Operators with smooth functional calculi

We introduce a class of (tuples of commuting) unbounded operators on a Banach space, admitting smooth functional calculi, that contains all operators of Helffer-Sj\"ostrand type and is closed under the action of smooth proper mappings. Moreover, the class is closed under tensor product of commuting operators. In general an operator in this class has no resolvent in the usual sense so the spectrum must be defined in terms of the functional calculus. We also consider invariant subspaces and spectral decompositions

One parameter regularizations of products of residue currents

We show that Coleff-Herrera type products of residue currents can be defined by analytic continuation of natural functions depending on one complex variable.Comment: 8 page

Segre numbers, a generalized King formula, and local intersections

Let $\mathcal J$ be an ideal sheaf on a reduced analytic space $X$ with zero set $Z$. We show that the Lelong numbers of the restrictions to $Z$ of certain generalized Monge-Amp\`ere products $(dd^c\log|f|^2)^k$, where $f$ is a tuple of generators of $\mathcal J$, coincide with the so-called Segre numbers of $\mathcal J$, introduced independently by Tworzewski and Gaffney-Gassler. More generally we show that these currents satisfy a generalization of the classical King formula that takes into account fixed and moving components of Vogel cycles associated with $\mathcal J$. A basic tool is a new calculus for products of positive currents of Bochner-Martinelli type. We also discuss connections to intersection theory

Living Labs as Tools for Open Innovation

This paper presents a Living Lab in Stockholm as a focal point for discussing how the Living Lab concept can be extended and used for engaging in multiorganizational open innovation. Although Living Labs have been found to have potential for driving innovation through collaboration, more research is necessary to find tangible ways of organizing this kind of collaboration. The paper is explorative and empirically induced from an ongoing development and practical implementation of a Living Lab at Stockholm-Arlanda Airport - Sweden's largest airport situated outside Stockholm. This Airport Living Lab involves a number of large industrial and academic stakeholders aiming at ensuring multi-organizational innovation delivery. Of special interest is how the Living Lab concept should evolve to continue creating conditions for user-oriented innovations through multi-organizational collaboration which would not necessarily take place otherwise. Congruent with the explorative aim of the paper it ends up in a discussion about five propositions that should be on the agenda of research and implementation for Living Lab founders in the coming years.Living Labs, Open innovation, Electronic Collaboration Tools

A note on smooth forms on analytic spaces

We prove that any smooth mapping between reduced analytic spaces induces a natural pullback operation on smooth differential forms

On non-proper intersections and local intersection numbers

Given pure-dimensional (generalized) cycles $\mu_1$ and $\mu_2$ on a complex manifold $Y$ we introduce a product $\mu_1\diamond_{Y} \mu_2$ that is a generalized cycle whose multiplicities at each point are the local intersection numbers at the point. % If $Y$ is projective, then given a very ample line bundle $L\to Y$ we define a product \mu_1\bl \mu_2 whose multiplicities at each point also coincide with the local intersection numbers. In addition, provided that $\mu_1$ and $\mu_2$ are effective, this product satisfies a B\'ezout inequality. If i\colon Y\to \Pk^N is an embedding such that i^*\Ok(1)=L, then \mu_1\bl \mu_2 can be expressed as a mean value of St\"uckrad-Vogel cycles on \Pk^N. There are quite explicit relations between \di_Y and \bl

Comparison and Evaluation of Multiple Users' Usage of the Exposure and Risk Tool: Stoffenmanager 5.1.

Stoffenmanager is an exposure and risk assessment tool that has a control banding part, with risk bands as outcome and a quantitative exposure assessment part, with the 90th percentile of the predicted exposure as a default outcome. The main aim of the study was to investigate whether multiple users of Stoffenmanager came to the same result when modelling the same scenarios. Other aims were to investigate the differences between outcomes of the control banding part with the measured risk quota and to evaluate the conservatism of the tool by testing whether the 90th percentiles are above the measured median exposures. We investigated airborne exposures at companies in four different types of industry: wood, printing, metal foundry, and spray painting. Three scenarios were modelled and measured, when possible, at each company. When modelled, 13 users visited each company on the same occasion creating individual assessments. Consensus assessments were also modelled for each scenario by six occupational hygienists. The multiple users' outcomes were often spread over two risk bands in the control banding part, and the differences in the quantitative exposure outcomes for the highest and lowest assessments per scenario varied between a factor 2 and 100. Four parameters were difficult for the users to assess and had a large impact on the outcome: type of task, breathing zone, personal protection, and control measures. Only two scenarios had a higher measured risk quota than predicted by the control banding part, also two scenarios had slightly higher measured median exposure value than modelled consensus in the quantitative exposure assessment part. Hence, the variability between users was large but the model performed well