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Let Λ be a commutative ring, A an augmented differential graded algebra over Λ (briefly, DGA-algebra) and X be a relatively free resolution of Λ over A. The standard bar resolution of Λ over A, denoted by B(A), provides an example of a resolution of this kind. The comparison theorem gives inductive formulae f : B(A) → X and g: X → B(A) termed comparison(More)
A genetic algorithm based robust blind digital watermarking scheme is presented. Starting from a binary image (the original watermark), a genetic algorithm is performed searching for a permutation of this image which is as uncorrelated as possible to the original watermark. The output of the GA is used as our final watermark, so that both security and(More)
A method for embedding cocyclic submatrices with " large " determinants of orders 2t in certain cocyclic Hadamard matrices of orders 4t is described (t an odd integer). If these determinants attain the largest possible value, we are embedding D-optimal designs. Applications to the pivot values that appear when Gaussian elimination with complete pivoting is(More)
We are concerned with the development of an useful software in order to improve the student knowledge and dexterity on discrete mathematics. We display a preliminary computer package which consists of five items: Fibonacci sequence, Euclides algorithm, prime numbers and factorisation, units in Z n and R.S.A. cryptography. This program is organized as(More)
Let G be a semidirect product of finitely generated Abelian groups. We provide a method for constructing an explicit contraction (special homotopy equivalence) from the reduced bar construction of the group ring of G, $${\overline{B}(\mathsf{\textstyle Z\kern-0.4em Z}[G])}$$ , to a much smaller DGA-module hG. Such a contraction is called a homological model(More)