In this two-part paper we introduce the notion of a stable code and give a new upper bound on the normalized covering radius ofa code. The main results are that, for fixed k and large n, the minimal covering radius t[n, k] is realized by a normal code in which all but one of the columns have multiplicity l; hence tin + 2, k] t[n, k] + for sufficiently large n. We also show that codes with n _-<...

We repeatedly measured the trabecular bone (TB) microstructure of the distal radius in 5 healthy volunteers using a compact magnetic resonance (MR) imaging system to evaluate the reproducibility of the TB structural parameters. The compact system was specially developed with a 1.0-tesla permanent magnet for the distal radius in a previous study. We measured the distal radius using a 3-dimension...

the center (periphery) of a graph is the set of vertices with minimum (maximum)eccentricity. in this paper, the structure of centers and peripheries of some classes ofcomposite graphs are determined. the relations between eccentricity, radius and diameterof such composite graphs are also investigated. as an application we determinethe center and periphery of some chemical graphs such as nanotor...

We show that for innnite-dimensional discrete-time positive systems the complex and real stability radius coincide. Furthermore, we provide a simple formula for the complex stability radius of positive systems by the associated transfer function. We illustrate our results with an example dealing with a simple type of diierential-diierence equations. 1. Introductory remarks This work is motivate...

We deal with dynamic equations on time scales, where we characterize the positivity of a system. Uniform exponential stability of a system is determined by the spectrum of its matrix. We investigate the corresponding stability radii with respect to structured perturbations and show that for positive systems the complex stability radius and the positive stability radius coincide. 2000 Mathematic...

We present two new algorithms for investigating the stability of large and sparse matrices subject to real perturbations. The first algorithm computes the real structured pseudospectral abscissa and is based on the algorithm for computing the pseudospectral abscissa proposed by Guglielmi and Overton [SIAM J. Matrix Anal. Appl., 32 (2011), pp. 1166-1192]. It entails finding the rightmost eigenva...

We study quasistatic perturbations in a cosmological background in the Dvali-Gabadadze-Porrati braneworld model. We identify the Vainshtein radius at which the nonlinear interactions of the brane bending mode become important in a cosmological background. The Vainshtein radius in the early universe is much smaller than the one in the Minkowski background, but in a self-accelerating universe it ...