K.-H. Grr ochenig and A. Haas asked whether for every expanding integer matrix A 2 M n (Z) there is a Haar-type orthonormal wavelet basis having dilation factor A and translation lattice Z n. They proved that this is the case when the dimension n = 1. This paper shows that this is also the case when the dimension n = 2.

Let U be a Haar distributed matrix in U(n) or O(n). We show that after centering the two-parameter process W (s, t) = ∑ i≤⌊ns⌋,j≤⌊nt⌋ |Uij | 2 converges in distribution to the bivariate tied-down Brownian bridge.

We realized an imaging Mueller matrix microscope for nanostructure characterization. For investigations on nanoform characterization via images, we measured and simulated images of specially designed nanostructures. As approach towards machine learning evaluation in ellipsometry, calculated Haar-like features the observed a higher sensitivity to subwavelength off-diagonal elements compared micr...

In this paper, we derive Haar wavelet operational matrix of the fractional integration and use it to obtain eigenvalues of fractional Sturm-Liouville problem. The fractional derivative is described in the Caputo sense. The efficiency of the method is demo nstrated by examples MSC: 26A33

In this paper, we derive Haar wavelet operational matrix of the fractional integration and use it to obtain eigenvalues of fractional Sturm-Liouville problem. The fractional derivative is described in the Caputo sense. The efficiency of the method is demonstrated by examples MSC: 26A33

Given any fixed N×N positive semi-definite diagonal matrix G ≥ 0 we derive the explicit formula for the density of complex eigenvalues for random matrices A of the form A = U √ G where the random unitary matrices U are distributed on the group U(N) according to the Haar measure.

Direct transformation amongst the Walsh, Haar, Arithmetic and Reed-Muller spectral domains is considered. Matrix based techniques are developed and it is shown that these can be implemented as fast in-place transforms. It is also shown that these transforms can be implemented directly on decision diagram representations.

In this paper, we present a computational method for solving stochastic VolteraFredholm integral equations which is based on the Haar wavelets and their stochastic operational matrix. Convergence and error analysis of the proposed method are worked out. Numerical results are compared with the block pulse functions method for some non-trivial examples. The obtained results reveal efficiency and ...

Let U be a Haar distributed matrix in U(n) or O(n). We show that after centering the two-parameter process W (s, t) = ∑ i≤⌊ns⌋,j≤⌊nt⌋ |Uij | 2 converges in distribution to the bivariate tied-down Brownian bridge.

This paper presents a proof of Stirling's formula using Haar wavelets and some properties of Hilbert space, such as Parseval's identity. The present paper shows a connection between Haar wavelets and certain sequences.