Maximin location: Discretization not always works

In this note we show by means of a simple example that, if the maximin problem with (nonlinear) concave increasing utility functions is solved by inspecting the extreme points of the (generalized) Voronoi diagram (as usually proposed), one may have to inspect an infinite number of candidate points. The research of the second and third authors is partially supported by Grant PB96-1416-C02-02 of Ministerio de Educación y Cultura, Spain     

Portfolio optimization with short-selling and spin-glass

In this paper, we solve a general problem of optimizing a portfolio in a futures markets framework, extending the previous work of Galluccio et al. [Physica A 259, 449 (1998)]. We allow for long buying/short selling of a relatively large number of assets, assuming a fixed level of margin requirement. Because of non-linearity in the constraint, we derive a multiple equilibrium solution, in a size exponential respect to the number of assets. That means that we can not obtain the unique efficiency frontier, but many of them and each one is related to different levels of risk. Such a problem is analogous to that of finding the ground state in long-ranged Ising spin glass with external field. In order to get the best portfolio (i.e. that is along the best efficiency frontier), we have to implement a two-step procedure, performing the exhaustive enumeration of all local minima. We develop a concrete application, where the different part of the proposed solution are computed. Received 31 December 2001     

A density functional for the correlation energy,deduced in the framework of the correlation factor approach

An approximate density functional is deduced from a wave function within the correlation factor method. The new functional does not include terms depending on the gradient of the density, but shows the simplicity of local density functionals without spin polarization. However, it includes correctly the inhomogeneity effects and, also, the nonlocal nature of an electronic system. The approach adopted here stresses the goodness of the expression taken by Colle and Salvetti for building a correlation factor and, at the same time, allows us to gain light on the nature of the deficiencies of those functionals obtained, up to now, from the perspective of the Hohenberg and Kohn theorem.     

D+D 2 Quasiclassical rate constant calculations on parallel computers

Summary The calculation of rate constant values of theH+H ₂ reaction for an extended range of excited vibrational states of the diatomic molecule and temperatures is relevant to the modeling ofH ^– sources. To investigate the effect of isotopic substitutions on the efficiency of vibrational deexcitation processes, we extended the calculations to theD+D ₂ system. These calculations were carried out using a program restructured to run on a shared memory vector and parallel computer. The dependence of the efficiency of vibrational deexcitation processes from both the initial vibrational state and temperature of reactants is reported. Restructuring strategies adopted for implementing the program on both shared and distributed memory computers as well as speedups achieved on both types of machines are also discussed.     

Identification and determination of corticosteroids in adrenal gland extracts for pharmaceutical use by HPLC

Summary Some HPLC procedures with isocratic or gradient elution are reported for the identification and determination of most of the characteristic components of cortical extracts. The proposed solvent systems were: A) for normal phase chromatography, mixtures of chloroform-methanol-water on silica columns. B) For reversed phase chromatography, mixtures of methanol-water or acetonitrile-water or tetrahydrofuran-water on octadecyl silica columns of different brands. With these systems it was possible to identify and determine, in addition to the principal corticosteroids, some minor components of the cortical extracts as the 20β-dihydroderivatives of compounds F, E, A, B, the 17-ketosteroids adrenosterone, 11β-hydroxyandrostendione and androstendione and finally, progesterone and 17-OH progesterone. In reversed phase chromatography it was also possible, by monitoring the effluent at 205 nm, to reveal the 5α- and 5β-tetrahydroderivatives of the main corticosteroids and to separate them from most of the steroidal components of the adrenal extracts; in these conditions it was also possible to reveal some characteristic, unknown components of the cortical extracts. Some results of quantitative analysis of cortical extracts are also reported, comparing different analytical procedures. Presented at the 15th International Symposium on Chromatography, Nürnberg, October 1984     

Implementazione di tests probabilistici di primalità

Sunto In questo lavoro si considerano due tests probabilistici di primalità per interi disparim di forma qualsiasi. Gli algoritmi sono tali che sem è dichiarato composto allora lo è certamente, mentre sem è dichiarato primo il risultato ha un certo margine di errore, che può essere reso arbitrariamente piccolo. Un programma scritto e compilato in linguaggio FORTRAN, applicabile ad interi fino a 10²⁰⁰⁰ ed adatto anche a personal computer, permette un confronto dei due tests sulla base del tipo dei risultati e del tempo di elaborazione, fornendo diverse opzioni ed una stima del limite superiore per l’eventuale errore in una dichiarazione di probabile primalità.

---

Summary In this paper we consider two probabilistic tests for determining the primality of any odd integerm. Both algorithms have the property that ifm is declared to be composite than it is guaranteed to be so. On the other hand, ifm is declared to be prime than it is sure to be prime only within a certain margin of error which can be made arbitrarily small. A program, written and compiled in the computer language FORTRAN enable this tests to be applied to integers up to 10²⁰⁰⁰, allowing a comparison between the two tests with respect to their running time and with an esplicit bound for the maximum possible error whenm is declared prime. The program is sufficiently compact to be implemented on a personal computer such as an IBM PS/2 with an arithmetic co-processor