This essay discusses Jesuit Priest Antonio Vieira's (1608-1697) Messianic writings, specifically the texts in which he comments on the impending arrival of the Kingdom of Christ, described as a most happy state suffused with divine grace. This Kingdom would be perfect and complete, and it would take place on earth, not in the purely spiritual sphere of heaven. I argue that the earthly dimension of Vieira's conception of the Kingdom of Christ opens his Messianism to a political dimension. It will lead him to consider the coexistence of nations during this Millenarian Kingdom in terms of perpetual peace, a notion later secularized by the thinkers of the Enlightenment.

We consider an M/M/1+M queue with a human server, who is influenced by incentives. Specifically, the server chooses his service rate by maximizing his utility function. Our objective is to guarantee the existence of a unique maximum. The complication is that most sensible utility functions depend on the server utilization, a non-simple expression. We derive a property of the utilization that guarantees quasiconcavity of any utility function that multiplies the server's concave (including linear) "value" of his service rate by the server utilization. (C) 2018 Elsevier B.V. All rights reserved.

The manuscripts of Jesuit mathematician Inacio Vieira (1678-1739) played a significant rule in treatise production in Portugal. The Tractado da A"ptica (1714) and Tractado de Prospectiva (1716) address the nature and properties of vision, the deception and disillusion of seeing and the fundaments of perspective. Geometric properties of visual rays, principles of optical illusion and values inherent in the optical and mathematical representation of space are explored, together with practical applications in architecture and painting. Although he does not make an original scientific contribution, he formulates operative statements applied to the arrangement of a sensitive space. This approach to optics and perspective brings up the relationship between reality and appearance in which the production of an image lies in the fact that to show an object, one has to show it as it is not. Vieira's work forges links between optics (perspectiva naturalis) and perspective (perspectiva artificialis), analyzing image distortion through spatial perception, illusion and quadratura Pursuing an empirical architecture, the simulated space of quadratura is understood as a challenge that creates a new dimension and experience of architectural space. Form and metric properties, from real and illusory construction, are interrelated contributing to an imaginary perception of spatiality. It is here that optics and perspective are established as architectural instruments for achieving a sensitive space.

We use the framework used by Bakry and Emery in their work on logarithmic Sobolev inequalities to define a notion of coarse Ricci curvature on smooth metric measure spaces alternative to the notion proposed by Y. Ollivier. This function can be used to recover the Ricci tensor on smooth Riemannian manifolds by the formula for any curve .

This technical note analyzes strategic overtaking equilibria in a single server queue, where customers observe the queue length and have the option of overtaking some of the customers already present in the queue by paying a fixed amount per overtaken customer.

Abstract An M/M/C M / M / C queueing system operating in a Markovian environment is studied. This paper focuses on the stationary behavior and presents the theoretical framework. For a special case, analytical results are derived that are analogous to the classical solutions for the simple M/M/C M / M / C queue. The elaborate analysis of a specific case is given to illustrate the basic idea of the framework. A technical proof with respect to the existence of d−1 d − 1 roots is displayed to sustain the corresponding theory.