Polynomials orthogonal with respect to a perturbation of the Freud weight function by the addition of a mass point at zero are considered. These polynomials, called Freud-type orthogonal polynomials, satisfy a second order linear differential equation with varying polynomial coefficients. It plays an important role in the electrostatic interpretation for the distribution of zeros of the corresp...

This paper proposes a new approach for image encryption using multi-dimensional orthogonal sequence. The sequence can provide an orthogonal transform for digital data, which is useful for image encryption. The key to decrypt is a set of the parameters to generate the sequence. For a gray scale image and a binary image, four different sequences are used to encrypt. Two of them are used to encryp...

We analyze eigenvalues fluctuations of the Laplacian of various networks under the random matrix theory framework. Analyses of random networks, scale-free networks and small-world networks show that nearest neighbor spacing distribution of the Laplacian of these networks follow Gaussian orthogonal ensemble statistics of random matrix theory. Furthermore, we study nearest neighbor spacing distri...

This paper defines the multivariate Krawtchouk polynomials, orthogonal on the multinomial distribution, and summarizes their properties as a review. The multivariate Krawtchouk polynomials are symmetric functions of orthogonal sets of functions defined on each of N multinomial trials. The dual multivariate Krawtchouk polynomials, which also have a polynomial structure, are seen to occur natural...

Global depth, tangent depth and simplicial depths for classical and orthogonal regression are compared in examles and properies that are usefull for calculations are derived. Algorithms for the calculation of depths for orthogonal regression are proposed and tests for multiple regression are transfered to orthogonal regression. These tests are distribution free in the case of bivariate observat...