(1b) Question. For which pairs (C0,H) does a lift exist? Note that the lifting problem for C0 is formally smooth. However we will see that in general the lifting problem for (C0,H) can be obstructed; in some cases a lifting does not exist, in several cases ramification in R is needed to make a lifting possible. In order to have a positive answer to this question it suffices to consider the case...

A compensation scheme is presented for general nonlinear actuator deadzones of unknown width. The compensator uses two neural networks (NN’s), one to estimate the unknown deadzone and another to provide adaptive compensation in the feedforward path. The compensator NN has a special augmented form containing extra neurons whose activation functions provide a “jump function basis set” for approxi...

We consider cosmological solutions of string and M-theory compactified to four dimensions by giving a general prescription to construct four-dimensional modular cosmologies with two commuting Killing vectors from vacuum solutions. By lifting these solutions to higher dimensions we analyze the existence of cosmological singularities and find that, in the case of non-closed Friedmann-Robertson-Wa...

I present an analytical expression for the relation of the packet loss rate (PLR) with respect to the channel optical signal-to-noise ratio measured nonintrusively in an all-optical, wavelength-routed network. This closed-form expression is aimed for rapid, nonintrusive fault detection of lambda services. This relation will help achieve reliable all-optical networks with no extra optoelectrical...

We consider the STIRAP process in a three-level atom. Viewed as a closed system, no geometric phase is acquired. But in the presence of spontaneous emission and/or collisional relaxation we numerically show that a nonvanishing, purely real, geometric phase is acquired during STIRAP, whose magnitude grows with the decay rates. We speculate that rather than viewing this decoherence-induced geomet...

In this paper, we develop a finite horizon model predictive control algorithm which is robust to modelling uncertainties. A moving average system matrix is constructed to capture modelling uncertainties and facilitate the future output prediction. The paper is mainly focused on the step tracking problem. Using linear matrix inequality techniques, the design is converted into a semi-definite opt...

A true adaptive nonlinear model predictive control (MPC) algorithm must address the issue of robustness to model uncertainty while the estimator is evolving. Unfortunately, this may not be achieved without introducing extra degree of conservativeness and/or computational complexity in the controller calculations. To attenuate this problem, we employ a finite time identifier and propose an adapt...

An orthogonal eigenstructure control method with collocated actuators and sensors was recently developed by the authors. In this paper the application of the method is extended beyond the collocation of the actuators and sensors, including the cases that different numbers of actuators and sensors are used. Orthogonal eigenstructure control is an output feedback control for multi-input multi-out...

1 is unique (1 = 11 = 1, so any left identity equals any right identity). A morphism takes 1 to the identity of φX (since φ(x) = φ(1x) = φ(1)φ(x)), but φ(1) = 1 is an extra property that ought to be satisfied by morphisms; its kernel is the sub-algebra φ(1); zero object is { 1 }; not Cartesian-closed (the terminal and initial objects are the same, yet not all groups are isomorphic). A quasi-gro...