We provide sufficient conditions for a monotone function with finite set of outcomes to be cyclically monotone. Using these conditions, we show that any defined on the domain gross substitutes is The result also extends generalized and complements.

A model of coherent upper conditional prevision for bounded random variables is proposed in a metric space. It is defined by the Choquet integral with respect to Hausdorff outer measure if the conditioning event has positive and finite Hausdorff outer measure in its Hausdorff dimension. Otherwise, when the conditioning event has Hausdorff outer measure equal to zero or infinity in its Hausdorff...

This paper provides an expository introduction to monotone and near-monotone biochemical network structures. Monotone systems respond in a predictable fashion to perturbations, and have very robust dynamical characteristics. This makes them reliable components of more complex networks, and suggests that natural biological systems may have evolved to be, if not monotone, at least close to monoto...

Abstract. We study the asymptotic behavior of solutions to stochastic evolution equations with monotone drift and multiplicative Poisson noise in the variational setting, thus covering a large class of (fully) nonlinear partial differential equations perturbed by jump noise. In particular, we provide sufficient conditions for the existence, ergodicity, and uniqueness of invariant measures. Furt...

In this paper, by using a monotone iterative technique in the presence of lower and upper solutions, we discuss the existence of solutions for a new system of nonlinear mixed type implicit impulsive integro-differential equations in Banach spaces. Under wide monotonicity conditions and the noncompactness measure conditions, we also obtain the existence of extremal solutions and a unique solutio...

In this paper, some hybrid fixed point theorems for the right monotone increasing multi-valued mappings in ordered Banach spaces are proved via measure of noncompactness and they are further applied to the neutral functional nonconvex differential inclusions involving discontinuous multi-functions for proving the existence results under mixed Lipschitz, compactness and right monotonicity condit...

The Fréchet distance is a distance measure for parameterized curves or surfaces. Using a discrete approximation, we show that for triangulated surfaces it is upper semi-computable, i.e., there is a non-halting Turing machine which produces a monotone decreasing sequence of rationals converging to the result. It follows that the decision problem, whether the Fréchet distance of two given surface...

In this paper, we introduce a kernel for monotone data derived from the Choquet integral with its underlying fuzzy measure. While a naïve computation of this kernel has a complexity that is exponential in the number of data attributes, we propose a more efficient approach with quadratic time complexity. Kernel PCA and SVM classification are employed to illustrate characteristics and benefits of...

We prove L1{contraction principle and uniqueness of solutions for quasilinear elliptic{parabolic equations of the form @t[b(u)] div[a(ru; b(u))] + f(b(u)) = 0 in (0; T ) ; where b is monotone nondecreasing and continuous. We only assume that u is a weak solution of nite energy (see [1]). In particular, we do not suppose that the distributional derivative @t[b(u)] is a bounded Borel measure or a...