Bures geometry of the three-level quantum systems. II

For the eight-dimensional Riemannian manifold comprised by the three-level quantum systems endowed with the Bures metric, we numerically approximate the integrals over the manifold of several functions of the curvature and of its (anti-)self-dual parts. The motivation for pursuing this research is to elaborate upon the findings of Dittmann in his paper, "Yang-Mills equation and Bures metric" (quant-ph/9806018).Comment: thirteen pages, LaTeX, four tables, two figures, this paper supersedes math-ph/0012031, "Numerical analyses of a quantum-theoretic eight-dimensional Yang-Mills fields," which will be withdrawn. For part I of this paper (to appear in J. Geom. Phys.), see quant-ph/000806

Irreducibility of Polynomials over Global Fields is Diophantine

Given a global field $K$ and a positive integer $n$, we present a diophantine criterion for a polynomial in one variable of degree $n$ over $K$ not to have any root in $K$. This strengthens the known result that the set of non-$n$-th-powers in $K$ is diophantine when $K$ is a number field. We also deduce a diophantine criterion for a polynomial over $K$ of given degree in a given number of variables to be irreducible. Our approach is based on a generalisation of the quaternion method used by Poonen and Koenigsmann for first-order definitions of $\mathbb{Z}$ in $\mathbb{Q}$

Block Trading, Ownership Structure, and the Value of Corporate Votes

This paper shows that open market block trading can provide a link between private benefits of control enjoyed by large shareholders and the ?voting premium?, i.e. the price difference between voting and non-voting shares. We first demonstrate in a microstructure model with informed traders and short-selling constraint that the trading activity of blockholders translates into a spread between the prices of voting and non-voting shares. In contrast to the extant theory, this model can explain the voting premium in the absence of corporate takeovers. In the empirical part of the paper, we show for a comprehensive sample of German dual-class companies that large trades occur more often in voting shares than in non-voting shares, and that the block trading activity in voting shares is strongly correlated with the voting premium. Moreover, the effect of the ownership structure on the voting premium becomes insignificant once we control for the block trading activity in voting shares. --

The Scalar Curvature of the Bures Metric on the Space of Density Matrices

The Riemannian Bures metric on the space of (normalized) complex positive matrices is used for parameter estimation of mixed quantum states based on repeated measurements just as the Fisher information in classical statistics. It appears also in the concept of purifications of mixed states in quantum physics. Here we determine its scalar curvature and Ricci tensor and prove a lower bound for the curvature on the submanifold of trace one matrices. This bound is achieved for the maximally mixed state, a further hint for the quantum statistical meaning of the scalar curvature.Comment: Latex, 9 page

Decomposition Theorems and Model-Checking for the Modal μ\mu-Calculus

We prove a general decomposition theorem for the modal $\mu$-calculus $L_\mu$ in the spirit of Feferman and Vaught's theorem for disjoint unions. In particular, we show that if a structure (i.e., transition system) is composed of two substructures $M_1$ and $M_2$ plus edges from $M_1$ to $M_2$, then the formulas true at a node in $M$ only depend on the formulas true in the respective substructures in a sense made precise below. As a consequence we show that the model-checking problem for $L_\mu$ is fixed-parameter tractable (fpt) on classes of structures of bounded Kelly-width or bounded DAG-width. As far as we are aware, these are the first fpt results for $L_\mu$ which do not follow from embedding into monadic second-order logic

Selecting Comparables for the Valuation of European Firms

This paper investigates which comparables selection method generates the most precise forecasts when valuing European companies with the enterprise value to EBIT multiple. We also consider the USA as a reference point. It turns out that selecting comparable companies with similar return on assets clearly outperforms selections according to industry membership or total assets. Moreover, we investigate whether comparables should be selected from the same country, from the same region, or from all OECD members. For most European countries, choosing comparables from the 15 European Union member states yields the best forecasts. In contrast, for the UK and the US, comparables should be chosen from the same country only.comparables, selection method, valuing companies, forecasts, EBIT, industry membership, ROA