where PQ denotes the polynomial multiplication (convolution). For given n this is an optimization problem in 2n unknowns with polynomials P,Q of degree n− 1. Denote the global minimum by μn. We have a very efficient algorithm to compute an upper bound for μn, and we strongly believe that our approximations are very close to the true minimum. The challenge is to compute rigorous lower bounds for...

This paper investigates the joint source-channel coding problem of sending a memoryless source over a memoryless broadcast channel. An inner bound and several outer bounds on the achievable distortion region are derived, which respectively generalize and unify several existing bounds. As a consequence, we also obtain an inner bound and an outer bound for degraded broadcast channel case. When sp...

Consider a multi-resolution source code for describing a stationary source at L resolutions. The description at the rst resolution is given at rate R1 and achieves an expected distortion no greater than D1. The description at the second resolution includes both the rst description and a re ning description of rate R2 and achieves expected distortion no greater than D2, and so on. Recently deriv...

Asymptotic expressions for the optimal scaling factor and resulting minimum distortion , as a function of codebook size N, are found for xed-rate k-dimensional lattice vector quantization of generalized Gaussian sources with decay parameter 1. These expressions are derived by minimizing upper and lower bounds to distortion. It is shown that the optimal scaling factor a N decreases as (lnN) 1== ...

In this paper, for the first time, a comprehensive experimental study is performed on hydroforming process of metallic bellows. For this purpose, the effects of the main process parameters and their interactions on the characteristics of hydroformed metallic bellows are investigated using Response Surface Methodology (RSM). The selected parameters as input variables are internal pressure, die s...

This paper contains bounds for the distortion in the spherical metric, that is to say bounds for the constant of Hölder continuity of mappings f : (R, q) → (R, q) where q denotes the spherical metric. The mappings considered are K-quasiconformal (K ≥ 1) and satisfy some normalizations or restrictions. All bounds are explicit and asymptotically sharp as K → 1.

Over the last 20 years, many of the most spectacular results in the field of dynamical systems dealt specifically with interval and circle maps (or perturbations and complex extensions of such maps). Primarily, this is because in the one-dimensional case, much better distortion control can be obtained than for general dynamical systems. However, many of these spectacular results were obtained s...