Odoardo Brugia

On certain Fibonacci‐type sums

The infinite sum of consecutive generalized Fibonacci numbers Ui (i = 1, 2, 3...) divided by ri (r an arbitrary non‐vanishing quantity) is investigated. After establishing the values of r for which the sum is integral, the set of all rational values of r satisfying this constraint is determined.

A note on the improper use of a formula for Fibonacci numbers

The improper use of a formula for Fibonacci numbers gives rise to an interesting class of integers (namely, the numbers Gn (k))governed by the integral parameters nand k.After establishing some properties of these numbers, we extend them to negative values of the subscript nand use this extension to obtain a Fibonacci identity. A glimpse of a possible further generalization is also caught.

Impact of long periods of identical bits on the choice of a scrambler for SDH

The statistical properties of sequences of consecutive identical bits at the output of various scrambler types are analyzed and discussed in order to provide designers of Synchronous Digital Hierarchy systems with a wide range of choices for scrambling implementation.

Functions of the Kronecker Square of the Matrix Q

As for the well-known matrix Q, [1], a number of matrices can be defined so that their successive powers contain entries related to certain Fibonacci numbers

A curious property of series involving terms of generalized sequences

Here we are concerned with series involving generalized Fibonacci numbers Un(p, q) and generalized Lucas numbers Vn(p, q). The aim of this paper is to find triples (p, q,r) for which the series Un(p, q)/r n and Vn(p, q)/r n (for r running from 0 to infinity) are unconcerned at the introduction of the factor n. The results established in this paper generalize the known fact that the series Fn/2 n (Fn the nth Fibonacci number) and the series nFn/2 n give the same result, namely −2/5.

Letter pointer overflows in SDH equipments

Particular situations of pointer overflows, which can take place either in the presence of high amplitude wander on STM-N signals entering SDH network elements or under severe failure conditions of the synchronization network, have been identified. In these situations waste of data results if no proper actions are carried out to handle pointer overflows. With reference to current regulations additional rules are proposed in order to avoid this kind of impairment on transported tributaries.

The Ring of Fibonacci (Fibonacci “Numbers” with Matrix Subscript)

Several authors (e.g., see [8]) have considered the Fibonacci numbers F x where the subscript x is an arbitrary real number and showed that these (complex) numbers enjoy most of the properties of the usual Fibonacci numbers F m (m integral). A quite natural extension of the numbers F x leads to the definition of the Fibonacci numbers F z and Lucas numbers L z

Letter: PLL Bandwidth Impact on Slave Clock Output Short Term Stability

{F_z} = \left( {{\alpha ^z} - {\beta ^z}} \right)/\sqrt 5