Faint counts as a function of morphological type in a hierarchical merger model

The unprecedented resolution of the refurbished Wide Field and Planetary Camera 2 (WFPC2) on the Hubble Space Telescope (HST) has led to major advances in our understanding of galaxy formation. The high image quality in the Medium Deep Survey and Hubble Deep Field has made it possible, for the first time, to classify faint distant galaxies according to morphological type. These observations have revealed a large population of galaxies classed as irregulars or which show signs of recent merger activity. Their abundance rises steeply with apparent magnitude, providing a likely explanation for the large number of blue galaxies seen at faint magnitudes. We demonstrate that such a population arises naturally in a model in which structure forms hierarchically and which is dynamically dominated by cold dark matter. The number counts of irregular, spiral and elliptical galaxies as a function of magnitude seen in the HST data are well reproduced in this model.We present detailed predictions for the outcome of spectroscopic follow-up observations of the HST surveys. By measuring the redshift distributions of faint galaxies of different morphological types, these programmes will provide a test of the hierarchical galaxy formation paradigm and might distinguish between models with different cosmological parameters.Comment: 5 pages, 3 postscript figures included. To be published as a Letter in Monthly Notices of the RAS. Postscript version available at http://star-www.dur.ac.uk/~cmb/counts.htm

End-of-Life Inventory Decisions for Consumer Electronics Service Parts

We consider a consumer electronics (CE) manufacturer’s problem of controlling the inventoryof spare parts in the final phase of the service life cycle. The final phase starts when thepart production is terminated and continues until the last service contract or warranty periodexpires. Placing final orders for service parts is considered to be a popular tactic to satisfy demandduring this period and to mitigate the effect of part obsolescence at the end of the servicelife cycle. To satisfy demand for service in the final phase, previous research focuses on repairingdefective products by replacing the defective parts with properly functioning spare ones.However, for consumer electronic products there is a remarkable price erosion while repaircosts may stay steady over time. As a consequence, this introduces the idea that there mightbe a point in time at which the unit price of the product is lower than repair associated costs.Therefore, it would be more cost effective to adopt an alternative policy to meet demands forservice such as offering customers a replacement of the defective product with a new one orgiving a discount on the next generation of the product. This paper examines the cost trade-offsof implementing alternative policies for the repair policy and develops an exact formulation forthe expected total cost function. Based on this developed cost function we propose policies tosimultaneously find the optimal final order quantity and the time to switch from the repair toan alternative replacement policy. Numerical analysis of a real world case study sheds lightover the effectiveness and advantage of these policies in terms of cost reduction and also yieldsinsights into the quantitative importance of the various cost parameters.consumer electronics;end-of-life inventory control;service parts

Two-dimensional rectangle packing: on-line methods and results

The first algorithms for the on-line two-dimensional rectangle packing problem were introduced by Coppersmith and Raghavan. They showed that for a family of heuristics 13/4 is an upper bound for the asymptotic worst-case ratios. We have investigated the Next Fit and the First Fit variants of their method. We proved that the asymptotic worst-case ratio equals 13/4 for the Next Fit variant and that 49/16 is an upper bound of the asymptotic worst-case ratio for the First Fit variant.

A note on a stochastic location problem

In this note we give a short and easy proof of the equivalence of Hakimi's one-median problem and the k-server-facility-loss median problem as discussed by Chiu and Larson in Computer and Operation Research. The proof makes only use of a stochastic monotonicity result for birth and death processes and the insensitivity of the M/G/k/k loss model.Hakimi median;stochastic location;stochastic monotonicity

Improved algorithms for machine allocation in manufacturing systems

In this paper we present two algorithms for a machine allocation problem occurring in manufacturing systems. For thetwo algorithms presented we prove worst-case performance ratios of 2 and 312, respectively. The machlne allocat~onproblem we consider is a general convex resource allocation problem, which makes the algorithms applicable to a varletyof resource allocation problems. Numerical results are presented for two real-life manufacturing systems.networks;manufacturing;allocation of machines;performance/productivity;queues

Order statistics and the linear assignment problem

Under mild conditions on the distribution functionF, we analyze the asymptotic behavior in expectation of the smallest order statistic, both for the case thatF is defined on (–, +) and for the case thatF is defined on (0, ). These results yield asymptotic estimates of the expected optiml value of the linear assignment problem under the assumption that the cost coefficients are independent random variables with distribution functionF.asymptotic analysis;linear assignment problem;order statistic

STOP - A computer program for supersonic transport trajectory optimization

IBM 7094 digital program using steepest ascent technique for optimizing flight path of supersonic transport aircraf

GALAXY DYNAMICS IN CLUSTERS

We use high resolution simulations to study the formation and distribution of galaxies within a cluster which forms hierarchically. We follow both dark matter and baryonic gas which is subject to thermal pressure, shocks and radiative cooling. Galaxy formation is identified with the dissipative collapse of the gas into cold, compact knots. We examine two extreme representations of galaxies during subsequent cluster evolution --- one purely gaseous and the other purely stellar. The results are quite sensitive to this choice. Gas-galaxies merge efficiently with a dominant central object while star-galaxies merge less frequently. Thus, simulations in which galaxies remain gaseous appear to suffer an ``overmerging'' problem, but this problem is much less severe if the gas is allowed to turn into stars. We compare the kinematics of the galaxy population in these two representations to that of dark halos and of the underlying dark matter distribution. Galaxies in the stellar representation are positively biased (\ie over-represented in the cluster) both by number and by mass fraction. Both representations predict the galaxies to be more centrally concentrated than the dark matter, whereas the dark halo population is more extended. A modest velocity bias also exists in both representations, with the largest effect, $\sigma_{gal}/\sigma_{DM} \simeq 0.7$, found for the more massive star-galaxies. Phase diagrams show that the galaxy population has a substantial net inflow in the gas representation, while in the stellar case it is roughly in hydrostatic equilibrium. Virial mass estimators can underestimate the true cluster mass by up to a factor of 5. The discrepancy is largest if only the most massive galaxies are used, reflecting significant mass segregation.Comment: 30 pages, self-unpacking (via uufiles) postscript file without figures. Eighteen figures (and slick color version of figure 3) and entire paper available at ftp://oahu.physics.lsa.umich.edu/groups/astro/fews Total size of paper with figures is ~9.0 Mb uncompressed. Submitted to Ap.J