Grouping and segmentation of images remains a challenging problem in computer vision. Recently, a number of authors have demonstrated a good performance on this task using spectral methods that are based on the eigensolution of a similarity matrix. In this paper, we implement a variation of the existing methods that combines aspects from several of the best-known eigenvector segmentation algori...

We show that an attempt to compute numerically a viscous flow in a domain with a piece-wise smooth boundary by straightforwardly applying well-tested numerical algorithms (and numerical codes based on their use, such as COMSOL Multiphysics) can lead to spurious multivaluedness and nonintegrable singularities in the distribution of the fluid’s pressure. The origin of this difficulty is that, nea...

In this paper, four incomplete boundary element formulations, including the real-part singular boundary element, the real-part hypersingular boundary element, the imaginary-part boundary element and the plane-wave element methods, are used to solve the free vibration problem. Among these incomplete boundary element formulations, the real-part singular and the hypersingular boundary elements are...

By considering a constraint on the energy profile, a new implicit approach is developed to solve nonlinear eigensolution problems. A corresponding minimax method is modified to numerically find eigensolutions in the order of their eigenvalues to a class of semilinear elliptic eigensolution problems from nonlinear optics and other nonlinear dispersive/diffusion systems. It turns out that the con...

The dynamic behavior of structural systems may be strongly characterized by the occurrence of multiple internal resonances for particular combinations of the mechanical parameters. The linear models governing these resonant or nearly-resonant systems tend to exhibit high sensitivity of the eigenvalues and eigenvectors to small parameter modifications. This pathological condition is recognized a...

Numerical issues arising in computations of viscous flows in corners formed by a liquidfluid free surface and a solid boundary are considered. It is shown that on the solid a Dirichlet boundary condition, which removes multivaluedness of velocity in the ‘moving contact-line problem’ and gives rise to a logarithmic singularity of pressure, requires a certain modification of the standard finite-e...

In this paper, the method of fundamental solutions (MFS) for solving the eigenfrequencies of multiply connected plates is proposed. The coefficients of influence matrices are easily determined when the fundamental solution is known. True and spurious eigensolutions appear at the same time. It is found that the spurious eigensolution using the MFS depends on the location of the inner boundary wh...

This paper describes the state-of-the-art on the small-signal stability analysis and design of FACTS assisted power systems. The benefits of integrating all these tools into a comprehensive package and properly employing graphical interface, including animation of algorithm results, are highly emphasized. ALGORITHMS FOR THE ANALYSIS AND CONTROL OF THE SMALL SIGNAL STABILITY OF LARGE SCALE POWER...