A semigroup characterization of well-posed linear control systems

We study the well-posedness of a linear control system $\Sigma(A,B,C,D)$ with unbounded control and observation operators. To this end we associate to our system an operator matrix $\mathcal{A}$ on a product space $\mathcal{X}^p$ and call it $p$-well-posed if $\mathcal{A}$ generates a strongly continuous semigroup on $\mathcal{X}^p$. Our approach is based on the Laplace transform and Fourier multipliers

Stability analysis of the self-phase-locked divide-by-2 optical parametric oscillator

The properties of all-optical phase-coherent frequency division by 2, based on a self-phase-locked continuous-wave (cw) optical parametric oscillator (OPO), are investigated theoretically. The coupled field equations of an OPO with intracavity quarter-wave plate are solved analytically in steady-state, yielding a condition for self-phase-locked operation. In the self-phase-locked state, two different values for the pump power at threshold are obtained. By using a linear stability analysis, it is proven that only the lower threshold value is stable, whereas the higher threshold value is unstable. The analytical investigations of the steady-state field values further reveal a twofold symmetry in phase space. The theoretical consideration is completed by a numerical analysis based on the integration of the envelopes of the three OPO fields, which allows for studying the temporal evolution of different initial values. The numerical investigation of the OPO subharmonic phases shows that the two-phase eigenstates are equivalent with respect to experimental parameters and are assumed by the self-phase-locked OPO in dependence of the initial phases of the subharmonic fields, dividing phase space into two symmetric basins of attraction

Monotonicity and Nash implementation in matching markets with contracts

We consider general two-sided matching markets, so-called matching with contracts markets as introduced by Hatfield and Milgrom (2005) and analyze (Maskin) monotonic and Nash implementable solutions. We show that for matching with contracts markets the stable correspondence is monotonic and implementable (Theorems 1 and 3). Furthermore, any solution that is Pareto efficient, individually rational, and monotonic is a supersolution of the stable correspondence (Theorem 2). In other words, the stable correspondence is the minimal solution that is Pareto efficient, individually rational, and implementable.matching with contracts, (Maskin) monotonicity, Nash implementation, stability.

Stability and Nash implementation in matching markets with couples

We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (2005, Theorem 3.3) and show that for any weakly responsive couples market there always exists a "double stable" matching, i.e., a matching that is stable for the couples market and for any associated singles market. Second, we show that for weakly responsive couples markets the associated stable correspondence is (Maskin) monotonic and Nash implementable. In contrast, the correspondence that assigns all double stable matchings is neither monotonic nor Nash implementable.matching with couples, (Maskin) monotonicity, Nash implementation, stability, weakly responsive preferences

Stability and Nash Implementation in Matching Markets with Couples

We consider two-sided matching markets with couples. First, we extend a result by Klaus and Klijn (2005, Theorem 3.3) and show that for any weakly responsive couples market there always exists a "double stable" matching, i.e., a matching that is stable for the couples market and for any associated singles market. Second, we show that for weakly responsive couples markets the associated stable correspondence is (Maskin) monotonic and Nash implementable. In contrast, the correspondence that assigns all double stable matchings is neither monotonic nor Nash implementable.Matching with Couples, (Maskin) Monotonicity, Nash Implementation, Stability, Weakly Responsive Preferences

Using an InGrid Detector to Search for Solar Chameleons with CAST

We report on the construction, operation experience, and preliminary background measurements of an InGrid detector, i.e. a MicroMegas detector with CMOS pixel readout. The detector was mounted in the focal plane of the Abrixas X-Ray telescope at the CAST experiment at CERN. The detector is sensitive to soft X-Rays in a broad energy range (0.3--10 keV) and thus enables the search for solar chameleons. Smooth detector operation during CAST data taking in autumn 2014 has been achieved. Preliminary analysis of background data indicates a background rate of $1-5\times 10^{-5}\,\mathrm{keV}^{-1}\mathrm{cm}^{-2}\mathrm{s}^{-1}$ above 2 keV and $\sim 3\times 10^{-4}\,\mathrm{keV}^{-1}\mathrm{cm}^{-2}\mathrm{s}^{-1}$ around 1 keV. An expected limit of $\beta_\gamma \lesssim 5\times 10^{10}$ on the chameleon photon coupling is estimated in case of absence of an excess in solar tracking data. We also discuss the prospects for future operation of the detector.Comment: Contributed to the 11th Patras Workshop on Axions, WIMPs and WISPs, Zaragoza, June 22 to 26, 201