arXiv subjects

Juan J. Nieto

Publications and source records attributed to Juan J. Nieto.

21 records · Page 2Linked to original sources

arXiv2015

Optimal Solutions to Relaxation in Multiple Control Problems of Sobolev Type with Nonlocal Nonlinear Fractional Differential Equations

We introduce the optimality question to the relaxation in multiple control problems described by Sobolev type nonlinear fractional differential equations with nonlocal control conditions in Banach spaces. Moreover, we consider the minimization problem of multi-integral functionals, with integrands that are not convex in the controls, of control systems with mixed nonconvex constraints on the controls. We prove, under appropriate conditions, that the relaxation problem admits optimal solutions. Furthermore, we show that those optimal solutions are in fact limits of minimizing sequences of systems with respect to the trajectory, multi-controls, and the functional in suitable topologies.

math.OC↗

arXiv2013

Analytic solution of a model of language competition with bilingualism and interlinguistic similarity

An in-depth analytic study of a model of language dynamics is presented: a model which tackles the problem of the coexistence of two languages within a closed community of speakers taking into account bilingualism and incorporating a parameter to measure the distance between languages. After previous numerical simulations, the model yielded that coexistence might lead to survival of both languages within monolingual speakers along with a bilingual community or to extinction of the weakest tongue depending on different parameters. In this paper, such study is closed with thorough analytical calculations to settle the results in a robust way and previous results are refined with some modifications. From the present analysis it is possible to almost completely assay the number and nature of the equilibrium points of the model, which depend on its parameters, as well as to build a phase space based on them. Also, we obtain conclusions on the way the languages evolve with time. Our rigorous considerations also suggest ways to further improve the model and facilitate the comparison of its consequences with those from other approaches or with real data.

physics.soc-ph↗

arXiv2011

Importance of interlinguistic similarity and stable bilingualism when two languages compete

In order to analyze the dynamics of two languages in competition, one approach is to fit historical data on their numbers of speakers with a mathematical model in which the parameters are interpreted as the similarity between those languages and their relative status. Within this approach, we show here, on the basis of a detailed analysis and extensive calculations, the outcomes that can emerge for given values of these parameters. Contrary to previous results, it is possible that in the long term both languages coexist and survive. This happens only when there is a stable bilingual group, and this is possible only if the competing languages are sufficiently similar, in which case its occurrence is favoured by both similarity and status symmetry.

physics.soc-ph↗