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*Correspondence: [email protected] 2School of Science, Jiangnan University, Lihu Road, Wuxi, 214122, China Full list of author information is available at the end of the article Abstract In the study of pattern formation in bi-stable systems, the extended Fisher-Kolmogorov (EFK) equation plays an important role. In this paper, a Fourier pseudo-spectral method for solving the EFK equation in ...

An heuristic proof of the Riemman conjecture is proposed. It is based on the old idea of Polya-Hilbert. A discrete/fractal derivative self adjoint operator whose spectrum may contain the nontrivial zeroes of the zeta function is presented. To substantiate this heuristic proposal we show using generalized index-theory arguments, corresponding to the (fractal) spectral dimensions of fractal brane...

Three methods, selecting characteristic lines of elements contained in the samples manually, selecting intensive spectral partitions manually and the whole spectra, were used to reduce dimensions of spectra of 27 steel samples acquired by Laser-Induced Breakdown Spectroscopy. The PLS models were built based on the data after dimension reduction to quantify the Mn concentration of samples. The r...