The minisymposium aims at presenting recent research in the area of numerical methods for time‐dependent partial differential equations. The topics of time integration, space discretizations, and convergence issues like that of convergence to a steady state are considered as well as new algorithms for detecting and treating singularities like shock waves.

In 1998 it was discovered that the requirement that a Hamiltonian be Dirac Hermitian (H = H†) can be weakened and generalized to the requirement that a Hamiltonian be PT symmetric ([H,PT] = 0); that is, invariant under combined space reflection and time reversal. Weakening the constraint of Hermiticity allows one to consider new kinds of physically acceptable Hamiltonians and, in effect, it amounts to extending quantum mechanics from the real (Hermitian) domain into the complex domain. Much work has been done on the analysis of various PT‐symmetric quantum‐mechanical models. However, only very little analysis has been done on PT‐symmetric quantum‐field‐theoretic models. Here, we describe some of what has been done in the context of PT‐symmetric quantum field theory and describe some possible fundamental applications.

Views Icon Views Article contents Figures & tables Video Audio Supplementary Data Peer Review Share Icon Share Twitter Facebook Reddit LinkedIn Tools Icon Tools Reprints and Permissions Cite Icon Cite Search Site Citation Sebastian Reich; Ensemble Kalman and H∞ Filters. AIP Conf. Proc. 30 September 2010; 1281 (1): 19–22. https://doi.org/10.1063/1.3498332 Download citation file: Ris (Zotero) Reference Manager EasyBib Bookends Mendeley Papers EndNote RefWorks BibTex toolbar search Search Dropdown Menu toolbar search search input Search input auto suggest filter your search All ContentAIP Publishing PortfolioAIP Conference Proceedings Search Advanced Search |Citation Search

In this paper we define a family of centrality measures for directed social networks from a game theoretical point of view. We follow the line started with our previous work (Gómez et al.., 2003). Besides the definition, we obtain both, a characterization and an additive decomposition of the measures.

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