Orderings and Probability Functionals Consistent with Preferences

This paper unifies the classical theory of stochastic dominance and investor preferences with the recent literature on risk measures applied to the choice problem faced by investors. First, we summarize the main stochastic dominance rules used in the finance literature. Then we discuss the connection with the theory of integral stochastic orders and we introduce orderings consistent with investors' preferences. Thus, we classify them, distinguishing several categories of orderings associated with different classes of investors. Finally, we show how we can use risk measures and orderings consistent with some preferences to determine the investors' optimal choices.     

Segregation in reaction-diffusion systems

Segregation of reactants in reaction-diffusion systems is a spatial structure that can be formed either as a result of a dynamical process or as an initially prepared system. In this paper we review our recent results on both such systems. First we study the dynamic segregation at a single trap, in particular in the presence of fields and disorder. Then we study properties of the dynamic reaction front produced due to initial segregation of the reactants in the A + B→C system. Both systems are shown to exhibit anomalous kinetic properties.     

Sacks forcing,Laver forcing,and Martin's axiom

Summary In this paper we study the question assuming MA+CH does Sacks forcing or Laver forcing collapse cardinals? We show that this question is equivalent to the question of what is the additivity of Marczewski's ideals ⁰. We give a proof that it is consistent that Sacks forcing collapses cardinals. On the other hand we show that Laver forcing does not collapse cardinals.Research partially supported by NSF grant 8801139     

General Approximate Solutions for some Common Inventory Models

Employing a group of general approximations introduced elsewhere, we derive explicit approximate solutions to the standard newsboy problem, to some (Q, r) models recently developed, and to a periodic review order up to R model. The solutions obtained are general in that no distributional assumptions need to be specified prior to their derivation, and merely knowledge of the first three or four moments (of the relevant random variables) is required. The accuracy achieved is satisfactory, while algebraic simplicity is preserved.     

RESEARCH NOTE

A previous report [Freeman et al. (1986) Photochem. Photobiol. 43S, 93S] indicated that irradiation of human skin in situ with 385 or 405 nm radiation produced detectable levels of pyrimidine dimers in DNA. Since these wavelengths are absorbed poorly by DNA, these results suggested that DNA damage was sensitized by other absorbing molecules present in skin. Examination of two experimental aspects of the previous work indicates that (1) the static gel electrophoresis method for DNA dispersion used in lesion determination gave accurate values of the levels of induced dimers, and (2) the DNA damage apparently induced by 385 nm was actually induced by shorter wavelength UV present in the 20 nm bandpass beam of the monochromator. The current results indicate that monochromatic 385 and 405 nm radiation are ineffective in dimer production in human skin in situ.     

Perfect sets of random reals

We show that the existence of a perfect set of random reals over a modelM ofZFC does not imply the existence of a dominating real overM, thus answering a well-known open question (see [BJ 1] and [JS 2]). We also prove that (the product of two copies of the random algebra) neither adds a dominating real nor adds a perfect set of random reals (this answers a question that A. Miller asked during the logic year at MSRI). The first author would like to thank the MINERVA-foundation for supporting him. The second author would like to thank the Basic Research Foundation (the Israel Academy of Sciences and Humanities) for supporting him.