Top-up fairly according to means

Convexity According to Means

Given a function f : I → J and a pair of means M and N, on the intervals I and J respectively, we say that f is MN -convex provided that f (M(x, y)) N(f (x), f (y)) for every x , y ∈ I . In this context, we prove the validity of all basic inequalities in Convex Function Theory, such as Jensen’s Inequality and the Hermite-Hadamard Inequality. Mathematics subject classification (2000): 26A51, 26D...

Derivations of UP-algebras by means of UP-endomorphisms

The notion of $f$-derivations of UP-algebras is introduced, some useful examples are discussed, and related properties are investigated. Moreover, we show that the fixed set and the kernel of $f$-derivations are UP-subalgebras of UP-algebras,and also give examples to show that the two sets are not UP-ideals of UP-algebras in general.

How to mark fairly

A network router that marks packets to signal congestion should do so fairly. We propose a deenition of fairness, using ideas from eeective band-width theory and economics. Our deenition measures both the level of congestion at a router and the contribution of each ow to that congestion, taking into account the ow's burstiness. We then use large deviations to analyse marking algorithms such as ...

How to Divide Things Fairly

We analyze a simple sequential algorithm (SA) for allocating indivisible items that are strictly ranked by n ≥ 2 players. It yields at least one Pareto-optimal allocation which, when n = 2, is envy-free unless no envy-free allocation exists. However, an SA allocation may not be maximin or Borda maximin—maximize the minimum rank, or the Borda score, of the items received by a player. Although SA...

Bottom-up, top-down