Structure of shape derivatives around irregular domains and applications

In this paper, we describe the structure of shape derivatives around sets which are only assumed to be of finite perimeter in $\R^N$. This structure allows us to define a useful notion of positivity of the shape derivative and we show it implies its continuity with respect to the uniform norm when the boundary is Lipschitz (this restriction is essentially optimal). We apply this idea to various cases including the perimeter-type functionals for convex and pseudo-convex shapes or the Dirichlet energy of an open set

Non-classical field state stabilization in a cavity by reservoir engineering

We propose an engineered reservoir inducing the relaxation of a cavity field towards non-classical states. It is made up of two-level atoms crossing the cavity one at a time. Each atom-cavity interaction is first dispersive, then resonant, then dispersive again. The reservoir pointer states are those produced by an effective Kerr Hamiltonian acting on a coherent field. We thereby stabilize squeezed states and quantum superpositions of multiple coherent components in a cavity having a finite damping time. This robust method could be implemented in state-of-the-art experiments and lead to interesting insights into mesoscopic quantum state superpositions and into their protection against decoherence.Comment: submitted to Phys.Rev.Let

The Long-run Performance of Seasoned Equity Offerings with rights evidence from the Swiss Market

We examine the long-run performance of firms that offer seasoned equity on the Swiss market. Swiss firms use offerings with rights to raise new equity and they can issue three types of securities. Moreover, the tax law has for some firms the effect of increasing the issuing frequency. We find that most SEOs are small as a percentage of the firm’s market capitalisation. The leverage ratios change often (up and down) during a three-period post-SEO horizon. The long-run abnormal returns are insignificant relative to size and book-to-market matching portfolios. These findings are corroborated by the fact that a portfolio of issuing firms do not exhibit a risk adjusted (Fama and French three factor model and Time-varying beta) abnormal performance. These findings are in accordance with the growing literature showing that the US SEOs do no more have abnormal negative performance. Finally, we show that Swiss firms have an incentive to use SEOs as a substitute to stock dividends. This particular feature help to explain the high frequency of SEOs in Switzerland before 1992.

Global well-posedness of a conservative relaxed cross diffusion system

We prove global existence in time of solutions to relaxed conservative cross diffusion systems governed by nonlinear operators of the form $u_i\to \partial_tu_i-\Delta(a_i(\tilde{u})u_i)$ where the $u_i, i=1,...,I$ represent $I$ density-functions, $\tilde{u}$ is a spatially regularized form of $(u_1,...,u_I)$ and the nonlinearities $a_i$ are merely assumed to be continuous and bounded from below. Existence of global weak solutions is obtained in any space dimension. Solutions are proved to be regular and unique when the $a_i$ are locally Lipschitz continuous

Precision performances of terminal conditions for short time horizons forward-looking systems

In this paper, we investigate both theoretically and empirically the numerical bias due to the truncation of structurally infinite time forward-Iooking models, by the means of various terminal conditions. We shed light on the difficulties of numerical control using the latter instrurnents, and recornrnend a prior investigation of the individual dynamics generated by each variable of the models under consideration