We describe a face authentication algorithm based on retinotopic sampling of the Gabor decomposition. A log{polar sampling grid is used to encode information from relevant regions of the face. Decision is based on a multi expert scheme, in which each expert independently authenticates the client based on a different facial feature. Implementation of the expert as Support Vector Machines is disc...

In this paper, we study properties of extended commuting operators. particular, provide the polar decomposition product (?,?)-commuting operators where ? and are real numbers with ?? > 0. Furthermore, find restriction for quasihyponormal to be quasihyponormal. We also give spectral local relations between ?-commuting Moreover, show that a unilateral shift representable as weighted composition

In this paper we consider the polar decomposition on a Lie group G endowed with an involutive automorphism , as considered in (Munthe-Kaas, Quispel & Zanna 2000). In that paper, among other things, it was shown that z = exp(tZ) 2 G, Z 2 g, can be decomposed as z = xy, where x = exp(X(t)) and y = exp(Y (t)), where X(t) 2 p and Y (t) 2 k, g = p k being a Cartan decomposition of the algebra g indu...

The Cartan decomposition in a semisimple Lie group is a generalization of the polar decomposition of matrices. In this paper we consider an even more general setting in which one obtains an analogous decomposition. In the semisimple case, this decomposition was worked out in a seminal paper of G. I. Ol'shanski 13]. In this paper we give general necessary and suucient conditions for this decompo...

Let H be a Hilbert space with an inner product that is conjugate linear in the first variable. We do not presume unless we say so that H is separable. We denote by B(H) the set of bounded linear operators H → H. For any A ∈ B(H), A∗A is positive and one proves that it has a unique positive square root |A| ∈ B(H). We call |A| the absolute value of A. We say that U ∈ B(H) is a partial isometry if...

In this article we apply proper splittings of matrices to develop an iterative process approximate solutions matrix equations the form TX=W. Moreover, by using partial order induced positive semidefinite matrices, obtain equivalent conditions convergence process. We also include some speed comparison results method. addition, for all T propose a splitting based on polar decomposition T.

In this paper, we propose a new multiuser nonlinear optical cryptosystem using fractional-order vortex speckle (FOVS) patterns as security keys. conventional cryptosystems, mostly random phase masks are used the keys which prone to various attacks such brute force attack. current study, FOVSs generated optically by scattering of beam, known for azimuthal and helical wavefronts, through ground g...