Open Access

A level graph G = (V,E,λ) is a graph with a mapping λ : V → {1,...,k}, k ≥ 1, that partitions the vertex set V as V = V1 ∪...∪ Vk, Vj = λ-1(j), Vi ∩ Vj = ∅ for i ≠ j, such that λ(v) = λ(u) + 1 for each edge (u, v) ∈ E. Thus a level planar graph can be drawn with the vertices of every Vj, 1 ≤ j ≤ k, placed on a horizontal line, representing the level lj , and without crossings of edges, which can be drawn as straight line segments between the levels. Healy, Kuusik and Leipert gave a complete characterization of minimal forbidden subgraphs for level planar graphs (MLNP patterns) for hierarchies [4]. Minimal in terms of deleting an ar- bitrary edge leads to level planarity. A radial graph partitions the vertex set on radii, which can be pictured as concentric circles, instead of levels, lj = (j cos(α), j sin(α)), α ∈ [0,2π), mapped around a shared center, where j, 1 ≤ j ≤ k indicates the concentric circles’ radius. Comparing embeddings of radial graphs with that of level graphs we gain a further possibility to place an edge and eventually avoid edge crossings which we wish to prevent for planarity reasons. This offers a new set of minimal radial non planar subgraphs (MRNP patterns). Some of the MLNP pat- terns can be adopted as MRNP patterns while some turn out to be radial planar. But based on the radial planar MLNP patterns and the use of augmentation we can build additional MRNP patterns that did not occur in the level case. Furthermore we point out a new upper bound for the number of edges of radial planar graphs. It depends on the subgraphs in- duced between two radii. Because of the MRNP patterns these subgraphs can either consist of a forest or a cycle with several branches. Applying the bound we are able to characterize extremal radial planar graphs. Keywords: radial graphs, minimal non-planarity, extremal radial planar

The increasing public awareness of business related impacts on environmental and social well-being, be it positive or negative, are nowadays key drivers of corporate success. Internal and external business environments exert pressure and force transparency as well as responsible action in terms of resolving environmental and social impacts. In line with this, Porter and Kramer regard business behaviour that addresses societal needs and challenges, as the “new way to achieve economic success”. However, whereas some companies “remain trapped in an out-dated approach to value creation” and restrict their CSR commitment to the compliance with governmental regulation, others proactively address stakeholder needs. By addressing these needs, companies can benefit from grasping the opportunity of enhanced cost efficiency and lowered risk or gaining competitive advantages through establishing unique value propositions, in a way that meets stakeholder demands. Apart from that, CSR performance can be seen as powerful tool to successfully influence stakeholder perceptions in terms of reputation, and thus an exceptional source of value creation. In addition to this, organisations can profit from win-win-win situations related to syncretic value creation by means of partnering with stakeholders. This, however, implies expanding the focus of cost- and risk-reduction towards increasing competitiveness through creating mutual benefits for environment, society and the economy alike. Although a growing number of companies have recognised the advantages coming along with Corporate Social Responsibility engagement, the accompanying efforts have not been sufficiently mature yet. Due to the fact that many organizations apply a rather narrow and out-dated approach to value creation, they fail to achieve a balance between environmental, social and economic objectives. This, in turn, implies a restriction in their ability to exploit the full value creation potential that is related to CSR engagement. But even organisations applying a broader perspective of value creation, struggle to internalise the opportunities. This is mainly due the challenge of balancing and integrating economic and non-economic criteria. At the same time, organizations are facing the challenge of getting support from senior management and staff. Thus, in order to profit from adopting a ‘broad perspective’, firms must build a deep understanding of the benefits resulting from mutual value creation. However, the main challenge remains the systematic and strategy related integration of Corporate Social Responsibility strategies into core business processes. In respect to this, organizations have to take into account that “social and environment performance are almost certainly unique to each organization”. Thus, value creation in terms of CSR has to be understood as a highly complex set of cause-an-effect relationships among mediating variables and situational contingencies, which is too specific to rely on poorly structured and generic approaches. In brief, organisations seem to struggle establishing an understanding that does not consider environmental, social and economic benefits as mutually exclusive. Notwithstanding, that such an understanding is established the complexity of factors influencing Corporate Social Responsibility impedes to balance between economic and non-economic criteria. Furthermore, organisations have difficulties to strategically integrate, manage and measure environmental and social performance drivers as well as outcome measures.

The amount of data produced and stored in multiple types of distributed data sources is growing steadily. A crucial factor that determines whether data can be analyzed efficiently is the use of adequate visualizations. Almost simultaneously with the ongoing availability of data numerous types of visualization techniques have emerged. Since ordinary business intelligence users typically lack expert visualization knowledge, the selection and creation of visualizations can be a very time- and knowledge-consuming task. To encounter these problems an architecture that aims at supporting ordinary BI users in the selection of adequate visualizations is developed in this thesis. The basic idea is to automatically provide visualization recommendations based on the concrete BI scenario and formalized visualization knowledge. Ontologies that formalize all relevant knowledge play an important role in the developed architecture and are the key to make the knowledge machine-processable.

Polyimides rank among the most heat-resistant polymers and find application in a variety of fields, including transportation, electronics, and membrane technology. The aim of this work is to study the structural, thermal, mechanical, and gas permeation properties of polyimide based nanocomposite membranes in flat sheet configuration. For this purpose, numerous advanced techniques such as atomic force microscopy (AFM), SEM, TEM, TGA, FT-IR, tensile strength, elongation test, and gas permeability measurements were carried out. In particular, BTDA–TDI/MDI (P84) co-polyimide was used as the matrix of the studied membranes, whereas multi-wall carbon nanotubes were employed as filler material at concentrations of up to 5 wt.% All studied films were prepared by the dry-cast process resulting in non-porous films of about 30–50 μm of thickness. An optimum filler concentration of 2 wt.% was estimated. At this concentration, both thermal and mechanical properties of the prepared membranes were improved, and the highest gas permeability values were also obtained. Finally, gas permeability experiments were carried out at 25, 50, and 100 ◦C with seven different pure gases. The results revealed that the uniform carbon nanotubes dispersion lead to enhanced gas permeation properties.