In this paper we study a one-dimensional quantum random walk with the Hadamard transformation which is often called the Hadamard walk. We construct the Hadamard walk using a transition matrix on probability amplitude and give some results on symmetricity of probability distributions for the Hadamard walk.

We establish weak and strong convergence of Ishikawa type iterates of two pointwise asymptotic nonexpansive maps in a Hadamard space. For weak and strong convergence results, we drop “rate of convergence condition”, namely , to answer in the affirmative to the open question posed by Tan and Xu [1] even in a general setup.     1 1 n n c x      

We introduce the notion of strongly h-convex functions (defined on a normed space) and present some properties and representations of such functions. We obtain a characterization of inner product spaces involving the notion of strongly h-convex functions. Finally, a Hermite–Hadamard–type inequality for strongly h-convex functions is given.

In 1867, Syvlester noted that the Kronecker product of two Hadamard matrices is an Hadamard matrix. This gave a way to obtain an Hadamard matrix of exponent four from two of exponent two. Early last decade, Agayan and Sarukhanyan found a way to combine two Hadamard matrices of exponent two to obtain one of exponent three, and just last year Craigen, Seberry and Zhang discovered how to combine f...

There is a well-known correspondence between symmetric 2-(4ju— 1,2/z — 1,/z — 1) designs and Hadamard matrices of order 4^. It is not so well known that there is a natural correspondence between Hadamard matrices of order 2\x and affine l-(4ju, 2^, 2(i) designs whose duals are also affine. Such a design is denoted by H^fi) in this paper. Under this natural correspondence, two H^fi) designs are ...

Hadamard matrices with a subjacent algebraic structure have been deeply studied as well as the links with other topics in algebraic combinatorics [1]. An important and pioneering paper about this subject is [5], where it is introduced the concept of Hadamard group. In addition, we find beautiful equivalences between Hadamard groups, 2-cocyclic matrices and relative difference sets [4], [7]. Fro...

In this paper all cocyclic Hadamard matrices of order less than 40 are classified. That is, all such Hadamard matrices are explicitly constructed, up to Hadamard equivalence. This represents a significant extension and completion of work by de Launey and Ito. The theory of cocyclic development is discussed, and an algorithm for determining whether a given Hadamard matrix is cocyclic is describe...

It is well-known that a Sylvester Hadamard matrix can be described by means of a cocycle. In this paper it is shown that the additional internal structure in a Sylvester Hadamard matrix, provided by the cocycle, is su cient to guarantee some kind of reduction in the computational complexity of calculating its permanent using Ryser's formula. A Hadamard matrix H of order n is an n× n matrix with...