We prove a ratio ergodic theorem for non-singular free Z and R actions, along balls in an arbitrary norm. Using a Chacon-Ornstein type lemma the proof is reduced to a statement about the amount of mass of a probability measure that can concentrate on (thickened) boundaries of balls in R. The proof relies on geometric properties of norms, including the Besicovitch covering lemma and the fact tha...

Cluster density maximization and (maximal) cluster covering have emerged as ordering principles for quasicrystalline structures. The concepts behind these ordering principles are reviewed and illustrated with several examples. For two examples, Gummelt’s aperiodic decagon model and a cluster model for octagonal Mn–Si–Al quasicrystals, these ordering principles can enforce perfectly ordered, qua...

given a non-abelian finite group $g$, let $pi(g)$ denote the set of prime divisors of the order of $g$ and denote by $z(g)$ the center of $g$. thetextit{ prime graph} of $g$ is the graph with vertex set $pi(g)$ where two distinct primes $p$ and $q$ are joined by an edge if and only if $g$ contains an element of order $pq$ and the textit{non-commuting graph} of $g$ is the graph with the vertex s...

The Maximal Covering Location Problem (MCLP) maximizes the population that has a facility within a maximum travel distance or time. Numerous extensions have been proposed to enhance its applicability, like the probabilistic model for the maximum covering location-allocation with constraint in waiting time or queue length for congested systems, with one or more servers per service center. In thi...

To improve the application of the maximal covering location problem (MCLP), several capacitated MCLP models were proposed to consider the capacity limits of facilities. However, most of these models assume only one fixed capacity level for the facility at each potential site. This assumption may limit the application of the capacitated MCLP. In this article, a modular capacitated maximal coveri...

In a routing framework, it might not be viable to visit every single customer separately due to resource limitations or e ciency concerns. In such cases, utilizing the notion of coverage; i.e., satisfying the demand of multiple customers by visiting a single customer location, may be advantageous. With this motivation, we study the time constrained maximal covering salesman problem (TCMCSP) in ...

In this paper, we improve the best-known upper bound on the size of maximal tournament codes, and solve the related problem of edge-covering a complete graph with a minimum number of bipartite graphs of bounded size. Tournament codes are sets of {0,1,∗} strings closely related to self-synchronizing codes. We improve the current asymptotic upper bound on the size of a length-k tournament code (g...

The algebraic monoid structure of an incidence algebra is investigated. We show that the multiplicative alone determines automorphisms algebra. present a formula expresses complexity with respect to two sided action its maximal torus in terms zeta polynomial poset. In addition, we characterize finite (connected) posets whose monoids have $$\le 1$$ . Finally, determine covering relations adheren...

Aalto University, P.O. Box 11000, FI-00076 Aalto www.aalto.fi Author Esa A. Seuranen Name of the doctoral dissertation Computational Methods in Codes and Games Publisher School of Electrical Engineering Unit Department of Communications and Networking Series Aalto University publication series DOCTORAL DISSERTATIONS 119/2011 Field of research Information Theory Manuscript submitted 30 May 2011 ...