Hadamard transform is an important tool in discrete signal processing. In this paper, we define the discrete fractional Hadamard transform which is a generalized one. The development of discrete fractional Hadamard is based upon the same spirit of discrete fractional Fourier transform.

In this paper, the authors give a new identity for Hadamard fractional integrals. By using of this identity, the authors obtain new estimates on generalization of Hadamard, Ostrowski and Simpson type inequalities for (α,m)-GA-convex functions via Hadamard fractional integrals.

In this paper security aspects of the existing symmetric key encryption schemes based on Hadamard matrices are examined. Hadamard matrices itself have symmetries like one circulant core or two circulant core. Here, we are exploiting the inherent symmetries of Hadamard matrices and are able to perform attacks on these encryption schemes. It is found that entire key can be obtained by observing t...

This note introduces a quantum random walk in R and proves the weak convergence of its rescaled n-step densities. Quantum walks of the type we consider in this note were introduced in [1], which defined and analyzed the Hadamard quantum walk on Z, and a “new type of convergence theorem” for such quantum walks on Z was discovered by Konno [4, 5]. A much simpler proof of Konno’s theorem has recen...

Forty years ago, Goethals and Seidel showed that if the adjacency algebra of a strongly regular graph X contains a Hadamard matrix then X is of Latin square type or of negative Latin square type [8]. We extend their result to complex Hadamard matrices and find only three additional families of parameters for which the strongly regular graphs have complex Hadamard matrices in their adjacency alg...

AHadamard matrix is said to be completely non-cyclic (CNC) if there are no two rows (or two columns) that are shift equivalent in its reduced form. In this paper, we present three new constructions of CNC Hadamard matrices. We give a primary construction using a flipping operation on the submatrices of the reduced form of a Hadamard matrix. We show that, up to some restrictions, the Kronecker p...

In this article, we study an inverse problem to determine an unknown source term in a space time fractional diffusion equation, whereby the data are obtained at a certain time. In general, this problem is ill-posed in the sense of Hadamard, so the Fourier truncation method is proposed to solve the problem. In the theoretical results, we propose a priori and a posteriori parameter choice rules a...

Using recent results on singularity analysis for Hadamard products of generating functions, we obtain the limiting distributions for additive functionals on m-ary search trees on n keys with toll sequence (i) nα with α ≥ 0 (α = 0 and α = 1 correspond roughly to the space requirement and total path length, respectively); (ii) ln ( n m−1 ) , which corresponds to the socalled shape functional; and...

In this paper we formalize three constructions for skew-Hadamard matrices from a Computational Algebra point of view. These constructions are the classical 4 Williamson array construction, an 8 Williamson array construction and a construction based on OD(16; 1, 1, 2, 2, 2, 2, 2, 2, 2), a 9-variable full orthogonal design of order 16. Using our Computational Algebra formalism in conjunction with...

The paper considers the long-time behavior for a class of generalized high-order Kirchhoff-type coupled equations, under corresponding hypothetical conditions, according to Hadamard graph transformation method, obtain equivalent norm in space , and we existence family inertial manifolds while such equations satisfy spectral interval condition.