Explicit constructions of binary linear codes that are efficiently list-decodable up to a fraction (1/2−ε) of errors are given. The codes encode k bits into n = poly(k/ε) bits and are constructible and list-decodable in time polynomial in k and 1/ε (in particular, in our results ε need not be constant and can even be polynomially small in n). These results give the best known polynomial depende...

We report on a calculation of εK/εK at next-to-leading in the 1/Nc expansion and to lowest order in Chiral Perturbation Theory. We discuss the short-distance matching, the scale and scheme dependence as well as the long-distance short-distance matching. We include the two known chiral corrections to our result and discuss further order p4 corrections to it. September 2000 Work supported in part...

The lowest eigenmode of thin axisymmetric shells is investigated for two physical models (acoustics and elasticity) as the shell thickness (2ε) tends to zero. Using a novel asymptotic expansion we determine the behavior of the eigenvalue λ(ε) and the eigenvector angular frequency k(ε) for shells with Dirichlet boundary conditions along the lateral boundary, and natural boundary conditions on th...

It is shown that for every K > 0 and ε ∈ (0, 1/2) there exist N = N(K) ∈ N and D = D(K, ε) ∈ (1,∞) with the following properties. For every metric space (X, d) with doubling constant at most K, the metric space (X, d1−ε) admits a bi-Lipschitz embedding into R with distortion at most D. The classical Assouad embedding theorem makes the same assertion, but with N →∞ as ε→ 0.

Developing boundary layer flow and the flow over a backward-facing step are studied here. The LRN PANS k − ε [1] and the WALE turbulence model [2] are used as SGS models. The PANS (Partially AveragedNavier-Stokes) modelling approach [3, 4] is a modified k − ε model that can operate in both RANS and LES mode. An extension of PANS based on a four-equation k− ε− ζ − f model was recently proposed [...

More than twenty years ago Erdős conjectured [4] that a triangle-free graph G of chromatic number k ≥ k0(ε) contains cycles of at least k2−ε different lengths as k →∞. In this paper, we prove the stronger fact that every triangle-free graph G of chromatic number k ≥ k0(ε) contains cycles of 1 64 (1− ε)k 2 log k4 consecutive lengths, and a cycle of length at least 14 (1− ε)k 2 log k. As there ex...