Lexicographic ordering by spectral moments ($S$-order) among all trees is discussed in this‎ ‎paper‎. ‎For two given positive integers $p$ and $q$ with $pleqslant q$‎, ‎we denote $mathscr{T}_n^{p‎, ‎q}={T‎: ‎T$ is a tree of order $n$ with a $(p‎, ‎q)$-bipartition}‎. Furthermore, ‎the last four trees‎, ‎in the $S$-order‎, ‎among $mathscr{T}_n^{p‎, ‎q},(4leqslant pleqslant q)$ are characterized‎.

This paper deals with the inverse homogenization or dehomogenization problem of recovering geometric information about the structure of a twocomponent composite medium from the effective complex permittivity of the composite. The approach is based on the reconstruction of moments of the spectral measure in the Stieltjes analytic representation of the effective property. The moments of the spect...

Let X(t) (t Z) be a discrete stable random field. The problem of estimating the spectral density field based on X(t) is considered. Moments and the asymptotic moments of the spectral sample, the periodogram, based on X(t) are calculated.

This paper studies parametric estimation of spectral moments of a zero-mean complex Gaussian stationary process immersed in independent Gaussian noise. With the merit of the maximum-likelihood (ML) approach as motivation, this work exploits a Whittle’s type objective function able to capture the relevant features of the log-likelihood function, while being much more manageable. The resulting es...

We calculate the logarithmic moment of the phonon frequency spectrum at a single density for 29 monatomic liquids using two methods, both suggested by Wallace’s liquid dynamics: The first method relies on liquid entropy data, the second on neutron scattering data in the crystal phase. Liquid dynamics predicts that for a class of elements called “normal melters,” including all 29 of these materi...

Abstmet-This correspondence studies parametric estimatioll of spectral moments of a zero-mean complex Gaussian stationary pmcess immersed in independent Gaussian noise. With the merit of the maximum-likelihood @lL) approach as motivation, this work exploits a Whittle's type objective function that is able to capture the relevant feabues of the log-likelihmdfunction while b e i i much more manag...