecewise-linear homeomorphisms

We describe the relation between two characterizations of conjugacy in groups of piecewise-linear homeomorphisms, discovered by Brin and Squier in [2] and Kassabov and Matucci in [5]. Thanks to the interplay between the techniques, we produce a simplified point of view of conjugacy that allows ua to easily recover centralizers and lends itself to generalization.

The simultaneous conjugacy problem in groups of piecewise linear functions

Guba and Sapir asked, in their joint paper [8], if the simultaneous conjugacy problem was solvable in Diagram Groups or, at least, for Thompson's group F. We give an elementary proof for the solution of the latter question. This relies purely on the description of F as the group of piecewise linear orientation-preserving homeomorphisms of the unit. The techniques we develop allow us also to solve the ordinary conjugacy problem as well, and we can compute roots and centralizers. Moreover, these techniques can be generalized to solve the same questions in larger groups of piecewise-linear homeomorphisms.