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We show that for n ≤ 5 all generic splitting types of semistable vector bundles of rank n on P^2 on which are in principle possible by the theorem of Grauert-Mülich actually occur. We prove this by constructing examples for all possible splitting types.

This paper presents a novel approach for the use of Axiomatic Design Theory in combination with agile project management methods like Scrum for an effective, structured and combined product design and development process. Agile project management methods give a guideline how to manage a project, but there is only minor assistance regarding the actual product development process itself. Axiomatic Design can be used to support these methods in this point. In concrete terms, the results of the decomposition process of this theory can be used to formulate and structure the work packages for the agile project managing process. The Independence Axiom of Axiomatic Design Theory has a substantial contribution by ensuring the independence of the work packages which can be assigned to different project team members and can be processed independently by them. The combination of the different methods not only helps to ensure a good design solution but also helps to work more agile within a project team. The here proposed approach is one part of a holistic product design and development process for changeable production units – called Adapt! – and is described within a use case in the automotive sector.

Since trends of our society are changing, the automotive industry has to handle new requirements within their production like vague quantities of production, fast integration of new technologies and an increasing variety of diversity. Therefore conventional life-cycles of production systems are broken up and re-design and changeability of complex systems have to be considered during their whole life time. Within this framework the paper proposes a novel approach to enable change during the life cycle of a production system and to enhance the usability of a re-design and change process by consistent interaction between the design and evaluation method. Thereby the focus is on the linkage of design and evaluation process to pursue a decrease of complexity and to point out the benefits which can be found by using Axiomatic Design Theory in this holistic context of the production system life-cycle. To validate the results of the paper and show up their benefits, a use case will describe and discuss the research.