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Arithmetics in numeration systems with negative quadratic base

Zuzana Masáková, Tomáš Vávra (2011)

Kybernetika

We consider positional numeration system with negative base - β , as introduced by Ito and Sadahiro. In particular, we focus on arithmetical properties of such systems when β is a quadratic Pisot number. We study a class of roots β > 1 of polynomials x 2 - m x - n , m n 1 , and show that in this case the set Fin ( - β ) of finite ( - β ) -expansions is closed under addition, although it is not closed under subtraction. A particular example is β = τ = 1 2 ( 1 + 5 ) , the golden ratio. For such β , we determine the exact bound on the number of fractional digits...

Artificial neural networks in time series forecasting: a comparative analysis

Héctor Allende, Claudio Moraga, Rodrigo Salas (2002)

Kybernetika

Artificial neural networks (ANN) have received a great deal of attention in many fields of engineering and science. Inspired by the study of brain architecture, ANN represent a class of non-linear models capable of learning from data. ANN have been applied in many areas where statistical methods are traditionally employed. They have been used in pattern recognition, classification, prediction and process control. The purpose of this paper is to discuss ANN and compare them to non-linear time series...

Aspects of Impatience in a Finite Buffer Queue

Medhi Pallabi, Amit Choudhury (2012)

RAIRO - Operations Research - Recherche Opérationnelle

In a multi server queuing system, buffer size is often larger than the number of servers. This necessitates queuing and waiting for some customers. Customers become impatient while waiting for service. Additionally, they may also become impatient if service is not offered at the desired rate. This paper analyses a finite buffer multi server queuing system with the additional restriction that customers may balk as well as renege. Closed form expressions of a number of performance measures are presented....

Aspects of Impatience in a Finite Buffer Queue

Medhi Pallabi, Amit Choudhury (2012)

RAIRO - Operations Research

In a multi server queuing system, buffer size is often larger than the number of servers. This necessitates queuing and waiting for some customers. Customers become impatient while waiting for service. Additionally, they may also become impatient if service is not offered at the desired rate. This paper analyses a finite buffer multi server queuing system with the additional restriction that customers may balk as well as renege. Closed form expressions...

Asymptotic analysis of a class of functional equations and applications

P. J. Grabner, H. Prodinger, R. F. Tichy (1993)

Journal de théorie des nombres de Bordeaux

Flajolet and Richmond have invented a method to solve a large class of divide-and-conquer recursions. The essential part of it is the asymptotic analysis of a certain generating function for z by means of the Mellin transform. In this paper this type of analysis is performed for a reasonably large class of generating functions fulfilling a functional equation with polynomial coefficients. As an application, the average life time of a party of N people is computed, where each person advances one...

Asymptotic behaviour of bi-infinite words

Wit Foryś (2004)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We present a description of asymptotic behaviour of languages of bi-infinite words obtained by iterating morphisms defined on free monoids.

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