An image watermarking scheme based on singular value decomposition and visual cryptography in discrete wavelet transform is proposed. We start with a survey of the current image watermarking technologies, and have noticed that majority of the existing schemes are not capable of resisting all attacks. We propose the idea to use of singular value decomposition and visual cryptography in discrete ...

We study convolution algebras associated with HeckmanOpdam polynomials. For root systems of type BC we derive three continuous classes of positive convolution algebras (hypergroups) by interpolating the double coset convolution structures of compact Grassmannians U/K with fixed rank over the real, complex or quaternionic numbers. These convolution algebras are linked to explicit positive produc...

Let p, q ∈ R such that 1 < p < 2 and 2 p = 1 + 1q . Define ‖f‖p = max x,G1 ( ∑ y∈G1 |f(xy)|p )1/p (*) where G1 is taken in some class of subgroups specified later. We prove the following two theorems about convolutions. Theorem 2. Let G = SL2(C) equipped with the discrete topology. Then there is a constant τ = τp > 0 such that for f ∈ `(G) ‖f ∗ f‖1/2 q ≤ C‖f‖1−τ p (‖f‖p) , where the maximum in ...

We study solvability of convolution equations for functions with discrete support in R, a special case being functions with support in the integer points. The more general case is of interest for several grids in Euclidean space, like the body-centred and face-centred tesselations of three-space, as well as for the non-periodic grids that appear in the study of quasicrystals. The theorem of exi...

We introduce a new method of constructing kernels on sets whose elements are discrete structures like strings trees and graphs The method can be applied iteratively to build a kernel on a in nite set from kernels involving generators of the set The family of kernels generated generalizes the family of radial basis kernels It can also be used to de ne kernels in the form of joint Gibbs probabili...

This paper considers the problem of discrete passive filter design method for singular systems with interval time-varying delay. A bounded real lemma (BRL) for discrete passivity with a dissipation of discretetime delayed singular systems by a Lyapunov function is derived. A delay-dependent discrete passive filter design method is proposed by linear matrix inequality (LMI) approach on the basis...

We study solutions to convolution equations for functions with discrete support in R, a special case being functions with support in the integer points. The Fourier transform of a solution can be extended to a holomorphic function in some domains in C, and we determine possible domains in terms of the properties of the convolution operator.

We consider the diffusive single species growth in a plug flow reactor model with distributed delay. For small delay, existence and uniqueness of such wavefronts are proved when the convolution kernel assumes the strong generic delay kernel. The approaches used in this paper are geometric singular perturbation theory and the center manifold theorem.

Suppose we have independent observations of a pair of independent random variables, one with a density and the other discrete. The sum of these random variables has a density, which can be estimated by an ordinary kernel estimator. Since the two components are independent, we can write the density as a convolution and alternatively estimate it by a convolution of a kernel estimator of the conti...

It is shown that the discrete time convolution of two absolutely summable nowhere zero sequences may be identically equal to zero. DEVELOPMENT Consider two absolutely summable sequences a = {a,,: n E Z } and b = { b,,: n E Z } of real numbers. Further, assume that the sequences a and b are nowhere zero. Does it follow that the discrete time convolution a * b is nowhere zero? Does it follow that...