An efficient technique is presented for optimum design of structures with both natural frequency and complex frequency response constraints. The main ideals to reduce the number of dynamic analysis by introducing high quality approximation. Eigenvalues are approximated using the Rayleigh quotient. Eigenvectors are also approximated for the evaluation of eigenvalues and frequency responses. A tw...

In this paper, we show that the eigenvectors of the zero Laplacian and signless Lapacian eigenvalues of a k-uniform hypergraph are closely related to some configured components of that hypergraph. We show that the components of an eigenvector of the zero Laplacian or signless Lapacian eigenvalue have the same modulus. Moreover, under a canonical regularization, the phases of the components of t...

Invariant pairs have been proposed as a numerically robust means to represent and compute several eigenvalues along with the corresponding (generalized) eigenvectors for matrix eigenvalue problems that are nonlinear in the eigenvalue parameter. In this work, we consider nonlinear eigenvalue problems that depend on an additional parameter and our interest is to track several eigenvalues as this ...

Insight into the behavior and simpliŽ ed control of a nonlinear dynamical system can be gained by analyzing the timescale structure. Near an equilibrium point, the eigenvalues and eigenvectors for the linearized system provide the necessary information. Nonlinear systems often operate on multiple timescales away from equilibrium, but there has been no general systematic approachto determine the...

Double criticality and its nonlinear implications are considered for stratified N−layer shallow water flows with N = 1, 2, 3. Double criticality arises when the linearization of the steady problem about a uniform flow has a double zero eigenvalue. We find that there are two types of double criticality: non-semisimple (one eigenvector, and one generalized eigenvector), and semi-simple (two indep...

INTRODUCTION The diffusion tensor is always measured in the presence of background noise. Recent experimental observations by Jeong et al.[1] and Lazar et al.[2,3] have shown that the cones of uncertainty (COU) [4,5,6] of the major eigenvectors of the diffusion tensors in the brain are mostly elliptical. Analytical approaches have also been developed to characterize the elliptical cone of uncer...

Analysis and control of underactuated mechanical systems in the nonzero velocity setting remains a challenging problem. In this paper, we demonstrate the utility of a recently developed alternative representation of the equations of motion for this large class of nonlinear control systems. The alternative representation gives rise to an intrinisic symmetric form. The generalized eigenvalues and...

Ng–Jordan–Weiss (NJW) method is one of the most widely used spectral clustering algorithms. For a K clustering problem, this method partitions data using the largest K eigenvectors of the normalized affinity matrix derived from the dataset. It has been demonstrated that the spectral relaxation solution of K-way grouping is located on the subspace of the largest K eigenvectors. However, we find ...