The Spectral Decomposition of Covariance Matrices for the Variance Components Models

AbstractThe aim of this paper is to propose a simple method to determine the number of distinct eigenvalues and the spectral decomposition of covariance matrix for a variance components model. The method introduced in this paper is based on a partial ordering of symmetric matrix and relation matrix. A method is also given for checking straightforwardly whether these distinct eigenvalues are linear dependent as functions of variance components. Some examples and applications to illustrate the results are presented

1,1′-[1,4-Phenyl­enebis(methyl­ene)]bis­(2-methyl-1H-imidazol-3-ium) 2,4-dicarb­oxy­benzene-1,5-dicarboxyl­ate monohydrate

In the dication of the title compound, C16H20N4 2+·C10H4O8 2−·H2O, the dihedral angles formed by mean planes of the imidazolium rings and the benzene ring are 69.05 (18) and 89.1 (2)°. In the crystal, the components are linked into a three-dimensional network by inter­molecular N—H⋯O and O—H⋯O hydrogen bonds

Methyl (1H-pyrrol-2-ylcarbonyl­amino)acetate

In the crystal structure of the title compound, C8H10N2O3, mol­ecules are linked by N—H⋯O hydrogen bonds, forming ribbons of centrosymmetric dimers extending along the c axis

Hexa­kis­(1-benzyl-1H-imidazole-κN 3)manganese(II) bis­(perchlorate)

In the title compound, [Mn(C10H10N2)6](ClO4)2, the MnII ion, located on an inversion center, is coordinated by six N atoms from three pairs of symmetry-related 1-benzyl-1H-imidazole ligands in a distorted octa­hedral geometry. In the crystal, weak inter­molecular C—H⋯O hydrogen bonds link the complex cations and perchlorate anions

Spectrum Comparative Study of Commutation Failure and Short-Circuit Fault in UHVDC Transmission System

When commutation failure occurs in UHVDC transmission system, the transient process of DC voltage and current are similar to grounding short-circuit fault. In order to differentiate them effectively, the paper introduces mathematical morphology methods to analysis the spectrum of transient current. Base on Yunnan-Guangzhou kV UHVDC transmission system, the paper simulates the commutation failure and DC line short-circuit fault under different fault conditions in PSCAD/EMTDC.  By modified morphology filter, the transient signal of DC () is decomposed into six scales, and morphological characteristics of aerial mode component of  is analyzed under different scales. The simulation results show that when DC line short-circuit faults occurs, wherever in the rectifier side, in the DC transmission line midpoint or in the inverter side, the aerial mode component of  have more high frequency weight in ~ and decays gradually; When commutation failures, which are caused by the inverter side AC system single-phase grounding fault, phase to phase fault, three phase grounding fault or the inverter side transformer ratio increased,  the aerial mode component of  have less frequency weight in

Nitrogen defects and ferromagnetism of Cr-doped AlN diluted magnetic semiconductor from first principles

High Curie temperature of 900 K has been reported in Cr-doped AlN diluted magnetic semiconductors prepared by various methods, which is exciting for spintronic applications. It is believed that N defects play important roles in achieving the high temperature ferromagnetism in good samples. Motivated by these experimental advances, we use a full-potential density-functional-theory method and supercell approach to investigate N defects and their effects on ferromagnetism of (Al,Cr)N with N vacancies (V_N). Calculated results are in agreement with experimental observations and facts of real Cr-doped AlN samples and their synthesis. Our first-principles results are useful to elucidating the mechanism for the ferromagnetism and exploring high-performance Cr-doped AlN diluted magnetic semiconductors.Comment: 8 pages with figures include