Abstract. The q-log-concavity of the q-Stirling polynomials S q [m + k, m] of the second kind is proved by using an explicit expression of the coefficients of such a polynomial, when k = 1, 2. Mathematics Subject Classification: 35G05, 35G16, 35G35

I remember reading in my distant youth an FCE book called Artificial Intelligence and the adolescent excitement for the realization of the promises of a world full of automatons serving in all spheres of daily life seemed to be realized. That was the early eighties and the world was not convulsing in the midst of a dizzying technological revolution.

The emergence of social networking is closely related with the new technologies improving user interface experience thus making the interaction between users more natural and intuitive. Before, the first online communities of interest were user lists and asynchronous discussion groups resembling more the form of mass mailings than informal discussions in a cafe or in a classroom. The impact of web 2.0 on scientific practices has become evident in establishing more and more epistemic communities as virtual communities and vice versa. With respect to the role of the paradigm in the constitution and operations of an epistemic community, the framework of values and the ethical reflection of that become its own form of binding and guiding principle of the theoretical action. Thus any individual who joins an online community with the ambition of an epistemic effect must develop the morals and ethics necessary to enable him/her to understand the relevant forms of their theoretical practice.

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The grand canonical thermodynamics of a bosonic system is studied in order to identify the footprint of its own high-density quantum phase transition. The phases displayed by the system at zero temperature establish recognizable patterns at finite temperature that emerged in the proximity of the boundary of the equilibrium diagram. The gapped phase underlines a state of collectivism/condensation at finite temperature in which particles coalesce into the ground state in spite of interacting attractively. The work establishes a framework that allows to study the phenomenon of condensation under the effect of attraction.