Solutions of Abreu's Equation with Rotation Invariance

Rotation Invariance

This chapter discusses the issue of rotational invariance of a texture analysis system: i.e. one desires that the outcome of the analysis is not aaected by the orientation of the input image. We argue that the orthogonal DWT (section 3.4) is very impractical for such an analysis due to its separable nature in 2 dimensions. We therefore employ the non-separable wavelet frames (section 3.3). We d...

Rotation Invariance Neural Network

Rotation invariance and translation invariance have great values in image recognition tasks. In this paper, we bring a new architecture in convolutional neural network (CNN) named cyclic convolutional layer to achieve rotation invariance in 2-D symbol recognition. We can also get the position and orientation of the 2-D symbol by the network to achieve detection purpose for multiple non-overlap ...

Invariance of the Schrödinger Equation

We study a model for quantum gravity on a circle in which the notion of a classical metric tensor is replaced by a quantum metric with an inhomogeneous transformation law under diffeomorphisms. This transformation law corresponds to the co–adjoint action of the Virasoro algebra, and resembles that of the connection in Yang–Mills theory. The transformation property is motivated by the diffeomorp...

Solutions of diffusion equation for point defects

An analytical solution of the equation describing diffusion of intrinsic point defects in semiconductor crystals has been obtained for a one-dimensional finite-length domain with the Robin-type boundary conditions. The distributions of point defects for different migration lengths of defects have been calculated. The exact analytical solution was used to verify the approximate numerical solutio...

WAVELET SOLUTIONS OF THE KLEIN-GORDON EQUATION