Piecewise convex transformations with no finite invariant measure

NONINVERTIBLE TRANSFORMATIONS ADMITTING NO ABSOLUTELY CONTINUOUS ct-FINITE INVARIANT MEASURE

We study a family of H-to-1 conservative ergodic endomorphisms which we will show to admit no rj-finite absolutely continuous invariant measure. We exhibit recurrent measures for these transformations and study their ratio sets; the examples can be realized as C°° endomorphisms of the 2-torus.

network optimization with piecewise linear convex costs

the problem of finding the minimum cost multi-commodity flow in an undirected and completenetwork is studied when the link costs are piecewise linear and convex. the arc-path model and overflowmodel are presented to formulate the problem. the results suggest that the new overflow model outperformsthe classical arc-path model for this problem. the classical revised simplex, frank and wolf and a ...

Identifying Q-processes with a given Finite Μ-invariant Measure

Let Q = (qij , i, j ∈ S) be a stable and conservative Q-matrix over a state space S consisting of an irreducible (transient) class C and a single absorbing state 0, which is accessible fromC. Suppose thatQ admits a finiteμ-subinvariant measure m = (mj , j ∈ C) on C. We consider the problem of identifying all Q-processes for which m is a μ-invariant measure on C.

Non convex technologies and economic efficiency measure with imprecise data

Complexity of piecewise convex transformations in two dimensions, with applications to polygonal billiards

ABSTRACT We introduce the class of piecewise convex transformations, and study their complexity. We apply the results to the complexity of polygonal billiards on surfaces of constant curvature.We introduce the class of piecewise convex transformations, and study their complexity. We apply the results to the complexity of polygonal billiards on surfaces of constant curvature.