An ill-posed problem which involves heterogonous data can yield good results if the weight of observations is properly introduced into the adjustment model. Variance component estimation can be used in this respect to update and improve the weights based on the results of the adjustment. The variance component estimation will not be as simple as that is in an ordinary adjustment problem, because the result of the solution of an ill-posed problem contains a bias due to stabilizing the adjustment model. This paper investigates the variance component estimation in those ill-posed problems solved by the truncation singular value decomposition. The biases of the variance components are analyzed and the biased-corrected and the biased-corrected non-negative estimators of the variance components are developed. The derivations show that in order to estimate unbiased variance components, it suffices to estimate and remove the bias from the estimated residuals.
Authors:Duk Hee Lee, Il Won Seo, Ho Chull Choe, and Hee Dae Kim
capabilities. Better coordination capabilities for communication mean greater dependence upon other actors and an upper hand over them. Third, eigenvector centrality measures centrality by reflecting the impacts of connected partners. Strong eigenvector
A citation matrix for the thirteen most cited journals in economics is constructed from data in theSocial Sciences Citation Index.tm The components of the eigenvector associated with the largest possible eigenvalue (the Frobenius root) of this matrix defines
“impact values” by which these journals may be ranked.
In this paper, we study dissipative q-Sturm—Liouville operators in Weyl’s limit circle case. We describe all maximal dissipative, maximal accretive, self adjoint extensions of q-Sturm—Liouville operators. Using Livšic’s theorems, we prove a theorem on completeness of the system of eigenvectors and associated vectors of the dissipative q-Sturm—Liouville operators.
Summary A direct method is developed for the discrete solution of Poisson's equation on a rectangle. The algorithm proposed is of the class of marching methods. The idea is to generalize the classical Cramer's method using Chebyshev matrix polynomials formalism. This results in the solution ofN independent diagonal system of linear equations in the eigenvector coordinate system. An elementary transformation to the original coordinate system is then carried out.
With this paper we want to stress that, on the basis of some matrix algebraic theorems, eigenvectors of similarity matrices are strictly related with clusters that we can obtain with clustering procedures applied to the same similarity matrices and that the fuzzy sets obtained by cluster analysis can be efficiently used as ordination axes and also as tools to measure the diagnostic value (or the indicator value) of attributes (species or other characters) of the ecological systems.
This paper is devoted to studying a q-analogue of Sturm-Liouville operators. We formulate a dissipative q-difference operator in a Hilbert space. We construct a self adjoint dilation of such operators. We also construct a functional model of the maximal dissipative operator which is based on the method of Pavlov and define its characteristic function. Finally, we prove theorems on the completeness of the system of eigenvalues and eigenvectors of the maximal dissipative q-Sturm-Liouville difference operator.
Authors:K. Shozugawa, A. Kuno, Y. Sano, and M. Matsuo
In order to estimate the source in pelagic sediments, principal component analysis (PCA) was applied to the data matrix which
was made by chemical compositions of sediments measured by instrumental neutron activation analysis (INAA) and prompt gamma-ray
analysis (PGA). The results of PCA represented 3-factor models in each sediment, explaining 58–98% of the total variations
in the sediments. A comparison of eigenvectors of terrigenous elements indicated the existence of 2 sources. Group 1 is suggested
to be continental dust, whereas Group 2 is suggested to be volcanic rock. Variation of K/Ti ratio and Eu anomaly of sediments
supported the above results.