Universal Taylor Series in Several Variables Depending on Parameters

We establish generic existence of Universal Taylor Series on products $$\varOmega = \prod \varOmega _i$$ Ω = ∏ Ω i of planar simply connected domains $$\varOmega _i$$ Ω i where the universal approximation holds on products K of planar compact sets with connected complements provided $$K \cap \varOmega = \emptyset $$ K ∩ Ω = ∅ . These classes are with respect to one or several centers of expansion and the universal approximation is at the level of functions or at the level of all derivatives. Also, the universal functions can be smooth up to the boundary, provided that $$K \cap \overline{\varOmega } = \emptyset $$ K ∩ Ω ¯ = ∅ and $$\{\infty \} \cup [{\mathbb {C}} {\setminus } \overline{\varOmega }_i]$$ { ∞ } ∪ [ C \ Ω ¯ i ] is connected for all i. All previous kinds of universal series may depend on some parameters; then the approximable functions may depend on the same parameters, as it is shown in the present paper.

DICE

This article deals with serious game design methods. More specifically, it focuses on the following question: is there any universal series of steps to design a serious game? Or is the availability of several different design methods unavoidable? To try to answer this question, we will study a corpus of ten design methods suited to Serious Games. Most of these theoretical tools are coming from or aimed to industry professionals. This literary review will allow us to perform a comparative analysis over the various steps used by these methods, in order to build a generic model for the design process of Serious Games: the Design / Imagine / Create / Evaluate (D.I.C.E.) model.