Since the Sobolev set W r p , 0 < p < 1, in general is not contained in Lq , 0 < q ≤ ∞. We limit ourselves to the set W r p ∩ L∞, 0 < p < 1. We prove that the Kolmogorov n-width of the latter set in Lq , 0 < q < 1 is asymptotically 1, that is, the set cannot be approximated by n-dimensional linear manifolds in the Lq-norm. We then describe a related set, the width of which is asymptotically n−r.

The courses on web are primarily pre-designed to cater the requirements of a broad base of learners or target groups. However, the target group in web is geographically spread all over the world with varying socio-economical background. If a course is designed to cater a wide spectrum of participants all over the globe, most of the participants would find a lot of redundancy. The present work a...

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We consider Poisson’s equation in an n-dimensional exterior domain G (n≥ 2) with a sufficiently smooth boundary. We prove that for external forces and boundary values given in certain Lq(G)-spaces there exists a solution in the homogeneous Sobolev space S2,q(G), containing functions being local in Lq(G) and having second-order derivatives in Lq(G). Concerning the uniqueness of this solution we ...

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This paper presents a baseline test for the listening quality (LQ) using voice over digital subscriber line (VoDSL) access technology by using voice/listening quality(V/LQ) transmission with voice compression while countinously downloading file. The design of an experimental VoDSL network architecture is presented. We identify the efficiency of the LQ based on the following digital subscriber l...

Certain frequency-shaped standard linear quadratic (LQ) controllers involving state feedback have attractive loop robustness properties. These robustness properties may vanish in passing to an output feedback scheme, as when state estimates are used instead of states. The known exception to date is when the plants are minimum phase and state estimation with loop recovery is used, as in LQG/LTR ...

In this paper, I propose a general pricing framework that allows the risk−neutral dynamics of loss given default (LQ) and default probabilities (λQ) to be separately and sequentially discovered. The key is to exploit the differentials in LQ exhibited by different securities on the same underlying firm. By using equity and option data, I show that one can efficiently extract pure measures of λQ ...

We study the average cost Linear Quadratic (LQ) control problem with unknown model parameters, also known as the adaptive control problem in the control community. We design an algorithm and prove that apart from logarithmic factors its regret up to time T is O( √ T ). Unlike previous approaches that use a forced-exploration scheme, we construct a high-probability confidence set around the mode...