Open Access

This paper presents a series of flow and temperature measurements on the principal heat network of :metabolon in Lindlar, Germany. These measurements intend to show the behaviour of the system on specific production areas of :metabolon for future monitoring and optimisation purposes. Such measurements allow the analysis of the system’s heat flow through the network, which showed that losses exist, some areas. The results demonstrate successfully that the temperature and flow changes deserve more detailed and fixed monitoring in specific areas to help the user decide the optimum measuring point.

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.

Resilience in the urban context can be described as a continuum of absorptive, adaptive, and transformative capacities. The need to move toward a sustainable future and bounce forward after any disruption has led recent urban resilience initiatives to engage with the concept of transformative resilience when and where conventional and top-down resilience initiatives are less likely to deliver effective strategies, plans, and implementable actions. Transformative resilience pathways emphasize the importance of reflexive governance, inclusive co-creation of knowledge, innovative and collaborative learning, and self-organizing processes. To support these transformative pathways, considering techno-social co-evolution and digital transformation, using new data sources such as Volunteered Geographic Information (VGI) and crowdsourcing are being promoted. However, a literature review on VGI and transformative resilience reveals that a comprehensive understanding of the complexities and capacities of utilizing VGI for transformative resilience is lacking. Therefore, based on a qualitative content analysis of available resources, this paper explores the key aspects of using VGI for transformative resilience and proposes a comprehensive framework structured around the identified legal, institutional, social, economic, and technical aspects to formalize the process of adopting VGI in transformative resilience initiatives.