On the eigenvalues of distance powers of circuits

Taking the d-th distance power of a graph, one adds edges between all pairs of vertices of that graph whose distance is at most d. It is shown that only the numbers -3, -2, -1, 0, 1, 2d can be integer eigenvalues of a circuit distance power. Moreover, their respective multiplicities are determined and explicit constructions for corresponding eigenspace bases containing only vectors with entries -1, 0, 1 are given.Comment: 14 page

Understanding informal networks in higher education institutions : theoretical concepts from a Russian and Norwegian perspective

This article discusses theoretical concepts with regard to informal networks in the Russian and Norwegian society and higher education institutions (HEI) in particular. Informal networks are operative in both public and private organizations criss-crossing social and job-related networks within these organizations. Formal and informal contacts between representatives of HEIs in the Barents region are often the result of years of close cooperation on student exchange, research projects and joint academic programmes. The aim of this study is to explain theoretical perspectives in relation to informal networks from a Norwegian and a Russian perspective. Understanding both perspectives is essential before describing informal networks across different HEIs in the Barents region and valuable if we seek to study the impact of informal networks on the formal decision-making process. Informal networks are perceived differently because the formal structure in which they operate is different. Analysing the formal structure is therefore suggested in order to better understand the different perspectives surrounding formal/informal networks.acceptedVersio

Well-balanced rr-adaptive and moving mesh space-time discontinuous Galerkin method for the shallow water equations

In this article we introduce a well-balanced discontinuous Galerkin method for the shallow water equations on moving meshes. Particular emphasis will be given on $r$-adaptation in which mesh points of an initially uniform mesh move to concentrate in regions where interesting behaviour of the solution is observed. Obtaining well-balanced numerical schemes for the shallow water equations on fixed meshes is nontrivial and has been a topic of much research. In [S. Rhebergen, O. Bokhove, J.J.W. van der Vegt, Discontinuous Galerkin finite element methods for hyperbolic nonconservative partial differential equations, J. Comput. Phys. 227 (2008) 1887–1922] we introduced a well-balanced discontinuous Galerkin method using the theory of weak solutions for nonconservative products introduced in [G. Dal Maso, P.G. LeFloch, F. Murat, Definition and weak stability of nonconservative products, J. Math. Pures Appl. 74 (1995) 483–548]. In this article we continue this approach and prove well-balancedness of a discontinuous Galerkin method for the shallow water equations on moving meshes. Numerical simulations are then performed to verify the $r$-adaptive method in combination with the space-time discontinuous Galerkin method against analytical solutions and showing its robustness on more complex problems

Early-Modern Magnetism: Uncovering New Textual Links between Leonardo Garzoni SJ (1543–1592), Paolo Sarpi OSM (1552–1623), Giambattista Della Porta (1535–1615), and the Accademia dei Lincei

William Gilbert’s work, De magnete (1600), often is referred to as the first monographic study on magnetism in the early-modern period. Recently, however, it has been argued that the Jesuit, Leonardo Garzoni, wrote an experimental study on the subject twenty years earlier and that his research influenced particularly the work of Giambattista Della Porta and Paolo Sarpi,two important protagonists in the history of studies in magnetism. However, to date, Garzoni’s authorship of an anonymous treatise in manuscript, located at the Biblioteca Ambrosiana in Milan, and taken to bear witness to his research, has been based only on circumstantial evidence. This article outlines the identification of two further manuscript copies of this treatise, which have not been studied so far. It shall be argued that the evidence contained in these manuscripts corroborates the assumption that Garzoni indeed is the author of the work that was transmitted anonymously. Moreover, it can be shown that the work was completed and prepared for print later on. These findings also allow us to argue more conclusively that Paolo Sarpi knew Garzoni’s work and passed it to Giambattista Della Porta, who bequethed his copy to the Accademia dei Lincei and thereby made it available to some of the academy’s most important members, Nicolas Claude Fabri de Peiresc and Cassiano Dal Pozzo. Finally, the dynamics of this textual transmission provide insights into how scholars approached the study of ‘magnetism’ in the early-modern period