The classes of monotone or convex (and necessarily monotone) densities on ℝ(+) can be viewed as special cases of the classes of k-monotone densities on ℝ(+). These classes bridge the gap between the classes of monotone (1-monotone) and convex decreasing (2-monotone) densities for which asymptotic results are known, and the class of completely monotone (∞-monotone) densities on ℝ(+). In this pap...

Strongly monotone systems of ordinary differential equations which have a certain translationinvariance property are shown to have the property that all projected solutions converge to a unique equilibrium. This result may be seen as a dual of a well-known theorem of Mierczyński for systems that satisfy a conservation law. As an application, it is shown that enzymatic futile cycles have a globa...

Topology control is the problem of assigning power levels to the nodes of an ad hoc network so as to create a specified network topology while minimizing the energy consumed by the network nodes. While considerable theoretical attention has been given to the issue of topology control in wireless ad hoc networks, all of that prior work has concerned stationary networks. When the nodes are mobile...

A regression is a function g from a partially ordered set to itself such that g(x)~_x for all z. A monotone k-chain is a chain of k elements xx<x2< . . . . .xk such that g(xO~g(x~)~_...~_g(xk). If a partial order has sufficiently many elements compared to the size of its largest antichain, every regression on it will have a monotone (k+ l)-chain. Fixing w, let f(w, k) be the smallest number suc...

Each clone C on a fixed base set A determines a quasiorder on the set of all operations on A by the following rule: f is a C-minor of g if f can be obtained by substituting operations from C for the variables of g. By making use of a representation of Boolean functions by hypergraphs and hypergraph homomorphisms, it is shown that a clone C on {0, 1} has the property that the corresponding C-min...

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.

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