Norm attaining operators and pseudospectrum

It is shown that if $11$, the operator $I+T$ attains its norm. A reflexive Banach space $X$ and a bounded rank one operator $T$ on $X$ are constructed such that $\|I+T\|>1$ and $I+T$ does not attain its norm.

The level sets of the resolvent norm and convexity properties of Banach spaces

We construct a bounded linear operator on a separable, reflexive and strictly convex Banach space whose resolvent norm is constant in a neighbourhood of zero.

Cloning and characterization of the Burkholderia vietnamiensis norM gene encoding a multi-drug efflux protein

Polymyxin B-sensitive mutants in Burkholderia vietnamiensis (Burkholderia cepacia genomovar V) were generated with a mini-Tn5 encoding tetracycline resistance. One of the transposon mutants had an insertion in the norM gene encoding a multi-drug efflux protein. Expression of B. vietnamiensis norM in an Escherichia coli acrAB deletion mutant complemented its norfloxacin hypersensitivity, indicating that the protein functions in drug efflux. However, no effect on antibiotic sensitivity other than sensitivity to polymyxin B was observed in the B. vietnamiensis norM mutant. We demonstrate that increased polymyxin sensitivity in B. vietnamiensis was associated with the presence of tetracycline in the growth medium, a phenotype that was partially suppressed by expression of the norM gene.

Distinguished algebraic semantics for t-norm based fuzzy logics:Methods and algebraic equivalencies

This paper is a contribution to Mathematical fuzzy logic, in particular to the algebraic study of t-norm based fuzzy logics. In the general framework of propositional core and ?-core fuzzy logics we consider three properties of completeness with respect to any semantics of linearly ordered algebras. Useful algebraic characterizations of these completeness properties are obtained and their relations are studied. Moreover, we concentrate on five kinds of distinguished semantics for these logics-namely the class of algebras defined over the real unit interval, the rational unit interval, the hyperreals (all ultrapowers of the real unit interval), the strict hyperreals (only ultrapowers giving a proper extension of the real unit interval) and finite chains, respectively-and we survey the known completeness methods and results for prominent logics. We also obtain new interesting relations between the real, rational and (strict) hyperreal semantics, and good characterizations for the completeness with respect to the semantics of finite chains. Finally, all completeness properties and distinguished semantics are also considered for the first-order versions of the logics where a number of new results are proved. © 2009 Elsevier B.V. All rights reserved.

A multiagent network for peer norm enforcement

In a multiagent system where norms are used to regulate the actions agents ought to execute, some agents may decide not to abide by the norms if this can benefit them. Norm enforcement mechanisms are designed to counteract these benefits and thus the motives for not abiding by the norms. In this work we propose a distributed mechanism through which agents in the multiagent system that do not abide by the norms can be ostracised by their peers. An ostracised agent cannot interact anymore and looses all benefits from future interactions. We describe a model for multiagent systems structured as networks of agents, and a behavioural model for the agents in such systems. Furthermore, we provide analytical results which show that there exists an upper bound to the number of potential norm violations when all the agents exhibit certain behaviours. We also provide experimental results showing that both stricter enforcement behaviours and larger percentage of agents exhibiting these behaviours reduce the number of norm violations, and that the network topology influences the number of norm violations. These experiments have been executed under varying scenarios with different values for the number of agents, percentage of enforcers, percentage of violators, network topology, and agent behaviours. Finally, we give examples of applications where the enforcement techniques we provide could be used.

Questions of 'h' in Northern Ireland: Breathing New Life on the Aspiration Theory

This paper considers existing ideas concerning pronunciation of the letter name for (LNH) in Northern Irish English (NIE). Traditionally, the status of LNH realisation as an ethnic marker has gone unquestioned: Catholics are thought to say [het&Mac186;] while the Protestant norm is assumed to be [etS]. The phonetic difference between these realisations is consistently described as word-initial aspiration versus non-aspiration, with aspiration attributed exclusively to Irish language influence. Here, we show that an explanation based on aspiration alone is phonologically unsatisfying and question whether aspiration is, in fact, an Irish language or ethnically dictated phenomenon. It is further suggested here that the overwhelming stigmatisation of LNH realisation may be responsible for blocking a potential sound change in NIE. While this paper is not intended as a detailed account of ethnolinguistic differences in NI phonology, it engages critically with the over-simplistic and widespread notion that LNH realisation is a result of transfer from the Irish language to the English used by Catholics in Northern Ireland.