Motivated by a question of J. R. Isbell, we show that 3 implies there is a non-P-point U ∈ βω \ ω such that neither 〈U ,⊇〉 nor 〈U ,⊇∗〉 is Tukey equivalent to 〈[c],⊆〉. We also show that 〈U ,⊇∗〉 ≡T 〈[c],⊆〉 for some U ∈ βω \ω, assuming cf(κ) = κ ≤ p = c. We also prove two negative ZFC results about the possible Tukey classes of ultrafilters on ω.

Our purpose in this paper is to illustrate how nonparametric probability density estimates« in particular the corresponding contour curves» are a useful adjunct to scatter diagrams when performing a preliminary examination of a set of random data in several dimensions. For a preliminary approach we generally want to perform fairly simple tasks with free-form techniques to uncover structures and...

The publication of the Cooley-Tukey fast Fourier transform (FIT) algorithm in 1965 has opened a new area in digital signal processing by reducing the order of complexity of some crucial computational tasks like Fourier transform and convolution from N 2 to N log2 N, where N is the problem size. The development of the major algorithms (Cooley-Tukey and split-radix FFT, prime factor algorithm and...

A Monte Carlo approximation algorithm for the Tukey depth problem in high 5 dimensions is introduced. The algorithm is a generalization of an algorithm presented by 6 Rousseeuw and Struyf (1998). The performance of this algorithm is studied both analyti7 cally and experimentally. 8

Wireless communication is the fastest growing industry from many aspects. Increasing number of users imposes bandwidth constraints on the communication system. Cognitive Radio (CR) finds the solution to this problem and uses the free portion of the spectrum. Energy based spectrum sensing is the simplest way and in frequency domain it can be performed by using Periodogram based spectrum sensing....