Method of image charges for describing deformation of bounded two-dimensional solids with circular inclusions

Two Dimensional Adsorbed Charges

Image Restoration with Two-Dimensional Adaptive Filter Algorithms

Two-dimensional (TD) adaptive filtering is a technique that can be applied to many image, and signal processing applications. This paper extends the one-dimensional adaptive filter algorithms to TD structures and the novel TD adaptive filters are established. Based on this extension, the TD variable step-size normalized least mean squares (TD-VSS-NLMS), the TD-VSS affine projection algorithms (...

VII.D Two Dimensional Solids

The rotational invariance of energy is ensured by the implicit sum over the indices (i, j) in the above expression. In the Fourier representation, the energy depends on the quantities q, |u|, and (q · u) which are clearly independent of rotations. For other lattices, there are more elastic coefficients, since the energy should only be invariant under lattice rotations. For example, the symmetry...

VII.D Two Dimensional Solids

The rotational invariance of energy is ensured by the implicit sum over the indices (i, j) in the above expression. In the Fourier representation, the energy depends on the quan­ tities q , |u|, and (q · u) which are clearly independent of rotations. For other lattices, there are more elastic coefficients, since the energy should only be invariant under lattice rotations. For example, the symme...

On the generalization of Trapezoid Inequality for functions of two variables with bounded variation and applications

In this paper, a generalization of trapezoid inequality for functions of two independent variables with bounded variation and some applications are given.