Over the past couple of years trace maps over Galois fields and Galois rings have been used very successfully to construct cocyclic Hadamard, complex Hadamard and Butson Hadamard matrices and subsequently to generate simplex codes over Z4,Z2s and Zp and new linear codes over Zps . Here we define a new map, the trace-like map and more generally the weighted-trace map and extend these techniques ...

We apply Computational Algebra methods to the construction of Hadamard matrices with two circulant cores, given by Fletcher, Gysin and Seberry. We introduce the concept of Hadamard ideal for this construction to systematize the application of Computational Algebra methods. Our approach yields an exhaustive search construction of Hadamard matrices with two circulant cores for this construction f...

We consider a new operation on the family of binary relations on integers called Hadamard star. View a binary relation R ⊆ N × N as a mapping of N into the power set of N and let R(n) denote the subset of integers m such that (n,m) ∈ R. Then the Hadamard star of R is the relation which assigns to each integer n the Kleene star of R(n). This is reminiscent of the Hadamard inverse of series with ...

In this paper we did a generalization of Hadamard product of Fibonacci Q matrix and Fibonacci Q−n matrix for continuous domain. We obtained Hadamard product of the golden matrices in the terms of the symmetrical hyperbolic Fibonacci functions and investigated some properties of Hadamard product of the golden matrices. Mathematics Subject Classification: Primary 11B25, 11B37, 11B39, Secondary 11C20

In this paper, comparison of various orthogonal transforms in Wiener filtering is discussed. The study involves the family of discrete orthogonal transforms called Complex Hadamard Transform, which has been recently introduced by the same authors. Basic definitions, properties and transformation kernel of Complex Hadamard Transform are also shown. key words: Complex Hadamard transform, digital ...

Some inequalities of Hermite-Hadamard type for h-convex functions de…ned on convex subsets in real or complex linear spaces are given. Applications for norm inequalities are provided as well. 1. Introduction The following inequality holds for any convex function f de…ned on R (1.1) (b a)f a+ b 2 < Z b a f(x)dx < (b a) + f(b) 2 ; a; b 2 R: It was …rstly discovered by Ch. Hermite in 1881 in the j...

We give a non-perturbative construction of a distinguished state for the quantized Dirac field in Minkowski space in the presence of a time-dependent external field of the form of a plane electromagnetic wave. By explicit computation of the fermionic signature operator, it is shown that the Dirac operator has the strong mass oscillation property. We prove that the resulting fermionic projector ...

We construct the Hadamard Green’s function by using the eigenfunction, which are obtained by solving the wave equation for the massless conformal scalar field on the Sn−1 of a n-dimensional closed, static universe. We also consider the half space case with both the Dirichlet and the Neumann boundary conditions. Solving of eigenfunction and eigenvalues of the corresponding field equation is inte...

Abstract In this paper we complete the first step, namely the uniform bound on completely convergent contributions, towards proving that a three dimensional interacting system of Fermions is a Fermi liquid in the sense of Salmhofer. The analysis relies on a direct space decomposition of the propagator, on a bosonic multiscale cluster expansion and on the Hadamard inequality, rather than on a Fe...

Any nonpositively curved symmetric space admits a topological compactification, namely the Hadamard compactification. For rank 1 spaces, this topological compactification can be endowed with a differentiable structure such that the action of the isometry group is differentiable. Moreover, the restriction of the action on the boundary leads to a flat model for some geometry (conformal, CR or qua...