A unification in the theory of linearization of second order nonlinear ordinary differential equations

In this letter, we introduce a new generalized linearizing transformation (GLT) for second order nonlinear ordinary differential equations (SNODEs). The well known invertible point (IPT) and non-point transformations (NPT) can be derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be linearized through NPT and IPT can be linearized by this GLT. We also illustrate how to construct GLTs and to identify the form of the linearizable equations and propose a procedure to derive the general solution from this GLT for the SNODEs. We demonstrate the theory with two examples which are of contemporary interest.Comment: 8 page

A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution - II

We present a semi-decision procedure to tackle first order differential equations, with Liouvillian functions in the solution (LFOODEs). As in the case of the Prelle-Singer procedure, this method is based on the knowledge of the integrating factor structure.Comment: 11 pages, late

A generalization of the S-function method applied to a Duffing-Van der Pol forced oscillator

In [1,2] we have developed a method (we call it the S-function method) that is successful in treating certain classes of rational second order ordinary differential equations (rational 2ODEs) that are particularly `resistant' to canonical Lie methods and to Darbouxian approaches. In this present paper, we generalize the S-function method making it capable of dealing with a class of elementary 2ODEs presenting elementary functions. Then, we apply this method to a Duffing-Van der Pol forced oscillator, obtaining an entire class of first integrals

A solvable model of the evolutionary loop

A model for the evolution of a finite population in a rugged fitness landscape is introduced and solved. The population is trapped in an evolutionary loop, alternating periods of stasis to periods in which it performs adaptive walks. The dependence of the average rarity of the population (a quantity related to the fitness of the most adapted individual) and of the duration of stases on population size and mutation rate is calculated.Comment: 6 pages, EuroLaTeX, 1 figur

The hidden prosumer: consumer-citizens participation in the invisible economy of advertising

Este artigo foca a participação do prosumidor - enquanto produtor e consumidor-cidadão – na publicidade e as suas implicações na construção dos conteúdo e dos públicos publicitários, formatando a indústria, produtos e perfis de consumo e a ecologia dos meios de comunicação. Com base na definição de prosumidor de Alvin Toffler, a dupla condição do indivíduo como produtor e consumidor, e sua designação da chamada economia invisível, analisaremos como a indústria da publicidade enfrenta os desafios colocados por esta participação, incorporando contribuições de prosumidores, como fonte de capital criativo e ferramentas operacionais. Além disso, discutiremos como a interação entre prosumidores e média, especialmente a publicidade, denota um empowerment paradoxal: os prosumidores co-criadores conquistam a sua própria voz na esfera pública, influenciando o conteúdo e ganhando poder de edição sobre a sua substância; mas porque são também são consumidores dos média, isto é, audiência, os prosumidores constroem valor mediático para a publicidade tornando-se parte dos produtos destinados ao consumo. Refletindo além da co-criação sobre a participação below-the-line, menos visível, enuncia-se ainda seu o potencial de cidadania, como meio de construir e influenciar a paisagem quotidiana

What’s in a place? The contribution of strategic communication to placemaking and territorial communication

Set in the field of territorial communication, the aim of this chapter is to summon the various contributions of strategic communication to placemaking and promotion, approaching them both through a mind frame path, as a multi-layered concept, and through an operational approach, as a pragmatic tool. Going through a number of examples we will reflect on several experiences to illustrate the potential of strategic communication to add value to places in different sets and scales, from building a place almost from scratch to nation branding strategies, from positioning and re-positioning objectives to building up notoriety or developing communities’ sense of belonging to a territory. We also set an evolutionary frame of the territorial communication in the light of its strategic dimension, drawing on key concepts and trends, influences and achievements. The performative value of strategic communication as a constructive tool of territorial development is discussed in addition to the communicational added value of territorial brands, namely by pointing emerging issues such as storytelling or participatory place communication. Furthermore, we summon ethical and pragmatic challenges to the debate as inspiration for future research.This work is supported by national funds through FCT – Fundação para a Ciência e a Tecnologia, I.P., under the project UIDB/00736/2020