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.

Generic Existence of Solutions of Symmetric Optimization Problems

In this paper we study a class of symmetric optimization problems which is identified with a space of objective functions, equipped with an appropriate complete metric. Using the Baire category approach, we show the existence of a subset of the space of functions, which is a countable intersection of open and everywhere dense sets, such that for every objective function from this intersection the corresponding symmetric optimization problem possesses a solution.

Strategic Vote Trading in Power Sharing Systems

This paper studies decentralized vote trading in a power sharing system that follows the rules of strategic market games. In particular, we study a two-party election in which prior to the voting stage, voters are free to trade votes for money. Voters hold private information about both their ordinal and cardinal preferences, whereas their utilities are proportionally increasing in the vote share of their favorite party. In this framework, we prove generic existence of a unique full trade equilibrium (an equilibrium in which nobody refrains from vote trading). Moreover, we argue that vote trading in such systems unambiguously improves voters' welfare. (JEL C72, D71, D72, D82)

GENERIC EXISTENCE OF MAD FAMILIES

In this note we study generic existence of maximal almost disjoint (MAD) families. Among other results we prove that Cohen-indestructible families exist generically if and only if b = c. We obtain analogous results for other combinatorial properties of MAD families, including Sacks-indestructibility and being +-Ramsey.

Ordinal ultrafilters versus P-hierarchy

An earlier paper [Starosolski A., P-hierarchy on βω, J. Symbolic Logic, 2008, 73(4), 1202–1214] investigated the relations between ordinal ultrafilters and the so-called P-hierarchy. The present paper focuses on the aspects of characterization of classes of ultrafilters of finite index, existence, generic existence and the Rudin-Keisler-order.

CANARDS FROM CHUA'S CIRCUIT

The aim of this work is to extend Benoît's theorem for the generic existence of "canards" solutions in singularly perturbed dynamical systems of dimension three with one fast variable to those of dimension four. Then, it is established that this result can be found according to the Flow Curvature Method. Applications to Chua's cubic model of dimension three and four enable to state the existence of "canards" solutions in such systems.