ABSTRACT Using full disc synoptic maps of solar background magnetic field captured from the Wilcox Solar Observatory for 30 latitudinal bands cycles 21–24, principal components (PCs) or eigenvectors oscillations are obtained. The PCs shown to come in pairs assigned waves produced by dipole, quadruple, sextuple, and octuple sources. first pair is linked dipole with their summary curve revealing ...

variace / covariance components of 227118 first lactaiom test-day milk yield records belonged to 31258 iranian holstein cows were estimated using nine random regression models. afterwards, different measures of persistency based on estimation breeding value were evaluated. three functions were used to adjust fixed lactation curve: ali and schaeffer (as), quadratic (le3) and cubic (le4) order of...

Our goal is to use the properties of the adjacency/Laplacian matrix of graphs to first understand the structure of the graph and, based on these insights, to design efficient algorithms. The study of algebraic properties of graphs is called algebraic graph theory. One of the most useful algebraic properties of graphs are the eigenvalues (and eigenvectors) of the adjacency/Laplacian matrix.

If the adjacency matrix contains degenerate eigenvalues, we must modify the approach using non-degenerate eigenvalues. We denote the eigenvalues as λki, where the index k runs over different eigenvalues and the index i runs over M associated eigenvectors of the same eigenvalue. Note that there is no unique way of choosing a basis for the eigenvectors of the unperturbed network since any linear ...