In this paper, firstly we will present basic properties of Hadamard matrix product and Dual matrices to built necessary background. Then define special real dual under product. Finally, some theorems regarding be given.

In the present investigation, we consider an unified class of functions of complex order using Hadamard’s convolution. We obtain a necessary and sufficient condition for functions to be in these classes.

In this paper we consider the Hadamard product ? of regular functions using the concept of subordination. Let P (A,B) denote the class of regular functions subordinated to the linear fractional transformation (1 +Az)/(1−Bz), where A+B 6= 0 and |B| ≤ 1. By P (A,B) ? P (C,D) we denote the set {f ? g : f ∈ P (A,B), g ∈ P (C,D)} . It is known ([3], [7]), that for some complex numbers A,B,C,D there ...

In this paper, by using the generalized Hadamard product and the orthogonal decomposition of projection matrix, we propose a new general approach to construct mixed-level orthogonal arrays. As an application of the method, some new mixed-level orthogonal array’s of run sizes 36 and 72 are constructed. c © 2001 Elsevier Science B.V. All rights reserved.

We prove that if there exist Hadamard matrices of order 4m, 4n, 4p, 4q then there exists an Hadamard matrix of order 16mnpq. This improves and extends the known result of Agayan that there exists an Hadamard matrix of order 8mn if there exist Hadamard matrices of order 4m and 4n.