We study the variation of the spectrum of matrices under perturbations which are selfor skew-adjoint with respect to a scalar product. Computable formulae are given for the associated μ-values. The results can be used to calculate spectral value sets for the perturbation classes under consideration. We discuss the special case of complex Hamiltonian perturbations of a Hamiltonian matrix in detail.

We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. We classify numerical methods and catalogue available software.

A second Leray spectral sequence of relative hypercohomology is constructed. (This is skew in generality to an earlier one constructed by S. Lubkin [(1968) Ann. Math. 87, 105-255].) The Mayer-Vietoris sequence of relative hypercohomology [Lubkin, S. (1968) Ann. Math. 87, 105-255] is also generalized.

The noise characteristics of supercontinuum generation are characterized using higherorder statistical moments. Measures of skew and kurtosis, and the coefficient of variation allow quantitative identification of spectral regions dominated by rogue wave like behaviour. OCIS codes: (030.1640) Coherence; (190.4370) Nonlinear optics, fibers; (320.6629) Supercontinuum generation.

The Ni(II) and Zn(II) complexes with phenylpyridylformamidine (PhPyF) ligand, [Ni(PhPyF)Cl2] and [Zn(PhPyF)Cl2], have been prepared and investigated using different chemical techniques such as elemental analysis, molar conductance, FT-IR, UV-vis spectra and magnetic moment. The obtained chemical analysis data showed the formation of 1:1 (metal: ligand) ratio. The square planar and tetrahedral g...

We survey the quadratic eigenvalue problem, treating its many applications, its mathematical properties, and a variety of numerical solution techniques. Emphasis is given to exploiting both the structure of the matrices in the problem (dense, sparse, real, complex, Hermitian, skew-Hermitian) and the spectral properties of the problem. We classify the available choices of methods and catalogue a...

 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 proposes a new nonparametric approach to the estimation of the mean Doppler velocity (first spectral moment) and the spectral width (square root of the second spectral centered moment) of a zero-mean stationary complex Gaussian process immersed in independent additive white Gaussian noise. By assuming that the power spectral density of the underlying process is bandlimited, the exac...