This paper shows that coprime right factorizations exist for the input to state mapping of a continuous time nonlinear system provided that the smooth feedback stabilization problem be solvable for this system. In particular, it follows that feedback linearizable systems admit such factorizations. In order to establish the result a Lyapunov-theoretic deenition is proposed for \bounded input bou...

We investigate good coprime interleavers that perform well in turbo codes and allow for memory-efficient implementation. We first evaluate the spread and the randomness properties of these interleavers using the cycle correlation sum (CCS) and the variance of the second order spread spectrum (VSSS) criteria, respectively. A critical parameter cpower is introduced for interleavers whose lengths ...

d|en d denote the number and the sum of exponential divisors of n, respectively. Properties of these functions were investigated by several authors, see [1], [2], [3], [5], [6], [8]. Two integers n,m > 1 have common exponential divisors iff they have the same prime factors and for n = ∏r i=1 p ai i , m = ∏r i=1 p bi i , ai, bi ≥ 1 (1 ≤ i ≤ r), the greatest common exponential divisor of n and m is

We propose a new computational approach based on descriptor state space algorithms for computing normalized coprime factorizations of arbitrary rational matrices. The proposed approach applies to both continuousand discrete-time rational transfer-function matrices and shows that each rational matrix possesses a normalized coprime factorization with proper factors. The new method is conceptually...

This paper addresses a problem recently raised by Laurent and Nogueira about inhomogeneous Diophantine approximation with coprime integers. A corollary of our main theorem is that for any irrational α ∈ R and for any γ ∈ R and > 0 there are infinitely many pairs of coprime integers m,n such that |nα−m− γ| ≤ 1/|n| . This improves upon previously known results, in which the exponent of approximat...

In this paper, the relationship between the Bezout and the set-theoretic approaches to left coprimeness is studied. It is shown that left coprimeness in the set-theoretic sense implies left coprimeness in the Bezout sense. In addition to these results, we investigate whether some properties for linear left coprime realizations carry over to the nonlinear case, for example we examine the relatio...

In this paper, the relationship between the Bezout and the set theoretic approaches to left co-primeness is studied. It is shown that left coprimeness in the set theoretic sense implies left coprimeness in the Bezout sense. In addition to these results, we investigate whether some properties for linear left coprime realizations carry over to the nonlinear case, for example we examine the relati...

For g, n coprime integers, let `g(n) denote the multiplicative order of g modulo n. Motivated by a conjecture of Arnold, we study the average of `g(n) as n ≤ x ranges over integers coprime to g, and x tending to infinity. Assuming the Generalized Riemann Hypothesis, we show that this average is essentially as large as the average of the Carmichael lambda function. We also determine the asymptot...

This paper considers the nonlinear left coprime factorization (NLCF) of a nonlinear system. In order to study the balanced realization of such NLCF first a dual system notion is introduced. The important energy functions for the original NLCF and their relation with the dual NLCF are studied and relations between these functions are established. These developments can be used for studying a rel...