Consider a two-person zero-sum stochastic game with Borel state space S, compact metric action sets A, B and law of motion q such that the integral under q of every bounded Borel measurable function depends measurably on the initial state s and continuously on the actions (a,b) of the players. Suppose the payoff is a bounded function f of the infinite history of states and actions such that f i...

It is shown that the integral functional I(y,z) = J"0 f(t,y(t), z(t))dp. is lower semicontinuous on its domain with respect to the joint strong convergence of yk -» y in Lp(G) and the weak convergence of zk -» z in LAG), where 1 < p < oo and 1 < q < oo, under the following conditions. The function/: (t,x,w) -*f(t,x,w) is measurable in / for fixed (x, w), is continuous in (x, w) for a.e. /, and ...

We consider the generalized elastica functional defined on L1(R2) as F(u) =  ∫ R2 |∇u|(α +β |div ∇u |∇u| |p)dx, if u ∈ C2(R2), +∞ else, where p > 1, α > 0, β ≥ 0. We study the L1-lower semicontinuous envelope F of F and we prove that, for any u ∈ BV(R2), F(u) can be represented by a coarea-type formula involving suitable collections of W2,p curves that cover the essential boundaries of the le...

Microalgae culture is a potential source of biodiesel and one of the best alternatives as raw material for biodiesel production. The first objective of this work is the pilot plant design for microalgae culture of high oil content species. The design was inspired by raceway large-scale culture. Although this kind of culture is usually in outdoor ponds, the pilot plant is an indoor raceway pond,...

We consider five different types of systems of generalized vector quasi-equilibrium problems and establish relationships among them by using different kinds of generalized pseudomonotonicities. We prove the existence of their solutions under lower semicontinuity for a family of multivalued maps involved in the formulation of these problems. The existence of solutions of these problems is also i...

We model strategic competition in a market with asymmetric information as a noncooperative game in which each seller competes for a buyer of unknown type by offering the buyer a catalog of products and prices. We call this game a catalog game. Our main objective is to show that catalog games have Nash equilibria. The Nash existence problem for catalog games is particularly contentious due to pa...

We show that a nite graph that is the inverse limit with a single surjective upper semi-continuous set valued function f : [0, 1] → 2[0,1] is either an arc or a simple triod. It is not known if there is such a simple triod.

Using the notion of formal ball, we present a few new results in the theory of quasi-metric spaces. With no specific order: every continuous Yoneda-complete quasi-metric space is sober and convergence Choquet-complete hence Baire in its d-Scott topology; for standard quasi-metric spaces, algebraicity is equivalent to having enough center points; on a standard quasi-metric space, every lower sem...

We give a lower semicontinuous type regularity condition and a closedness type one which turn out to be necessary and sufficient for the fulfillment of two different formulae involving the εsubdifferential of a perturbation function, respectively. These regularity conditions prove to be sufficient also for having formulae for the classical subdifferential of a perturbation function. Some recent...

Let L be finite CW complex. By [L] we denote extension type of L. The following generalization of Michael’s selection theorem is proved: Theorem. Consider [L] ≤ [S]. Let F be a lower semi-continuous map between polish space X and metrizable compactum Y , such that ed(X) ≤ [L], F is equi-LC collection and F (x) ∈ AE([L]) for any x ∈ X. Let A be a closed subset of X such that there exists a conti...