Browsing Departament d'Economia i Empresa by Author "Viader, Pelegrí"

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Browsing Departament d'Economia i Empresa by Author "Viader, Pelegrí"

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  • Paradís, Jaume; Viader, Pelegrí; Bibiloni, Lluís (1997)
    We start with a generalization of the well-known three-door problem: the n-door problem. The solution of this new problem leads us to a beautiful representation system for real numbers in (0,1] as alternated series, known ...
  • Viader, Pelegrí; Paradís, Jaume; Bibiloni, Lluís (1997)
    The well--known Minkowski's? $(x)$ function is presented as the asymptotic distribution function of an enumeration of the rationals in (0,1] based on their continued fraction representation. Besides, the singularity of ...
  • Villanova, Ramon; Paradís, Jaume; Viader, Pelegrí (1999)
    This paper presents a classical Cournot oligopoly model with some peculiar features: it is non--quasi--competitive as price under N-poly is greater than monopoly price; Cournot equilibrium exists and is unique with each ...
  • Paradís, Jaume; Bibiloni, Lluís; Viader, Pelegrí (1996)
    In this article two aims are pursued: on the one hand, to present a rapidly converging algorithm for the approximation of square roots; on the other hand and based on the previous algorithm, to find the Pierce expansions of ...
  • Paradís, Jaume; Viader, Pelegrí; Bibiloni, Lluís (1999)
    Minkowski's ?(x) function can be seen as the confrontation of two number systems: regular continued fractions and the alternated dyadic system. This way of looking at it permits us to prove that its derivative, as it ...
  • Paradís, Jaume; Viader, Pelegrí; Bibiloni, Lluís (1998)
    A `next' operator, s, is built on the set R1=(0,1]-{ 1-1/e} defining a partial order that, with the help of the axiom of choice, can be extended to a total order in R1. Besides, the orbits {sn(a)}n are all dense in R1 ...
  • Paradís, Jaume; Pla, Josep; Viader, Pelegrí (2004)
    The Treatise on Quadrature of Fermat (c. 1659), besides containing the first known proof of the computation of the area under a higher parabola, R x+m/n dx, or under a higher hyperbola, R x-m/n dx— with the appropriate ...
  • Viader, Pelegrí; Bibiloni, Lluís; Paradís, Jaume (1998)
    Alfréd Rényi, in a paper of 1962, A new approach to the theory of Engel's series, proposed a problem related to the growth of the elements of an Engel's series. In this paper, we reformulate and solve Rényi's problem for ...
  • Bibiloni, Lluís; Viader, Pelegrí; Paradís, Jaume (2004)
    Theorem 1 of Euler’s paper of 1737 'Variae Observationes Circa Series Infinitas', states the astonishing result that the series of all unit fractions whose denominators are perfect powers of integers minus unity has sum ...
  • Viader, Pelegrí; Paradís, Jaume; Bibiloni, Lluís (2000)
    The approximants to regular continued fractions constitute `best approximations' to the numbers they converge to in two ways known as of the first and the second kind. This property of continued fractions provides a ...
  • Villanova, Ramon; Paradís, Jaume; Viader, Pelegrí; Miralles, Joan (2002)
    It is widely accepted in the literature about the classical Cournot oligopoly model that the loss of quasi–competitiveness is linked, in the long run as new firms enter the market, to instability of the equilibrium. In ...
  • Paradís, Jaume; Viader, Pelegrí; Bibiloni, Lluís (2006)
    In 1952 F. Riesz and Sz.Nágy published an example of a monotonic continuous function whose derivative is zero almost everywhere, that is to say, a singular function. Besides, the function was strictly increasing. Their ...

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