A comparison result for a linear differential equation with piecewise constant delay

We present a new comparison result for an equation of the form u\u27(t) + m u(t) + n u([t]) = (t), t [0,T] where [ ] denotes the greatest integer function

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.Comment: to appear in New Journal of Physic

Periodic solutions for third order ordinary differential equations

summary:In this paper, we introduce the concept of upper and lower solutions for third order periodic boundary value problems. We show that the monotone iterative technique is valid and obtain the extremal solutions as limits of monotone sequences. We first present a new maximum principle for ordinary differential inequalities of third order that is interesting by itself

Optical binding of cylinder photonic molecules in the near-field of partially coherent fluctuating Gaussian Schell model sources. A coherent mode representation

We present a theory and computation method of radiation pressure from partially coherent light by establishing a coherent mode representation of the radiation forces. This is illustrated with the near field emitted from a Gaussian Schell model source, mechanically acting on a single cylinder with magnetodielectric behavior, or on a photonic molecule constituted by a pair of such cylinders. Thus after studying the force produced by a single particle, we address the effects of the spatial coherence on the bonding and anti-bonding states of two particles. The coherence length manifests the critical limitation of the contribution of evanescent modes to the scattered fields, and hence to the nature and strength of the electromagnetic fores, even when electric and/or magnetic partial wave resonances are excited

Mathematical modeling of Zika disease in pregnant women and newborns with microcephaly in Brazil

We propose a new mathematical model for the spread of Zika virus. Special attention is paid to the transmission of microcephaly. Numerical simulations show the accuracy of the model with respect to the Zika outbreak occurred in Brazil.Comment: This is a preprint of a paper whose final and definite form is with 'Mathematical Methods in the Applied Sciences', ISSN 0170-4214. Submitted Aug 10, 2017; Revised Nov 13, 2017; accepted for publication Nov 14, 201