Construction of nice nilpotent Lie groups

We illustrate an algorithm to classify nice nilpotent Lie algebras of dimension $n$ up to a suitable notion of equivalence; applying the algorithm, we obtain complete listings for $n\leq9$. On every nilpotent Lie algebra of dimension $\leq 7$, we determine the number of inequivalent nice bases, which can be $0$, $1$, or $2$. We show that any nilpotent Lie algebra of dimension $n$ has at most countably many inequivalent nice bases.Comment: v3: Condition (N3) has been changed to exclude diagrams with arrows with the same label as the starting node, this will not affect the rest of the paper or the results, since this condition was implicitly assumed through the paper. Added a final remark 3.9. Presentation improved and bibliography updated. Article 28 Pages; Tables in ancillary file 137 page

Ricci-flat and Einstein pseudoriemannian nilmanifolds

This is partly an expository paper, where the authors' work on pseudoriemannian Einstein metrics on nilpotent Lie groups is reviewed. A new criterion is given for the existence of a diagonal Einstein metric on a nice nilpotent Lie group. Classifications of special classes of Ricci-flat metrics on nilpotent Lie groups of dimension $\leq8$ are obtained. Some related open questions are presented.Comment: 30 pages, 1 figure. v2: added a comment on a recent example of an Einstein nilpotent Lie algebra of dimension 7; added a remark and a question concerning the characteristically nilpotent case; replaced the "\sigma-compatible" condition with the more general "\sigma-diagonal"; added 3 reference

The role of competencies and interests in developing complex IT-artefacts: the case of a metering system.

In this paper we aim at contributing to the ongoing debate on the relationship between artefacts and organizational structuration. Current literature emphasises the role of artefacts as mediators between interests of different categories of actors, namely between designers and users. Alternatively, it concentrates on the processes of learning and interacting between each actor and the artefacts themselves. We explore an arrangement which is not captured by these characterizations, and yet is becoming more and more common, that is situations in which complexity imposes an integration of different actors focusing on knowledge domains which are only partly overlapping. To explore these issues, we examine the dynamics surrounding the design of a complex artefact: an electronic metering system developed by a consortium of firms. The main results emerging from the case study are 1) the relevance of each actor's interests as the main rationale for explaining the technical features of the artefact; 2) the role of negotiation and consensus in determining the final shape of the artefact in term of its features; 3) the bundling/unbundling of features within the physical object as the cooperative effort rises/falls.artefacts; interests; ambiguity; competencies

Removal of electrostatic artifacts in magnetic force microscopy by controlled magnetization of the tip: application to superparamagnetic nanoparticles

Magnetic force microscopy (MFM) has been demonstrated as valuable technique for the characterization of magnetic nanomaterials. To be analyzed by MFM techniques, nanomaterials are generally deposited on flat substrates, resulting in an additional contrast in MFM images due to unavoidable heterogeneous electrostatic tip-sample interactions, which cannot be easily distinguished from the magnetic one. In order to correctly interpret MFM data, a method to remove the electrostatic contributions from MFM images is needed. In this work, we propose a new MFM technique, called controlled magnetization MFM (CM-MFM), based on the in situ control of the probe magnetization state, which allows the evaluation and the elimination of electrostatic contribution in MFM images. The effectiveness of the technique is demonstrated through a challenging case study, i.e., the analysis of superparamagnetic nanoparticles in absence of applied external magnetic field. Our CM-MFM technique allowed us to acquire magnetic images depurated of the electrostatic contributions, which revealed that the magnetic field generated by the tip is sufficient to completely orient the superparamagnetic nanoparticles and that the magnetic tip-sample interaction is describable through simple models once the electrostatic artifacts are removed

Indefinite Einstein metrics on nice Lie groups

We introduce a systematic method to produce left-invariant, non-Ricci-flat Einstein metrics of indefinite signature on nice nilpotent Lie groups. On a nice nilpotent Lie group, we give a simple algebraic characterization of non-Ricci-flat left-invariant Einstein metrics in both the class of metrics for which the nice basis is orthogonal and a more general class associated to order two permutations of the nice basis. We obtain classifications in dimension 8 and, under the assumption that the root matrix is surjective, dimension 9; moreover, we prove that Einstein nilpotent Lie groups of nonzero scalar curvature exist in every dimension $\geq 8$.Comment: 29 pages, 5 tables. v2: presentation improved, definition of sigma-compatible metrics replaced with the more general definition of sigma-diagonal metric. v3: misprints correcte