Asymptotic behavior of reduction numbers

Asymptotic behavior of the numbers of runs and microruns

The notion of run (also called maximal repetition) allows a compact representation of the set of all tandem periodicities, even fractional, in a string. Since the work of Kolpakov and Kucherov in [8, 9], it is known that ρ(n), the maximum number of runs in a string, is linear in the length n of the string. Lower bounds haven been provided by Franek et al. and Matsubara et al. (0.9445...) [5, 6,...

Asymptotic Behavior of Multivariate Reward Processes with Nonlinear Reward Functions

Md-numbers and Asymptotic Md-numbers of Operators

First, the basic properties of mean dilatation (MD-) numbers for linear operators acting from a finite-dimensional Hilbert space are investigated. Among other results, in terms of first and second order MD-numbers, a characterization of isometries is obtained and a dimension-free estimation of the p-th order MD-number by means of the first order MD-number is established. After that asymptotic M...

Asymptotic behavior of ACMA

The algebraic constant modulus algorithm (ACMA) is a noniterative blind source separation algorithm. It computes jointly beamforming vectors for all constant modulus sources as the solution of a joint diagonalization problem. In this paper we analyze its asymptotic properties and show that (unlike the iterative CMA) it converges to the Wiener solution in samples or SNR. We also sketch its conne...

ASYMPTOTIC BEHAVIOR OF THE APPROXIMATION NUMBERS OF THE HARDY - TYPE OPERATOR FROM L p INTO L

We consider the Hardy-type operator (Tf) (x) := v(x) ∫ x a u(t)f(t)dt, x > a, and establish properties of T as a map from L(a, b) into L(a, b) for 1 < p ≤ q ≤ 2, 2 ≤ p ≤ q < ∞ and 1 < p ≤ 2 ≤ q < ∞. The main result is that, with appropriate assumptions on u and v, the approximation numbers an(T ) of T satisfy the inequality c1 ∫ b a |uv|dt ≤ lim inf n→∞ nan(T ) ≤ lim sup n→∞ nan(T ) ≤ c2 ∫ b a ...