where w = ((ei)i≥0, (fi)i≥0 ) are disturbances which excite the system in a linear and a bilinear form. We assume that the system is augmented with the output function y i = Cx w i , i ≥ 0. Let ε be a tolerance index on the output. The disturbance w is said to be ε-admissible if ‖y i −yi‖ ≤ ε, ∀ i ≥ 0, where (yi)i≥0 is the output signal associated with the case of an uninfected system. The set ...

A new and powerful indentation hardness (H) approach to evaluating the true stress (σ)-true plastic strain (ε), σ(ε), constitutive behavior of materials is described. Since measurements of H intrinsically probe a wide-range of ε (up to ≈0.5) , accurate assessment of the corresponding yield (σy) stress and strain hardening [σsh(ε)] pose a significant challenge. Extensive elastic-plastic finite ...

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 analyze measures of the azimuthal asymmetry, in particular the participant harmonic moments, ε∗, in a variety of Glauber-like models for the early stage of collisions at RHIC. Quantitative comparisons indicate substantial model dependence for ε∗, reflecting different effective number of sources, while the dependence of the scaled standard deviation σ(ε∗)/ε∗ on the particular Glauber model is...

Erdős and Rényi claimed and Vu proved that for all h ≥ 2 and for all ε > 0, there exists g = gh(ε) and a sequence of integers A such that the number of ordered representations of any number as a sum of h elements of A is bounded by g, and such that |A ∩ [1, x]| À x1/h−ε. We give two new proofs of this result. The first one consists of an explicit construction of such a sequence. The second one ...

A quantile summary is a data structure that approximates to ε-relative error the order statistics of a much larger underlying dataset. In this paper we develop a randomized online quantile summary for the cash register data input model and comparison data domain model that uses O( 1 ε log 1 ε ) words of memory. This improves upon the previous best upper bound of O( 1 ε log 1 ε ) by Agarwal et. ...

For any ε > 0, we construct an explicit smooth Riemannian metric on the sphere Sn, n ≥ 3, that is within ε of the round metric and has a geodesic for which the corresponding orbit of the geodesic flow is ε-dense in the unit tangent bundle. Moreover, for any ε > 0, we construct a smooth Riemannian metric on S, n ≥ 3, that is within ε of the round metric and has a geodesic for which the complemen...

Let X and Y be independent 2-dimensional Brownian motions, X(0) = (0, 0), Y (0) = (ε, 0), and let p(ε) = P (X[0, 1] ∩ Y [0, 1] = ∅), q(ε) = {Y [0, 1] does not contain a closed loop around 0}. Asymptotic estimates (when ε → 0) of p(ε), q(ε), and some related probabilities, are given. Let F be the boundary of the unbounded connected component of R2\Z[0, 1], where Z(t) = X(t) − tX(1) for t ∈ [0, 1...

Much attention has been brought to determinization and ε-removal in previous work. This article describes an algorithm for extracting all ε-cycles, which are a special type of non-determinism, from an arbitrary finite-state transducer (FST). The algorithm factorizes (decomposes) the FST, T , into two FSTs, T1 and T2, such that T1 contains no ε-cycles and T2 contains all ε-cycles of T . Since ε-...

We investigate the effects of annealing microstructure on low-cycle fatigue (LCF) life (Nf), cyclic stress behaviour and a Fe–15Mn–10Cr–8Ni–4Si alloy that exhibits deformation-induced transformation austenite (γ-phase) into ε-martensite (ε-phase). The rolled at 800°C was annealed 600°C, 700°C, 900°C to vary grain size, fraction recrystallised grains texture intensity. Fully reversed axial strai...