The concept of the iterative parabolic approximation based on the multiscale technique is discussed. This approach is compared with the traditional ways to derive the wide-angle parabolic equation. While the latter fail in the nonlinear case, the multiscale derivation technique leading to iterative parabolic equations can be easily adapted to handle it. The nonlinear iterative parabolic approxi...

We consider the problem of detecting stop consonants in continuously spoken speech. We pose the problem as one of finding the optimal filter (linear or non-linear) that operates on a particular appropriately chosen representation. We discuss the performance of several variants of a canonical stop detector and consider its implications for human and machine speech recognition.

In this paper we study general lp regularized unconstrained minimization problems. In particular, we derive lower bounds for nonzero entries of the firstand second-order stationary points and hence also of local minimizers of the lp minimization problems. We extend some existing iterative reweighted l1 (IRL1) and l2 (IRL2) minimization methods to solve these problems and propose new variants fo...

In this paper, we investigate the relation between the autocorrelation of a cubic Boolean function f ∈ Bn at a ∈ F2n and the kernel of the bilinear form associated with Daf , the derivative of f at a. Further, we apply this technique to obtain the tight upper bounds of absolute indicator and sum-of-squares indicator for avalanche characteristics of various classes of highly nonlinear non-bent c...

This article is concerned with symmetry properties of the solutions of the reaction-diiusion equation u + f (u) = 0 in a bounded connected domain in R N (N = 2; 3; : : :). Of especial interest are nonlinear source terms f of the type f (u) = u p ? u q with 0 q < p 1. Two results are presented. The rst result concerns the solution of a free boundary problem, where the domain is unknown and u and...

Time dispersion plays an important role in the propagation of femtosecond pulses through water. The combined e ects of time dispersion, radial di raction and the Kerr nonlinearity on the pulse propagation are analyzed and it is shown that normal time dispersion leads to signi cant temporal broadening of ultrashort pulses and that it increases the threshold power for catastrophic self-focusing.

Abstract. A possibility of tuning the phase of the third-order Kerr-type nonlinear susceptibility in a system consisting of two interacting metal nanospheres and a nonlinearly polarizable molecule is investigated theoretically and numerically. It is shown that by varying the relative inter-sphere separation, it is possible to tune the phase of the effective nonlinear susceptibility χ(ω;ω, ω,−ω)...

This paper is concerned with the problem of H control of fuzzy nonlinear impulsive systems with quantized feedback. New results on the H feedback control are established for one class of fuzzy nonlinear uncertain impulsive systems and one class of fuzzy nonlinear impulsive systems with nonlinear uncertainties by choosing appropriately quantized strategies and applying Lyapunov function approach...

We consider the nonlinear eigenvalue problem −∆u+ g(u) = λ sinu in Ω, u > 0 in Ω, u = 0 on ∂Ω, where Ω ⊂ RN (N ≥ 2) is an appropriately smooth bounded domain and λ > 0 is a parameter. It is known that if λ 1, then the corresponding solution uλ is almost flat and almost equal to π inside Ω. We establish an asymptotic expansion of uλ(x) (x ∈ Ω) when λ 1, which is explicitly represented by g.