A Time-Periodic Lyapunov Approach for Motion Planning of Controllable Driftless Systems on SU(n)

For a right-invariant and controllable driftless system on SU(n), we consider a time-periodic reference trajectory along which the linearized control system generates su(n): such trajectories always exist and constitute the basic ingredient of Coron's Return Method. The open-loop controls that we propose, which rely on a left-invariant tracking error dynamics and on a fidelity-like Lyapunov function, are determined from a finite number of left-translations of the tracking error and they assure global asymptotic convergence towards the periodic reference trajectory. The role of these translations is to avoid being trapped in the critical region of this Lyapunov-like function. The convergence proof relies on a periodic version of LaSalle's invariance principle and the control values are determined by numerical integration of the dynamics of the system. Simulations illustrate the obtained controls for $n=4$ and the generation of the C--NOT quantum gate.Comment: Submitte

Tendências fluviométricas nas áreas estuarinas de Goiana-Megaó e Pirapama/Jaboatão e das tabuas de maré no Porto de Suape-PE.

Os estuários são ambientes de transição entre o oceano e o continente, ocorrendo na desmbocadura dos rios, resultando na diluição da água salgada

Notes on the Two-brane Model with Variable Tension

Motivated by possible extensions of the braneworld models with two branes, we investigate some consequences of a variable brane tension using the well established results on consistency conditions. By a slight modification of the usual stress-tensor used in order to derive the braneworld sum rules, we find out some important constraints obeyed by time dependent brane tensions. In particular it is shown that the tensions of two Randall-Sundrum like branes obeying, at the same time, an Eotvos law, aggravate the fine tuning problem. Also, it is shown that if the hidden brane tension obeys an Eotvos law, then the visible brane has a mixed behavior allowing a bouncing-like period at early times while it is dominated by an Eotvos law nowadays. To finalize, we discuss some qualitative characteristics which may arise in the scope of dynamical brane tensions, as anisotropic background and branons production.Comment: 7 pages, 1 figure, accepted for publication in Physical Review

The core-periphery model with three regions

We study a 3-region core-periphery model à la Krugman and compare our results with those of the standard 2-region model. The conditions for the stability of the dispersion and concentration configurations are established. Like in the 2-region model, dispersion and concentration can be simultaneously stable. We show that the 2- region (3-region) model favors the dispersion (concentration) of economic activity. Finally, we extend the core-periphery model to the case of n regions and show that stability of concentration with 2 regions implies stability of concentration with any even number of regions.new economic geography, core-periphery