Bracing cubic grids—a necessary condition

A Necessary Condition for Weyl-Heisenberg Frames

A necessary condition for multiple objective fractional programming

In this paper, we establish a proof for  a  necessary condition for  multiple objective fractional programming. In order to derive the set of necessary conditions, we employ an equivalent parametric problem. Also, we  present the related semi parametric model.

Necessary Condition for Path Partitioning Constraints

Given a directed graph G, the K node-disjoint paths problem consists in finding a partition of G into K node-disjoint paths, such that each path ends up in a given subset of nodes in G. This article provides a necessary condition for the K node-disjoint paths problem which combines (1) the structure of the reduced graph associated with G, (2) the structure of each strongly connected component o...

An efficient necessary condition for compatibility

Composing services makes sense only if they are compatible, i.e. composition does not lead to problems such as livelocks or deadlocks. In general, compatibility can be checked using state space explorations on any kind of formal models of services. Petri nets, one of the formal models in use, offer a rich theory for reasoning without exploring a state space. Among the techniques is the so-calle...

Necessary condition for the quantum adiabatic approximation

A gapped quantum system that is adiabatically perturbed remains approximately in its eigenstate after the evolution. We prove that, for constant gap, general quantum processes that approximately prepare the final eigenstate require a minimum time proportional to the ratio of the length of the eigenstate path to the gap. Thus, no rigorous adiabatic condition can yield a smaller cost. We also giv...