We present a general construction that starts from a family of interior-preserving open coverings of a given subspace and results in a partial metric with respect to which all subspace elements have self-distance zero. A necessary and sufficient condition is derived for when this partial metric induces the given topology. The condition is particularly satisfied if the members of each covering a...

We characterize the generalized Chebyshev polynomials of the second kind (Chebyshev-II), and then we provide a closed form of the generalized Chebyshev-II polynomials using the Bernstein basis. These polynomials can be used to describe the approximation of continuous functions by Chebyshev interpolation and Chebyshev series and how to efficiently compute such approximations. We conclude the pap...

Aiming at reduction of complexity, this work is concerned with two-time-scale Markov chains and applications to quasi-birth-death queues. Asymptotic expansions of probability vectors are constructed and justified. Lumping all states of the Markov chain in each subspace into a single state, an aggregated process is shown to converge to a continuous-time Markov chain whose generator is an average...

This report gives an overview of the Quasi-Adaptive NonInteractive Zero Knowledge proof system introduced recent papers by Joy and Rutla ([JR13a,JR13b]). This system reduces the proof size for linear subspace languages to constant-sized proofs under the k-linear assumption.

Quasi-stationary signals have been widely found in practical applications, which have time-varying second-order statistics while staying static within local time frames. In this paper, we develop a robust direction-of-arrival (DOA) estimation algorithm for quasi-stationary signals based on the Khatri-Rao (KR) subspace approach. A partly-calibrated array is considered, in which some of the senso...

In this paper, we represent an inexact inverse subspace iteration method for computing a few eigenpairs of the generalized eigenvalue problem Ax = Bx [Q. Ye and P. Zhang, Inexact inverse subspace iteration for generalized eigenvalue problems, Linear Algebra and its Application, 434 (2011) 1697-1715 ]. In particular, the linear convergence property of the inverse subspace iteration is preserved.

Quasi-orthogonal space-time block codes (QO-STBCs) are proposed for long-code WCDMA systems which exploit the subspace structure of the long-code WCDMA transmission. QOSTBCs achieve full code rate at the expense of loss in diversity gain. In this paper, we propose a feedback method for QO-STBCS in WCDMA to achieve full diversity and full code rate. The bit error rate (BER) performance for the p...

In this workshop, the powerful subspace identification method (SIM) is described for the well understood case of linear time-invariant (LTI) systems. Recent extensions are show for linear parameter-varying (LPV), Quasi-LPV, and general nonlinear (NL) systems such as polynomial systems. The presentation, following the extended tutorial paper (Larimore, ACC2013), includes detailed conceptual deve...

We consider the natural generating system for a cyclic subspace of a Hilbert space generated by a dual integrable unitary representation of a countable abelian group. We prove, under mild hypothesis, that whenever the generating system is a quasi-greedy basis it must also be an unconditional Riesz basis. A number of applications to Gabor systems and to general Vilenkin systems are considered. I...

Keywords: Set-valued mapping Chebyshev center Uniformly convex Locally uniformly convex Chebyshev fixed point a b s t r a c t The existence of a continuous Chebyshev selection for a Hausdorff continuous set-valued mapping is studied in a Banach space with some uniform convexity. As applications, some existence results of Chebyshev fixed point for condensing set-valued mappings are given, and th...