Considering a sample of 20 eclipsing binary systems with δ Scuti type primaries, we discovered that there is a possible relation among the pulsation periods of the primaries and the orbital periods of the systems. According to this empirical relation, the longer the orbital period of a binary, the longer the pulsation period of its pulsating primary. Among the sample, the masses of the secondaries and the separations between the components are known for eight systems for which a log Ppuls versus log F (the gravitational pull exerted per gram of the matter on the surface of the primaries by the secondaries) diagram also verifies such an interrelation between the periods. So, as the gravitational force applied by the secondary component onto the pulsating primary increases, its pulsation period decreases. The detailed physics underlying this empirical relation between the periods needs further confirmation, especially theoretically. However, one must also consider the fact that the present sample does not contain a sufficiently large sample of longer period (P > 5 d) binaries.

We consider an assemble-to-order generalized M-system with multiple components and multiple products, batch ordering of components, random lead times, and lost sales. We model the system as an infinite-horizon Markov decision process and seek an optimal policy that specifies when a batch of components should be produced (i.e., inventory replenishment) and whether an arriving demand for each product should be satisfied (i.e., inventory allocation). We characterize optimal inventory replenishment and allocation policies under a mild condition on component batch sizes via a new type of policy: lattice-dependent base stock and lattice-dependent rationing.

Abstract. We present the results of multisite observations of the δ Scuti star V 1162 Ori. The observations were done in the period October 1999 -May 2000, when 18 telescopes at 15 observatories were used to collect 253 light extrema during a total of 290 hours of time-series observations. The purpose of the observations was to investigate amplitude and period variability previously observed in this star, and to search for low-amplitude frequencies. We detect, apart from the main frequency and its two first harmonics, four additional frequencies in the light curves, all with low amplitudes (1-3 mmag). Combining the present data set with data obtained in 1998-99 at ESO confirms the new frequencies and reveals the probable presence of yet another pulsational frequency. All five low-amplitude frequencies are statistically significant in the data, but at least one of them (f5) suffers from uncertainty due to aliasing. Using colour photometry we find evidence for a radial main frequency (f1), while most or all low-amplitude frequencies are likely non-radial. We show that the main frequency of V 1162 Ori has variable amplitude and period/phase, the latter is also displayed in the O-C diagram from light extrema. The amplitude variability in our data is cyclic with a period of 282 d and a range of nearly 20 mmag, but earlier amplitude values quoted in the literature cannot be explained by this cyclic variation. O-C analysis including data from the literature show that the period of V 1162 Ori displays a linear period change as well as sudden or cyclic variations on a time scale similar to that of the amplitude variations.

Using a mechanism design approach, we consider a firm's optimal pricing policy when consumers are heterogeneous and learn their valuations at different times. We show that by offering a menu of advance-purchase contracts that differ in when, and for how much, the product can be returned, a firm can more easily price discriminate between privately-informed consumers. In particular, we show that screening on when the return option can be exercised increases firm profits, relative to screening on the size of the refund alone, only if the expected gains from trade are higher for consumers who learn later. We show that in some settings (mean-preserving spread) the firm can achieve the complete-information profits and analyze the optimal contract in other settings (first-order stochastic dominance) in which the first-best allocation is not always feasible.Keywords: price discrimination, revenue management, dynamic pricing, intertemporal price discrimination, dynamic mechanism design This paper analyzes an optimal advance-purchase pricing, or revenue-management, problem when consumers learn their valuations for future consumption over time. We assume that each consumer begins with private information about both the distribution of her valuation and the time when she will learn her valuation. Later, once she has learned her valuation, she also has private information about the realization of her valuation. For ease of analysis, we assume that each consumer's type, or initial private information, is the time that she will learn her valuation, and that the distribution of each consumer's valuation is a function of her type. In this way, consumers begin with private information about two characteristics, the distribution of their valuations and the time that they will learn their valuation, but their initial private information can be represented as a single dimension of information.We formulate the firm's optimal pricing problem as a dynamic mechanism design problem. The firm maximizes its profit over the set of dynamically incentive-compatible direct-revelation mechanisms when the firm knows only the ex ante distribution of consumers' private information. We characterize the optimal direct-revelation mechanism and show that the firm can implement the optimal mechanism with a menu of contracts with different prices and different $ We would like to thank Johannes Hörner, Hao Li, Larry Samuelson and Kathryn Spier, as well as the editor, Alessandro Pavan, an anonymous associate editor, and two referees, for very helpful comments and suggestions on earlier versions of the paper. Thanks also to seminar participants

In this paper, we present the results of a multisite photometric campaign devoted to the γ Doradus type variable HR 8799. From Johnson and Strömgren data, we were able to identify three independent frequencies (f1= 1.9791 cycle d‐1, f2=1.7268 cycle d‐1 and f3=1.6498 cycle d‐1) as well as another signal, which we are able to identify as the coupling term between two of the frequencies (f4=f1‐f2=0.2479 cycle d‐1). These four frequencies are able to account for all of the observed variations down to the 1σ significance level. We discuss another possible interpretation of these frequencies using a model of quasi‐stochastic amplitude modulation. In this scenario, we are able to show that HR 8799 might be pulsating with two independent frequencies, one of which undergoes amplitude modulation similar to other γ Dor objects. In addition, we discuss a preliminary mode identification based on the observed colour curves. Finally, 18 simultaneous, high‐resolution echelle spectra were collected on two nights and we qualitatively compare the radial velocities from these data with our photometry.