We consider a congested traffic network where users behave according to the Wardrop equilibrium principle, but data are uncertain and only known through their probability distributions. Within this framework, we propose stochastic model analyse performance, which allows for nonlinear cost functions. The effectiveness of our approach is shown numerical experiments on medium-size networks.

A general notion of completely monotone functionals on an ordered Banach algebra B into a proper H*-algebra A with an integral representation for such functionals is given. As an application of this result we have obtained a characterization for the generalized completely continuous monotone functions on weighted foundation semigroups. A generalized version of Bochner’s theorem on foundation se...

A monotone seminorm p on a Riesz space L is called a Fatou if p(a„)tp(«) holds for every u e L and sequence {u„} in L satisfying 0 < un\u. A monotone seminorm p on L is called strong Fatou if p(u )tp(u) holds for every u e L and directed system {«„} in L satisfying 0 < «„tu. In this paper we determine those Riesz spaces L which have the property that, for any monotone seminorm p on L, the large...

In this paper, Lebesgue decomposition type theorems for non-additive measure are shown under the conditions of null-additivity, converse null-additivity, weak null-additivity and σ-null-additivity, etc.. In our discussion, the monotone continuity of set function is not required.

This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance. The contraction property determines the asymptotic behavior of the network, which is either finite-time synchronization or asymptotic convergence to a splay state.

We prove that, under a mild summability condition on the growth of the derivative on critical orbits any piecewise monotone interval map possibly containing discontinuities and singularities with infinite derivative (cusp map) admits an ergodic invariant probability measures which is absolutely continuous with respect to Lebesgue measure.

Sets of points are called separable if their convex hulls are disjoint. We suggest a technique for optimally partitioning of a set N into two separable subsets, N,, N2. We assume that a monotone measure, p, is defined over the subsets of N, and the objective is to minimize

It is proved that the stochastic porous media equation in a bounded domain of R, with multiplicative noise, with a monotone nonlinearity of polynomial growth has a unique nonnegative solution in H−1 (in particular is nonnegative measure-valued), provided the initial data is in H−1 and nonnegative. AMS subject Classification 2000: 76S05, 60H15.

In this note, we discuss when the concave integral coincides with the panintegral with respect to the standard arithmetic operations + and ·. The subadditivity of the underlying monotone measure is one sufficient condition for this equality. We show also another sufficient condition, which, in the case of finite spaces, is necessary, too.