The fundamental property of strongly monotone systems, and strongly cooperative systems in particular, is the limit set dichotomy due to Hirsch: if x(0) < y(0), then either ω(x) < ω(y), or ω(x) = ω(y) and both sets consist of equilibria. We provide here a counterexample showing that this property need not hold for (non-strongly) cooperative systems.

We prove a new lower bound on the randomized decision tree complexity of monotone graph properties. For a monotone graph property $A$ of graphs on $n$ vertices, let $p=p(A)$ denote the threshold probability of $A$, namely the value of $p$ for which a random graph from $G(n,p)$ has property $A$ with probability $1/2$. Then the expected number of queries made by any decision tree for $A$ on such ...

A re exive Banach space X with a basis (ei) is constructed having the property that every monotone basis is block nitely representable in each block basis of X. x

We study systems that are monotone in a generalized sense with respect to cones of rank 2. The main result of the paper is the existence of a Poincaré-Bendixson property for some solutions of those systems.

For positive integers n and q and a monotone graph property A, we consider the two player, perfect information game WC(n, q,A), which is defined as follows. The game proceeds in rounds. In each round, the first player, called Waiter, offers the second player, called Client, q + 1 edges of the complete graph Kn which have not been offered previously. Client then chooses one of these edges which ...

According to Mack a space is countably paracompact if and only if its product with [0, 1] is δ-normal, i.e. any two disjoint closed sets, one of which is a regular Gδ-set, can be separated. In studying monotone versions of countable paracompactness, one is naturally led to consider various monotone versions of δ-normality. Such properties are the subject of this paper. We look at how these prop...

The objective of data mining is the extraction of knowledge from databases. In practice, one often encounters difficulties with models that are constructed purely by search, without incorporation of knowledge about the domain of application. In economic decision making such as credit loan approval or risk analysis, one often requires models that are monotone with respect to the decision variabl...

Monotone systems are dynamical systems for which the flow preserves a partial order. Some applications will be briefly reviewed in this paper. Much of the appeal of the class of monotone systems stems from the fact that roughly, most solutions converge to the set of equilibria. However, this usually requires a stronger monotonicity property which is not always satisfied or easy to check in appl...

A notion of “radially monotone” cut paths is introduced as an effective choice for finding a non-overlapping edge-unfolding of a convex polyhedron. These paths have the property that the two sides of the cut avoid overlap locally as the cut is infinitesimally opened by the curvature at the vertices along the path. It is shown that a class of planar, triangulated convex domains always have a rad...

In this paper, we prove some coupled fixed point theorems satisfying a Meir-Keeler type contractive condition for mappings enjoying the mixed monotone property in ordered partial metric spaces.