Narrow Results

In this paper, we describe the recursion relations between two parameter HOMFLY and Kauffman polynomials of framed links. These relations correspond to embeddings of quantized universal enveloping algebras. The relation corresponding to embeddings g_n ⊃ g_k × sl_n-k where g_n is either so_2n+1, so_2n or sp_2n is new.

Industrial networks offer a prime example of the tension between system stability and change. Change is necessary as a response to environmental variation, whereas stability provides the underpinning for long-term investment and the exploitation of efficiencies. Whilst one of the key themes in industrial network research has been the dynamics of change, relatively little work, empirical or theoretical, has been devoted to the dynamics of stability. This paper presents a new approach to this problem by using Boolean networks, which were originally devised by Stuart Kauffman as an abstract model of genetic networks. The elements in the model are connected by rules of Boolean logic, and a novel aspect of this research is that the elements represent the industrial network exchanges rather than stock entities (the organizations). The model structure consists of interactions between the exchanges, and the results represent the pattern of exchange episodes. A total of 42 networks were modeled and the dynamics analyzed in detail, and five of these cases are presented in this paper. The models produced realistic behavior and provided some insights into the reasons for stability in industrial networks.