Let M a Riemannian manifold of dimension m ≥ 3, let Σ be a closed smooth submanifold of M of co-dimension at least 2, and let H be a Hadamard manifold with pinched sectional curvatures. We prove the existence and uniqueness of harmonic maps φ : M \ Σ → H with prescribed singularities along Σ. When M = R, and H = H C , the complex hyperbolic space, this result has applications to the problem of ...

In this paper we establish several polynomials similar to Bernstein's polynomials and several refinements of  Hermite-Hadamard inequality for convex functions.

For every n divisible by 4, we construct a square matrix H of size n, with coeecients 1, such that H H t nI mod 32. This solves the 32-modular version of the classical Hadamard conjecture. We also determine the set of lengths of 16-modular Golay sequences. 0. Introduction Hadamard matrices can be constructed from various binary sequences, either from Golay complementary sequences, or Williamson...

In [2] Bussemaker and Tonchev constructed six doubly even (56,28, 12) codes from two Hadamard matrices of order 28. But two of them were not distinguished. In [11] and [12] we characterized Hadamard matrices of order 28 and there are exactly 487 Hadamard matrices, up to equivalence. In this paper we show that only two of the above 487 matrices produce six doubly even (56,28,12) codes and that t...

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

Modular addition modulo a power of two, is one of the most applicable operators in symmetric cryptography; therefore, investigating cryptographic properties of this operator has a significant role in design and analysis of symmetric ciphers. Algebraic properties of modular addition modulo a power of two have been studied for two operands by Braeken in fse’05. Also, the authors of this paper, ha...

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 ...