The weak compactification of locally compact groups

We further investigate the weak topology generated by the irreducible unitary representations of a group G. A deep result due to Ernest [13] and Hughes [22] asserts that every weakly compact subset of a locally compact (LC) group G is compact in the LC-topology, generalizing thereby a previous result of Glicksberg [19] for abelian locally compact (LCA) groups. Here, we first survey some recent findings on the weak topology and establish some new results about the preservation of several compact-like properties when going from the weak topology to the original topology of LC groups. Among others, we deal with the preservation of countable compactness, pseudocompactness and functional boundedness.Funding for open access charge: CRUE-Universitat Jaume

Dual topologies on non-abelian groups

The notion of locally quasi-convex abelian group, introduced by Vilenkin, is extended to maximally almost periodic non-necessarily abelian groups. For that purpose, we look at certain bornologies that can be defined on the set rep(G)rep(G) of all finite dimensional continuous representations on a topological group G in order to associate well behaved group topologies (dual topologies) to them. As a consequence, the poset of all Hausdorff totally bounded group topologies on a group G is shown to be isomorphic to the poset of certain special subsets of rep(Gd)rep(Gd). Moreover, generalizing some ideas of Namioka, we relate the structural properties of the dual topological groups to topological properties of the bounded subsets belonging to the associate bornology. In like manner, certain type of bornologies that can be defined on a group G allow one to define canonically associate uniformities on the dual object View the MathML sourceGˆ. As an application, we prove that if for every dense subgroup H of a compact group G we have that if View the MathML sourceHˆ and View the MathML sourceGˆ are uniformly isomorphic, then G is metrizable. Thereby, we extend to non-abelian groups some results previously considered for abelian topological groups

Modeling RTL Fault Models Behavior to Increase the Confidence on TSIM-based Fault Injection

Future high-performance safety-relevant applications require microcontrollers delivering higher performance than the existing certified ones. However, means for assessing their dependability are needed so that they can be certified against safety critical certification standars (e.g ISO26262). Dependability assessment analyses performed at high level of abstraction inject single faults to investigate the effects these have in the system. In this work we show that single faults do not comprise the whole picture, due to fault multiplicities and reactivations. Later we prove that, by injecting complex fault models that consider multiplicities and reactivations in higher levels of abstraction, results are substantially different, thus indicating that a change in the methodology is needed.The research leading to these results has received funding from the Ministry of Science and Technology of Spain under contract TIN2015-65316-P and the HiPEAC Network of Excellence. Carles Hern´andez is jointly funded by the Spanish Ministry of Economy and Competitiveness (MINECO) and FEDER funds through grant TIN2014-60404-JIN. Jaume Abella has been partially supported by the MINECO under Ramon y Cajal postdoctoral fellowship number RYC-2013-14717.Postprint (author's final draft

Computing worst-case contention delays for networks on chip

Computing performance needs in domains such as automotive, avionics, railway, and space are on the rise. This is fueled by the trend towards implementing an increasing number of product functionalities in software that ends up managing huge amounts of data and implementing complex artificial-intelligence functionalities [1], [2]. Manycores are able to satisfy, in a cost-efficient manner, the computing needs of embedded real-time industry [3], [4]. In this line, building as much as possible on manycore solutions deployed in the high-performance (mainstream) market [5], [6], contributes to further reduce costs and increase availability. However, commercial off the shelf (COTS) manycores bring several challenges for their adoption in the critical embedded market. One of those is deriving timing bounds to tasks’ execution times as part of the overall timing validation and verification processes [7]. In particular, the network-on-chip (NoC) has been shown to be the main resource in which contention arises, and hence hampers deriving tight bounds to the timing of tasks [8]

A countable free closed non-reflexive subgroup of Zc

We prove that the group G = Hom(ZN, Z) of all homomorphisms from the Baer-Specker group ZN to the group Z of integer numbers endowed with the topology of pointwise convergence contains no infinite compact subsets. We deduce from this fact that the second Pontryagin dual of G is discrete. As G is non-discrete, it is not reflexive. Since G can be viewed as a closed subgroup of the Tychonoff product Zc of continuum many copies of the integers Z, this provides an example of a group described in the title, thereby resolving a problem by Galindo, Recoder-N´u˜nez and Tkachenko. It follows that an inverse limit of finitely generated (torsion-)free discrete abelian groups need not be reflexive

Subgroups of direct products closely approximated by direct sums

Let I be an infinite Π set, fGi : i 2 Ig be a family of (topological) groups and G = i∈I Gi be its direct product. For J I, pJ : G ! Π j∈J Gj denotes the projection. We say that a subgroup H of G is: (i) uniformly controllable in G provided that for every finite set J I there exists a finite set K I such that pJ (H) = pJ (H \ ⊕ i∈K Gi); (ii) controllable in G provided that pJ (H) = pJ (H \⊕ i∈I Gi) for every finite set J I; (iii) weakly controllable in G if H \⊕ i∈I Gi is dense in H, when G is equipped with the Tychonoff product topology. One easily proves that (i)!(ii)!(iii). We thoroughly investigate the question as to when these two arrows can be reversed. We prove that the first arrow can be reversed when H is compact, but the second arrow cannot be reversed even when H is compact. Both arrows can be reversed if all groups Gi are finite. When Gi = A for all i 2 I, where A is an abelian group, we show that the first arrow can be reversed for all subgroups H of G if and only if A is finitely generated. Connections with coding theory are highlighted