The computation of lower eigenvalue bounds for the biharmonic operator in the buckling of plates is vital for the safety assessment in structural mechanics and highly on demand for the separation of eigenvalues for the plate’s vibrations. This paper shows that the eigenvalue provided by the nonconformingMorley finite element analysis, which is perhaps a lower eigenvalue bound for the biharmonic...

While several methods aimed at understanding the causes of model behavior have been proposed in recent years, formal model analysis remains an important and challenging area in system dynamics. This paper describes a mathematical method to incorporate eigenvectors to the more traditional eigenvalue analysis of dynamic models. The proposed method derives basic formulas that characterize how a ch...

This paper presents small signal stability study carried over the 140-Bus, 31-Machine, 5-Area MEPE system and validated on free and open source software: PSAT. Well-established linearalgebra analysis, eigenvalue analysis, is employed to determine the small signal dynamic behavior of test system. The aspects of local and interarea oscillations which may affect the operation and behavior of power...

The plant genetic resources are important, because they have most valuable national basis resources in the each country. In this study, to grouping the almond progenies from ‘Shahrood ’ × ‘Shahrood ’ and comparing them in terms of heritability with their parents, measured on the basis of almond universal descriptor. Principal component analysis (PCA) was used to compare morphological and phonol...

This paper analyzes the important steps of an O(n 2 log n) algorithm for nding the eigenvalues of a complex Hankel matrix. The three key steps are a Lanczos-type tridiagonalization algorithm, a fast FFT-based Hankel matrix-vector product procedure, and a QR eigenvalue method based on complex-orthogonal transformations. In this paper, we present an error analysis of the three steps, as well as r...

This paper focuses on the problem of stability in homogeneous systems with dilation. First, we propose an ‘homogeneous eigenvalue’ for homogeneous systems. Next, we analyze the stability of homogeneous systems using homgeneous eigenvalues, and we show that the use of positive real homogeneous eigenvalues implies instability. Finally, we show the effectiveness of the proposed method through an e...