Stabilization of high-order solutions of the cubic Nonlinear Schrodinger Equation

In this paper we consider the stabilization of non-fundamental unstable stationary solutions of the cubic nonlinear Schrodinger equation. Specifically we study the stabilization of radially symmetric solutions with nodes and asymmetric complex stationary solutions. For the first ones we find partial stabilization similar to that recently found for vortex solutions while for the later ones stabilization does not seem possible

An operadic proof of Baez-Dolan stabilization hypothesis

We prove a stabilization theorem for algebras of n-operads in a monoidal model category. It implies a version of Baez-Dolan stabilization hypothesis for Rezk's weak n-categories and some other stabilization results.Comment: 14 pages, the paper is now in its final form accepted for publication in Proceedings of AM

An Unemployment Re-Insurance Scheme for the Eurozone? Stabilizing and Redistributive Effects: Summary of the study

The study summarized here is the first analysis to evaluate an unemployment re-insurance scheme for the euro area as regards potential stabilizing and redistributive effects. The results show that such a scheme can stabi- lize economies in the euro area and could thus contribute to cushioning large labor market shocks. More specifically, this study runs a series of simulations to show that an unemployment re-insurance scheme would have had a counter-cyclical effect in all euro area countries during the simulation period and would not have led to permanent transfer payments. The novel feature of the study is that it separates the stabilization effects of the unemployment re-insurance scheme into two channels relevant to the current political debate: First, it indicates the potential for stabilization through payments between countries (so-called interregional stabilization). Stabili- zation through this channel arises because labor market fluctuations differ across countries, i.e., shocks are not completely "symmetric". Second, the study estimates the so-called intertemporal stabilization potential. This channel describes the stabilization that member states can achieve when taking out loans in times of crisis and repaying them in good times. Thus, this channel is indicative of the stabilization potential of loan-based re-insur- ance models as set out in the BMF proposal. The distinction between the two stabilization channels is crucial for assessing the possible value added of different reform options. Intertemporal stabilization can be achieved through national debt or through financial assistance programs of the European Stability Mechanism (ESM) in the case of loss of market access. By contrast, interregional stabilization only arises by pooling contribution pay- ments within a common fund and disbursing transfers from it if a member state is hit by a large labor market shock

Stabilization of behaviours

In this paper we characterize the set of all restrictions on the behaviour of a plant that shape the characteristic polynomial of the closed-loop system. These control laws include both classical feedback laws and singular feedback laws. One of the results is the behavioural version of the Youla-Jabr-Bongiorno-Kucera-parameterization of all stabilizing control laws for a given plant. We also study robust stability, deriving the real and complex stability radius for systems described in kernel representation. Finally we characterize the set of all control laws that make the stability radius greater than or equal to some desired leve