The initial-value problem for the focusing nonlinear Schrödinger (NLS) equation is solved numerically by following the various steps of the inverse scattering transform. Starting from the initial value of the solution, a Volterra integral equation is solved followed by three FFT to arrive at the reflection coefficient and initial Marchenko kernel. By convolution these initial data are propagate...

This paper proposes a general approach to obtain asymptotic lower bounds for the estimation of random functionals. The main result is an abstract convolution theorem in a non parametric setting, based on an associated LAMN property. This result is then applied to the estimation of the integrated volatility, or related quantities, of a diffusion process, when the diffusion coefficient depends on...

A filtered data sequence can be obtained by multiplying the Fourier ordinates of the data by the ordinates of the frequency response of the filter and by applying the inverse Fourier transform to carry the product back to the time domain. Using this technique, it is possible, within the constraints of a finite sample, to design an ideal frequency-selective filter that will preserve all elements...

Perrin et al. (1995) and Geubelle and Rice (1995) have introduced a spectral method for numerical solution of twoand three-dimensional elastodynamic fracture problems. The method applies for ruptures confined to a plane separating homogeneous elastic half spaces. In this method, the physical variables, such as the traction components of stress and displacement discontinuity on the rupture plane...

The aim of this article was to assess and apply the in vitro to in vivo profiling (IVIVP), a new biowaiver approach, in designing a product with specific release pattern. The IVIVP was established by plotting the observed and predicted plasma drug concentrations. For IVIVP, convolution approach was employed to estimate plasma drug concentrations from in vitro dissolution profiles. The IVIVP for...

This paper proposes two new methods to detect the fingerprints of different persons based on one-dimensional and two-dimensional discrete wavelet transformations (DWTs). Recent literature shows that fingerprint detection based on DWT requires less memory space compared to pattern recognition and moment-based image recognition techniques. In this study four statistical parameters cross correlati...

A maximum a posteriori (MAP) approach, based on the Bayesian criterion, is proposed to overcome the low cross-range resolution problem in forward-looking imaging. We adapt scanning radar system to record received data and exploit deconvolution method to enhance the real-aperture resolution because the received echo is the convolution of target scattering coefficient and antenna pattern. The Gen...

Abstract. Here we utilize operator–valued Lq → Lp Fourier multiplier theorems to establish lower bound estimates for large class of elliptic integrodifferential equations in R. Moreover, we investigate separability properties of parabolic convolution operator equations that arise in heat conduction problems in materials with fading memory. Finally, we give some remarks on optimal regularity of ...

The purpose of this paper is to obtain sufficient bound estimates for harmonic functions belonging to the classes S∗ H [A,B], KH [A,B] defined by subordination, and we give some convolution conditions. Finally, we examine the closure properties of the operator D on these classes under the generalized Bernardi integral operator.