Showing papers by "University of Lisbon published in 1980"

The Optimal Weighting of Indicators for a Crawling Peg

Abstract: This paper derives optimal weights for current-account and reserve indicators for adjusting the exchange rate (a "crawling peg"). Keven (1975)showed that use of a current account indicator alone would not stabi1iereserves, while a reserve indicator results in unstable fluctuations in the exchange rate. This paper begins by analyzing the problem in the frame work of Phillips (1954), in which the current account indicator is "proportional" and the reserve indicator is "integral." We then analyze the problem in a deterministic optimal control framework, and finally as a problem in stochastic control. In all cases the optimal combination is a weighted average, which we call the Keven-Phillips formula. With a fairly low variance of the current account, its weight falls in the range 0.47-0.65. Rising variance reduces its weight in the optimal formula.

A Relational Model for Non-Deterministic Programs and Predicate Transformers

Abstract: A relational model for non-deterministic programs is presented. Several predicate transformers are introduced and it is shown that one of them satisfies all the healthiness criteria indicated by Dijkstra for a useful total correctness predicate transformer.

Notes and announcements

Abstract: This section is devoted to the announcement and exchange of information that may be of interest to readers. Recent publications and theses on cognitive-clinical topics will be noted along with conference announcements and occasional bibliographies. Readers are invited to submit items for this section. In publicizing meetings or conferences, the announcement must be received by the editor no less than 6 months prior to the issue in which it will appear. Please submit all material for this section to Diane B. Arnkoff, Department of Psychology, Catholic University, Washington, D.C. 20064.

Deformed tensor interactions in deuteron elastic and inelastic scattering

Abstract: The various forms of tensor potentials present in deuteron elastic and inelastic scattering on a deformed target nucleus are derived using a folding model for the deuteron-nucleus interaction Approximate expressions for the radial dependence of the deformed tensor interactions parametrized with the derivatives of Woods-Saxon potentials are obtained and discussed for the case of a rotational nucleus

Adiabatical Invariance in Microphysics

Abstract: Adiabatical Invariance made its first appearance in Physics in the Solvay Meeting of 1911 (Reunions Solvay1), when the President — who was Henrik Anton Lorentz himself — asked to the attendants what would become the oscillations of a classical pendulum if one undertakes to shorten its length very slowly. The answer to that question was immediately given by Einstein: under such conditions the quotient between the total energy E and the frequency v should remain the same.

Nonlinear Problems Arising in the Study of Nematic Liquid Crystals

Abstract: Following [2] and [1], we deduce, from Leslie’s model (cf C9]), a weak formulation for the time dependent coupled equations of an incompressible nematic liquid crystal submitted to a strong homogeneous magnetic field We also give some results about the existence, uniqueness, regularity and asymptotic behavior of weak solutions (cf [2], [4],[1] and [5])

Limit laws for the maximum values of a class of strong mixing discrete random variables

Abstract: Let X , n31 be a stationary strong mixing sequence of random variables satisfying an additional weak dependence conditidn . Let F(x) be the marginal distribution function of the X's and let M ,n,>1 be the associated sequence of maximum values .When the support of F(x) consists of all sufficiently large positive integers some of the asymptotic results of extreme value theory fail to apply but weaker limit laws for M , as n-, are obtained . n Seja {Xn}n>1 uma sucessáo estacionária de variáveis aleatórias(v .a .'s) . Admitamos ainda que a sucessáo {Xn } n>,1 e \"strong mixing\", isto é, existe uma fun(~áo g(k) definida nos inteiros positivos, tal que g(k)-0 quando k-, e para acontecimentos Ac I(X1, . . .,XM) e BE :I(XM+k, . . .) IP(An B)-P (A)-P(B)ISg(k) (1) Se a sucessáo estacionária {Xn}n31 for tal que (1) é válido com g(k) substituida por ~(k)-P(A), ande O(k) -> 0 quando k-, diremos que {X } é n n:1 uma sucessáo estacionária, \"~-mixing\" . Seja F( .) a funráo de distribuigáo(f .d .) marginal da sucessáo {Xn }n31 e seja {Yn}niI1 uma sucessáo constituida por variáveis aleatórias independentes e identicamente distribuidas(i .i .d .) com f .d . F( .), coincidente pois com a f .d . de cada um dos Xn' n,>1 . Para o caso i .i .d . é trivial a validade da le¡ dos grandes números para máximos desde que exista x0 tal que F(x0 )=1 e F(x0-ó)<1, para todo o5>0 . Research partially supported by Calouste Gulbenkian Foundation . Gnedenko(1943) demonstrou que se F(x)<1 para todo o x1, isto é,exis te uma sucessáo {An}n,1 tal que P(IMn _An i0, se e só se, lim (1-F(x+8))/(1-F(x))=0 para todo o¿>0 . x->_ Consideremos agora uma classe especial de sucessóes reais . Uma sucessáo {cn}n>1 de números reais satisfaz a condigáo C se c n _,1, e se existirem sucessóes de inteiros positivos {ni } i>1' {mi}i,1 e {ki}i>,1 tais que ki ->-, mi/ni->O, (niki)/(ni_lki-1)->1, kig(m¡)->O, quando i~, g( .) a fungáo de mistura em (1) e Definamos u n (C)= inf {x :1-F(x-),>I/n,>1-F(x)} e punhamos Mn=max(X1, . . .,Xn), xeR Tem-se entáo o seguinte resultado (demonstrado em O'Brien,3 .) . Lema 1 . Se lim sup P(Mn 0 e se {un(~)}n>1 satisfin-» zar a condigáo C para todo o E>0, entáo para qualquer sucessáo de números reais {d } n -n,>1' lim E (ni -j) P(Xj+1 >cr l' X 1 >cr . )/ni =0, com ri=kn .+m . . i, j=1 i i . P(Mn~ 1 quando n se e só se Fn(dn ) -> 1 quando n->-, P(M n ~ 0 quando n->se e só se Fn (dn ) -+ 0 quando n->. cessáo {M*}n>1 . Consideremos a fungáo auxiliar Fc(.x)=1-exp(_-hc(x)), x,>1, onda hc (x) é obti da a partir da fungáo de argumento inteiro h(n)=-log(.1-F(.n)) por interpóla ráo linear . Enunciaremos sem demonstraráo o seguinte resultado : 140 Este lema imediatamente implica a validade da le¡ dos grandes números para a sucessáo de máximos de um processo ~-mixing se e só se tal le¡ for válida para a sucessáo de máximos do processo i .i .d . associado . A partir de agora suporemos que a f .d . F está na classe O . e óbvio que a le¡ dos grandes números náo pode entáo ser válida para a sucessáo M*, n:1, pois escolhendo 6x(0,1), (1-F(n+e))/(1-F(n))->1 quando n. 0 mesmo acontece para a sucessáo Mn , n,>1, e também nesta situac~áo podemos obter uma análoga da le¡ dos grandes números semelhante á le¡ obtida por Anderson(1970) para a suTeorema 1 . Seja {Xn}n>1 uma sucessáo de v .a .'s, estacionaria e \" strong mixing\", tal que F( .), f .d . marginal de {Xn}n?,1' pertence a ; . Admita-se que as condisóes impostas no lema 1 sao válidas para qualquer sucessáo {un (~)} n>1 ' j>0 . Entáo existe uma sucessáo de inteiros {In}n>1' tal que