Local energy optimality of periodic sets

Periodic Sets of Integers

Local Optimality of Minimum Phase Balanced Truncation

Balanced model truncation has been considered by many authors, since it is a simple and, nevertheless, efficient model reduction technique. In many cases the approximation error may be bounded by a function of the neglected singular values. In this paper the performance of balanced truncation of state space models for ARMA processes is analysed, where the goodness of fit is measured by the asym...

Symbolic Verification with Periodic Sets

Symbolic approaches attack the state explosion problem by introducing implicit representations that allow the simultaneous manipulation of large sets of states. The most commonly used representation in this context is the Binary Decision Diagram (BDD). This paper takes the point of view that other structures than BDD’s can be useful for representing sets of values, and that combining implicit a...

Local Covering Optimality of the Leech Lattice

We show the highly non–surprising fact that the Leech lattice gives a sphere covering which is locally least dense among lattice coverings. This gives a first example of a locally optimal lattice covering having a non–simplicial Delone subdivision. Hereby, we in particular answer a question of Dickson posed in 1968. By showing that the Leech lattice is rigid, our answer is even strongest possib...

Periodic Control and the Optimality of Aircraft Cruise

ENGINEERING NOTES are short manuscripts describing new developments or important results of a preliminary nature. These Notes cannot exceed 6 manuscript pages and 3 figures; a page of text may be substituted for a figure and vice versa. After informal review by the editors, they may be published within a few months of the date of receipt. Style requirements are the same as for regular contribut...