A natural starting point in a systematic search for co cyclic Hadamard matrices is the study of the case of co cycles over the groups Zt x Z~, for t odd. The solution set includes all Williamson Hadamard matrices, so this set of groups is potentially a uniform source for generation of Hadamard matrices. We present our analytical and computational results.

In this paper we introduce operator preinvex functions and establish a Hermite–Hadamard type inequality for such functions. We give an estimate of the right hand side of a Hermite–Hadamard type inequality in which some operator preinvex functions of selfadjoint operators in Hilbert spaces are involved. Also some Hermite–Hadamard type inequalities for the product of two operator preinvex functio...

We use combinatorial and Fourier analytic arguments to prove various non-existence results on systems of real and complex unbiased Hadamard matrices. In particular, we prove that a complete system of complex mutually unbiased Hadamard matrices (MUHs) in any dimension cannot contain more than one real Hadamard matrix. We also give new proofs of several known structural results in low dimensions.

In this paper, we introduce a class of generalized Hadamard matrices, called a Butson Hadamard matrix with partially cyclic core. Then a new construction method for Butson Hadamard matrices with partially cyclic core is proposed. The proposed matrices are constructed from the optimal balanced low-correlation zone(LCZ) sequence set which has correlation value −1 within LCZ.

Abstract: Completing the results achieved in a previous paper, we prove the symmetry of Hadamard/Seeley-deWitt off-diagonal coefficients in smooth D-dimensional Lorentzian manifolds. To this end, it is shown that, in any Lorentzian manifold, a sort of “local Wick rotation” of the metric can be performed provided the metric is a locally analytic function of the coordinates and the coordinates ar...

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Watermarking technology.play a central role in the digital right management for multimedia data. Especially a video watermarking is a real challenge, because of very high compression ratio (about 1:200). Normally the watermarks can barely survive such massive attacks, despite very sophisticated embedding strategies. It can only work with a sufficient error correcting code method. In this paper,...