The largest step path following algorithm for monotone linear complementarity problems

Path-following algorithms take at each iteration a Newton step for approaching a point on the central path, in such a way that all the iterates remain in a given neighborhood of that path. This paper studies the case in which each iteration uses a pure Newton step with the largest possible reduction in complementarity measure (duality gap). This algorithm is known to converge superlinearly in objective values. We show that with the addition of a computationally trivial safeguard it achieves Q-quadratic convergence, and show that this behaviour cannot be proved by usual techniques for the original method. Research done while visiting Delft University of Technology, and supported in part by CAPES-Brazil.     

Study of the inertial effect and the nonlinearities of?the?CRONE suspension based on the hydropneumatic technology

In this paper, we emphasize two main effects involved in the CRONE car suspension technology (CRONE: French acronym for Commande Robuste d??Ordre Non Entier). In a first time, we present the influence of the inductive or inertial effect of the pipes that links the different cells of the hydropneumatic car suspension. These components are mainly resistive and capacitive devices. Then, we analyze the nonlinear relations that link the hydraulic power variables (the flow and the pressure) of the hydraulic resistors and the hydropneumatic accumulators and we study the effect of the nonlinear terms on the car suspension response. Our study is based on the gamma RC arrangement developed in Altet et al. (In: Analysis and design of hybrid systems??proceedings of ADHS03, pp. 63?C68. Elsevier, Amsterdam, 2003) and Serrier et al. (In: Proceedings of IDETC/CIE 2005: ASME 2005 international design engineering technical conferences and computers and information in engineering conference, Long Beach, CA, USA, 24?C28 September 2005). In a second time, we focus only on the gamma RLC arrangement, introduced in Abi Zeid Daou et al. (Int. J. Electron. 96(12):1207?C1223, 2009). We show whether the parasite effect due to the pipes or the nonlinear RC components affect the system??s response. The simulation results show that neither the inertial effect caused by these parasite pipes of one meter length nor the use of the nonlinear resistors or the accumulators modifies the response of the gamma RC arrangement.     

Gravitational force between two electrons in superconductors

The attractive gravitational force between two electrons in superconductors is deduced from the Eddington–Dirac large number relation, together with Beck and Mackey electromagnetic model of vacuum energy in superconductors. This force is estimated to be weaker than the gravitational attraction between two electrons in the vacuum.