We construct the Darboux-Bäcklund transformation for the sigma model describing static configurations of the 2-dimensional classical continuum Heisenberg chain. The transformation is characterized by a non-trivial normalization matrix depending on the background solution. In order to obtain the transformation we use a new, more general, spectral problem. PACS Numbers: 02.30.Ik, 03.50.Kk, 05.45Yv.

The matrix volume is a generalization, to rectangular matrices, of the absolute value of the determinant. In particular, the matrix volume can be used in change-of-variables formulæ, instead of the determinant (if the Jacobi matrix of the underlying transformation is rectangular). This result is applicable to integration on surfaces, illustrated here by several examples. SIAM J. Matrix Analysis...

The Capon-MVDR (Minimum Variance Distortionless Response) method of frequency-wavenumber spectral estimation requires an invertible spatial covariance estimate. Increasingly, however, one must deal with a singular covariance matrix. The ubiquity of inexpensive sensors implies that the dimension of the covariance matrix is ever-increasing, but coherence times have not changed, so the number of v...

In this paper, we propose a robust blind watermarking algorithm for high-definition video contents. For the security of watermark information, a matrix of random numbers is generated using a secret key. We perform inverse steerable pyramid transformation (SPT) to the matrix to produce a transformed matrix. The 2-dimensional fast Fourier transformation (2D FFT) is performed to the luminant compo...

Let χ denote the space of all gai sequences and Λ the space of all analytic sequences. First we show that the set E = { s(k) : k = 1, 2, 3, · · · } is a determining set for χM . The set of all finite matrices transforming χM into FKspace Y denoted by (χM : Y ) . We characterize the classes (χM : Y ) when Y = (c0)π , cπ, χM , `π, `s,Λπ, hπ. In summary we have the following table: ↗ (c0)π cπ χM `...

A new image compression algorithm is proposed and demonstrated in the context of structured light 3D reconstruction. Structured light images contain patterns of light, which are captured by the sensor at very high resolution. The algorithm steps involve a two level Discrete Wavelet Transformation (DWT) followed by a Discrete Cosine Transformation (DCT) to generate a DC-Column and an MA-Matrix (...

Abstract We present a matrix method for obtaining new classes of exact solutions for Einstein’s equations representing static perfect fluid spheres. By means of a matrix transformation, we reduce Einstein’s equations to two independent Riccati type differential equations for which three classes of solutions are obtained. One class of the solutions corresponding to the linear barotropic type flu...