Finding an appropriate representation of planning operators is crucial for theorem provers that work with proof planning. We show a new representation of operators and demonstrate how diagonalization can be represented by operators. We explain how a diagonalization operator used in one proof-plan can be analogically transferred to an operator used in another proof-plan. Finally, we nd an operat...

The problem of Blind Identification of linear mixtures of independent random processes is known to be related to the diagonalization of some tensors. This problem is posed here in terms of a non conventional joint approximate diagonalization of several matrices. In fact, a congruent transform is applied to each of these matrices, the left transform being rectangular full rank, and the right one...

A language is defined by closure under safe iteration and under a new form of safe diagonalization that, unlike other forms of diagonalization used in literature to define sub-recursive hierarchies, is constructive and decidable. By counting the nesting levels of these schemes, an ordinal is assigned to each program. This yields a hierarchy Tα (α < ωω) that singles-out the complexity classes DT...

In the present paper, we give a fast algorithm for block diagonalization of k-tridiagonal matrices. The block diagonalization provides us with some useful results: e.g., another derivation of a very recent result on generalized k-Fibonacci numbers in [M.E.A. El-Mikkawy, T. Sogabe, A new family of k-Fibonacci numbers, Appl. Math. Comput. 215 (2010) 4456– 4461]; efficient (symbolic) algorithm for...

The exact numerical diagonalization of the Hamiltonian of a 2D circular quantum dot is performed for 2, 3, and 4 electrons.The results are compared with those of the perturbation theory.Our numerical results agree reasonably well for small values of the dimensionles coupling constant λ = a a B where a is the dot radius and a B is the effective Bohr radius.Exact diagonalization results are compa...

The aim of this work is to give a comprehensive overview of the problem of jointly block-diagonalizing a set of matrices. We discuss how to implement methods in the common case of only approximative block-diagonalizability using Jacobi algorithms. Standard Jacobi optimization techniques for diagonalization and joint diagonalization are reviewed first, before we study their generalizations to th...

This paper introduces an extension of an earlier method of the author for separating stationary sources, based on the joint approximated diagonalization of interspectral matrices, to the case of cyclostationary sources, to take advantage of their cyclostationarity. the proposed method is based on the joint block approximate diagonlization of cyclic interspectral density. An algorithm for this d...

Cantor’s diagonalization idea: reminder. Most mathematicians are familiar with diagonalization from Cantor’s proof that the set of all real numbers is not countable. Indeed, if it was countable, i.e., if we could enumerate all (decimal) real numbers d1d2 . . . di.f1 . . . fj . . . into a sequence d (k) 1 d (k) 2 . . . d (k) i .f (k) 1 . . . f (k) j . . ., k = 1, 2, . . ., then we would be able ...