A singular function and its relation with the number systems involved in its definition

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 also happens for many other non-decreasing singular functions from [0,1] to [0,1], when it exists can only attain two values: zero and infinity. It is also proved that if the average of the partial quotients in the continued fraction expansion of x is greater than k* =5.31972, and ?'(x) exists then ?'(x)=0. In the same way, if the same average is less than k**=2 log2(F), where F is the golden ratio, then ?'(x)=infinity. Finally some results are presented concerning metric properties of continued fraction and alternated dyadic expansions.Singular function, number systems, metric number theory

A total order in [0,1] defined through a 'next' operator

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 and are constituted by elements of the same arithmetical character: if a is an algebraic irrational of degree k all the elements in a's orbit are algebraic of degree k; if a is transcendental, all are transcendental. Moreover, the asymptotic distribution function of the sequence formed by the elements in any of the half-orbits is a continuous, strictly increasing, singular function very similar to the well-known Minkowski's ?(×) function.Total orders, pierce series, singular functions

Approximation of quadratic irrationals and their pierce expansions

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 a certain class of quadratic irrationals as an alternative way to the method presented in 1984 by J.O. Shallit; we extend the method to find also the Pierce expansions of quadratic irrationals of the form $2 (p-1) (p - \sqrt{p^2 - 1})$ which are not covered in Shallit's work.Quadratic irrationals, Pierce series

Una Llei perque tot continuï igual

Abstract not availabl

El Ministeri d'Educació i Ciència tindrà en compte el pla de noves infraestructures i la seva dotació econòmica en el traspàs de les competències universitàries

Abstract not availabl

Conjuntura i desestabilitzacio del mercatun cas de l'impacte del cors en el comerç mallorqui del segle XVII

De les diferents formes que adquireix cl comerç en temps de guerra el cors esdevé una manifestació de primer ordre. L'alteració de les rutes i dels habituals titulars del transport afavoreix que els comerciants mallorquins accedeixin directament a uns productes que en època de pau aconsegueixen per mediació de tercers. La conducció de les captures a l'illa pot provocar, en funció de la seva magnitud, la saturació del mercat, una reacció dels importadors que restringeixen la demanda, l'aparició de fortes oscil·lacions interanuals en cl volum dels productes desembarcats i l'existència d'una via d'acumulació de capital, conjunturalment, espectacular.