The periodic b-equation and Euler equations on the circle

In this note we show that the periodic b-equation can only be realized as an Euler equation on the Lie group Diff(S^1) of all smooth and orientiation preserving diffeomorphisms on the cirlce if b=2, i.e. for the Camassa-Holm equation. In this case the inertia operator generating the metric on Diff(S^1) is given by A=1-d^2/dx^2. In contrast, the Degasperis-Procesi equation, for which b=3, is not an Euler equation on Diff(S^1) for any inertia operator. Our result generalizes a recent result of B. Kolev.Comment: 8 page

Traveling Dark Solitons in Superfluid Fermi Gases

Families of dark solitons exist in superfluid Fermi gases. The energy-velocity dispersion and number of depleted particles completely determines the dynamics of dark solitons on a slowly-varying background density. For the unitary Fermi gas we determine these relations from general scaling arguments and conservation of local particle number. We find solitons to oscillate sinusoidally at the trap frequency reduced by a factor of $1/\sqrt{3}$. Numerical integration of the time-dependent Bogoliubov-de Gennes equation determines spatial profiles and soliton dispersion relations across the BEC-BCS crossover and proves consistent with the scaling relations at unitarity.Comment: Small changes in response to referee's comments; fig 1 revised and refs updated. Cross listed to nucl-th due to interest in the unitary Fermi ga

The Multiplicative Inverse Eigenvalue Problem over an Algebraically Closed Field

Let $M$ be a square matrix and let $p(t)$ be a monic polynomial of degree $n$. Let $Z$ be a set of $n\times n$ matrices. The multiplicative inverse eigenvalue problem asks for the construction of a matrix in $Z$ such that the product matrix $MZ$ has characteristic polynomial $p(t)$. In this paper we provide new necessary and sufficient conditions when $Z$ is an affine variety over an algebraically closed field.Comment: 9 Page

Product market competition, corporate governance and firm performance: an empirical analysis for Germany

Productivity growth has been slow in many continental European countries over the last few decades, especially in comparison with the United States. It has been argued that lack of product market competition and poor corporate governance are two of the main reasons for this phenomenon. However, predictions from theoretical models are far from unambiguous, and empirical evidence is sparse, in particular at the level of individual firms. In this paper, we aim to close this gap with an econometric analysis of firm performance in Germany. Based on a unique panel data set with detailed information on almost 400 manufacturing firms over the 1986-94 period, we find that firms operating in industries which are characterized by more intensive product market competition experience higher rates of productivity growth. We also find weak evidence for the notion that in Germany?s bank-based system of internal control, ownership concentration is harmful for productivity growth. --competition,corporate governance,productivity

Feedback Enhanced Sensitivity in Optomechanics: Surpassing the Parametric Instability Barrier

The intracavity power, and hence sensitivity, of optomechanical sensors is commonly limited by parametric instability. Here we characterize the parametric instability induced sensitivity degradation in a micron scale cavity optomechanical system. Feedback via optomechanical transduction and electrical gradient force actuation is applied to suppress the parametric instability. As a result a 5.4 fold increase in mechanical motion transduction sensitivity is achieved to a final value of $1.9\times 10^{-18}\rm m Hz^{-1/2}$.Comment: 4 pages, 4 figure