We compare several algorithms for computing the discrete Fourier transform of n numbers. The number of “operations” of the original Cooley-Tukey algorithm is approximately 2n A(n), where A(n) is the sum of the prime divisors of n. We show that the average number of operations satisfies (l/x)Z,,,2n A(n) (n2/9)(x2/log x). The average is not a good indication of the number of operations. For examp...

Abstract This article deals with kinetic Fokker–Planck equations essentially bounded coefficients. A weak Harnack inequality for nonnegative super-solutions is derived by considering their log-transform and adapting an argument due to S. N. Kružkov (1963). Such a result rests on new Poincaré sharing similarities the one introduced W. Wang L. Zhang in series of works about ultraparabolic (2009, ...

We present a sublinear randomized algorithm to compute a sparse Fourier transform for nonequispaced data. Suppose a signal S is known to consist of N equispaced samples, of which only L < N are available. If the ratio p = L/N is not close to 1, the available data are typically non-equispaced samples. Then our algorithm reconstructs a near-optimal B-term representation R with high probability 1−...

Detecting stratigraphic discontinuities using well log data is a fundamental task in petroleum geosciences projects. Wavelet transforms (WT) and S-transform (ST) of well log data can provide objective identification of lithological interfaces to aid in this effort. The continuous wavelet transform (CWT) of a time series gives the wavelet correlation coefficients (i.e. similarity) between the gi...

There are two methods for identifying formation interface in oil wells: core analysis, which is a precise approach but costly and time consuming, and well logs analysis, which petrophysists perform, which is subjective and not completely reliable. In this paper, a novel coupled method was proposed to detect the formation interfaces using GR logs. Second approximation level (a2) of GR log gained...

This paper presents a parallel algorithm for the weighted distance transform and the nearest feature transform of an n n binary image. We show that the algorithm runs in O(log n) time using n2= logn processors on the EREW PRAM and in O(log log n) time using n2= log log n processors on the common CRCW PRAM. We also show that the algorithm runs in O(n2=p2 + n) time on a p p mesh and in O(n2=p2 +(...