We present a general theory for the closed-form parametric estimation of the unitary mixing matrix after prewhitening in the blind separation of two source signals from two noiseless instantaneous linear mixtures. The proposed methodology is based on the algebraic formalism of bicomplex numbers and is able to treat both real and complex valued mixtures indiscriminately. Existing analytic method...

In this study, by using Fibonacci Q-matrix and Lucas Q^'-matrix we define bicomplex Q^'-matrix. After that matrix representation, give some identities.

We discuss intrinsic aspects of Krupka's approach to nite{order variational sequences. We recover in an intrinsic way the second{order varia-tional calculus for aane Lagrangians by means of a natural generalisation of rst{ordertheories. Moreover, we nd an intrinsic expressionfor the Helmholtz morphism using a technique introduced by Koll a r that we have adapted to our context. Introduction The...

We present a family of complexes playing the same rôle, for homogeneous variational problems, that the horizontal parts of the variational bicomplex play for variational problems on a fibred manifold. We show that, modulo certain pullbacks, each of these complexes (apart from the first one) is globally exact. All the complexes may be embedded in bicomplexes, and we show that, again modulo pullb...

We prove that the stable homotopy of any Γ-module F is the homology of a bicomplex Ξ(F), in which the (q − 1)st row is the twosided bar construction B(Lieq,Σq, F[q]). This gives a natural homotopical cotangent bicomplex for graded commutative algebras, in a form suitable for use in a new obstruction theory for classifying E∞ ring structures on spectra. The E∞ structure on certain Lubin-Tate spe...

The conception of multi-alphabetical genetics is considered. Matrix forms of the representation of the multi-level system of molecular-genetic alphabets have discovered algebraic properties of this system. These properties are connected with well-known notions of dyadic groups and dyadic-shift matrices. Matrix genetics shows relations of the genetic alphabets with some types of hypercomplex num...