2008 NOV 24 - (VerticalNews.com) -- "In this article, we propose a probabilistic approach to the study of the characteristic polynomial of a random unitary matrix," scientists in Paris, France report.

  "We recover the Mellin-Fourier transform of such a random polynomial, first obtained by Keating and Snaith in [8] using a simple recursion formula, and from there we are able to obtain the joint law of its radial and angular parts in the complex plane. In particular, we show that the real and imaginary parts of the logarithm of the characteristic polynomial of a random unitary matrix can be represented in law as the sum of independent random variables," wrote P. Bourgade and colleagues ...read more

  2008 NOV 17 - (VerticalNews.com) -- "The discrete Fourier transform (DFT) is the base of modern signal processing. 1-dimensional fast Fourier transform (1D FFT) and 2D FFT have time complexity O(N log N) and O(N-2 log N) respectively. Since 1965, there has been no more essential breakthrough for the design of fast DFT algorithm," scientists in Chengdu, People's Republic of China report.

  "DFT has two properties. One property is that DFT is energy conservation transform. The other property is that many DFT coefficients are close to zero. The basic idea of this paper is that the generalized Grover's iteration can perform the computation of DFT which acts on the entangled states to search the big DFT coefficients until these big cofficients contain nearly all energy. One-dimensional quantum DFT (1D QDFT) and two-dimensional quantum DFT (2D QDFT) are presented in this paper. The quantum algorithm for convolution estimation is also presented in this paper. Compared with FFT, 1D and 2D QDFT have time complexity O(root N) and O(N) respectively," wrote C.Y. Pang and colleagues, Sichuan Normal University ...read more

  2008 NOV 17 - (VerticalNews.com) -- "The spectral Green's function (SGF) method is used to solve numerically the transport of neutrons in an infinite homogeneous cylindrical domain," scientists in Turkey report.

  "In the method, the scattering of neutrons is assumed to be isotropic and the transport equation in cylindrical geometry is reduced to plane-like transport equation by using our reasonable approach. Then, the plane-like transport equation is solved by using the SGF method and the results are compared with those already obtained by the Diamond Difference (DD) scheme to check the accuracy of the results," wrote H. Ozturk and colleagues ...read more