Approximation properties of certain operator-induced norms on Hilbert spaces

We consider a class of operator-induced norms, acting as finite-dimensional surrogates to the L2 norm, and study their approximation properties over Hilbert subspaces of L2 . The class includes, as a special case, the usual empirical norm encountered, for example, in the context of nonparametric regression in reproducing kernel Hilbert spaces (RKHS). Our results have implications to the analysis of M-estimators in models based on finite-dimensional linear approximation of functions, and also to some related packing problems

Discrete Adaptive Second Order Sliding Mode Controller Design with Application to Automotive Control Systems with Model Uncertainties

Sliding mode control (SMC) is a robust and computationally efficient solution for tracking control problems of highly nonlinear systems with a great deal of uncertainty. High frequency oscillations due to chattering phenomena and sensitivity to data sampling imprecisions limit the digital implementation of conventional first order continuous-time SMC. Higher order discrete SMC is an effective solution to reduce the chattering during the controller software implementation, and also overcome imprecisions due to data sampling. In this paper, a new adaptive second order discrete sliding mode control (DSMC) formulation is presented to mitigate data sampling imprecisions and uncertainties within the modeled plant's dynamics. The adaptation mechanism is derived based on a Lyapunov stability argument which guarantees asymptotic stability of the closed-loop system. The proposed controller is designed and tested on a highly nonlinear combustion engine tracking control problem. The simulation test results show that the second order DSMC can improve the tracking performance up to 80% compared to a first order DSMC under sampling and model uncertainties.Comment: 6 pages, 6 figures, 2017 American Control Conferenc

Evaluation of the inhibitory synergic effects of the Persian Gulf brittle star extract and taxol on ovarian cancer A2780cp

Paclitaxel is a current standard chemotherapeutic drug for ovarian cancer with several side effects. Recurrences of drug resistant clones have been considered the serious problem in the failure of chemotherapy. Medicinal marine natural products have been intensively proposed as diverse chemotherapeutic agents. Therefore there is an affinity to find efficient modality to overwhelm ovarian cancer chemo resistance complication. Here we examine whether brittle star extract as marine echinoderm natural resources can remarkably improve the cytotoxicity of paclitaxel in human ovarian cancer. MTT (dimethyl thiazol-2-yl]-2, 5-diphenyl tetrazolium bromide) assay, PI (Propodium Iodide) assay, DAPI (4', 6-diamidino-2-phenylindole) staining, Acridine orange staining, caspase-3 and caspase-9 were performed to investigate cytotoxic effect. We found that a combination of sub-toxic concentrations of brittle star methanolic extract (lower than IC_50) can significantly enhance ovarian cell growth inhibition and intrinsic apoptosis pathways induced by paclitaxel. Consequently a combination of paclitaxel and brittle star extract may offer novel innovative strategies for ovarian cancer chemotherapy

Comment on "Anderson transition in disordered graphene"

We comment on a recent letter by Amini et al. (EPL 87, 37002 (2009)) concerning the existence of a mobility edge in disordered graphene.Comment: 3 pages, 3 figure