Local-Global Principle for the Baum–Connes Conjecture with Coefficients

The local-global conjecture for scheduling with non-linear cost

We consider the classical scheduling problem on a single machine, on which we need to schedule sequentially n given jobs. Every job j has a processing time pj and a priority weight wj , and for a given schedule a completion time Cj . In this paper we consider the problem of minimizing the objective value ∑ j wjC β j for some fixed constant β > 0. This non-linearity is motivated for example by t...

The Local to Global Principle

A Local-global Principle for Densities

This expository note describes a method for computing densities of subsets of Z described by infinitely many local conditions.

A Local-Global Principle for Macaulay Posets

We consider the shadow minimization problem (SMP) for cartesian powers Pn of a Macaulay poset P . Our main result is a local-global principle with respect to the lexicographic order Ln. Namely, we show that under certain conditions the shadow of any initial segment of the order Ln for n ≥ 3 is minimal iff it is so for n = 2. These conditions include such poset properties as additivity , shadow ...

Simple Counterexamples to the Local-global Principle

After Hasse had found the first example of a Local-Global principle in the 1920s by showing that a quadratic form in n variables represented 0 in rational numbers if and only if it did so in every completion of the rationals, mathematicians investigated whether this principle held in other situations. Among the first counterexamples to the Hasse principle were curves of genus 1 constructed by L...