This paper considers self-tuning blind identification and equalization of fractionally spaced IIR channels. One recursive estimator is used to generate parameter estimates of the numerators of IIR systems, while the other estimates denominator of IIR channel. Equalizer parameters are calculated by solving Bezout type equation. It is shown that the numerator parameter estimates converge (a.s.) t...

In this note, we investigate the blind source separability of linear FIR-MIMO systems. The concept of semi-reversibility of a system is presented. It is shown that for a semi-reversible system, if the input signals belong to a binary alphabet, then the source data can be blindly separated. One sufficient condition for a system to be semi-reversible is obtained. It is also shown that the propose...

In this paper, algorithms for the computation of all matrices of the generalized polynomial Bezout identity are proposed. The algorithms are based on the computation of minimal polynomial basis for the right null spaces of certain polynomial matrices. For this reason, an algorithm for the computation of minimal polynomial bases is also proposed. Since this algorithm relies solely on singular va...

In this paper, we prove two versions of an arithmetic analogue of Bezout’s theorem, subject to some technical restrictions. The basic formula proven is deg(V )h(X∩Y ) = h(X) deg(Y )+h(Y ) deg(X)+O(1), where X and Y are algebraic cycles varying in properly intersecting families on a regular subvariety VS ⊂ PS . The theorem is inspired by the arithmetic Bezout inequality of Bost, Gillet, and Soul...

For a tropical prevariety in R given by a system of k tropical polynomials in n variables with degrees at most d, we prove that its number of the connected components is less than ( k+7n−1 3n ) · d k+n+1 . On a number of 0-dimensional connected components a better bound ( k n ) · d n k−n+1 is obtained, which extends the Bezout bound due to B. Sturmfels from the case k = n to an arbitrary k ≥ n....

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...

let r be an associative ring with unity. an element a in r is said to be r-clean if a = e+r, where e is an idempotent and r is a regular (von neumann) element in r. if every element of r is r-clean, then r is called an r-clean ring. in this paper, we prove that the concepts of clean ring and r-clean ring are equivalent for abelian rings. further we prove that if 0 and 1 are the only idempotents...