License prices for financially constrained firms

It is often alleged that high auction prices inhibit service deployment. We investigate this claim under the extreme case of financially constrained bidders. If demand is just slightly elastic, auctions maximize consumer surplus if consumer surplus is a convex function of quantity (a common assumption), or if consumer surplus is concave and the proportion of expenditure spent on deployment is greater than one over the elasticity of demand. The latter condition appears to be true for most of the large telecom auctions in the US and Europe. Thus, even if high auction prices inhibit service deployment, auctions appear to be optimal from the consumers’ point of view

Multiwavelength study of the high-latitude cloud L1642: chain of star formation

L1642 is one of the two high galactic latitude (|b| > 30deg) clouds confirmed to have active star formation. We examine the properties of this cloud, especially the large-scale structure, dust properties, and compact sources in different stages of star formation. We present high-resolution far-infrared and submm observations with the Herschel and AKARI satellites and mm observations with the AzTEC/ASTE telescope, which we combined with archive data from near- and mid-infrared (2MASS, WISE) to mm observations (Planck). The Herschel observations, combined with other data, show a sequence of objects from a cold clump to young stellar objects at different evolutionary stages. Source B-3 (2MASS J04351455-1414468) appears to be a YSO forming inside the L1642 cloud, instead of a foreground brown dwarf, as previously classified. Herschel data reveal striation in the diffuse dust emission around L1642. The western region shows striation towards NE and has a steeper column density gradient on its southern side. The densest central region has a bow-shock like structure showing compression from the west and a filamentary tail extending towards east. The differences suggest that these may be spatially distinct structures, aligned only in projection. We derive values of the dust emission cross-section per H nucleon for different regions of the cloud. Modified black-body fits to the spectral energy distribution of Herschel and Planck data give emissivity spectral index beta values 1.8-2.0 for the different regions. The compact sources have lower beta values and show an anticorrelation between T and beta. Markov chain Monte Carlo calculations demonstrate the strong anticorrelation between beta and T errors and the importance of mm Planck data in constraining the estimates. L1642 reveals a more complex structure and sequence of star formation than previously known.Comment: 22 pages, 18 figures, accepted to Astronomy & Astrophysics; abstract shortened and figures reduced for astrop

Remarks on Shannon's Statistical Inference and the Second Law in Quantum Statistical Mechanics

We comment on a formulation of quantum statistical mechanics, which incorporates the statistical inference of Shannon. Our basic idea is to distinguish the dynamical entropy of von Neumann, $H = -k Tr \hat{\rho}\ln\hat{\rho}$, in terms of the density matrix $\hat{\rho}(t)$, and the statistical amount of uncertainty of Shannon, $S= -k \sum_{n}p_{n}\ln p_{n}$, with $p_{n}=$ in the representation where the total energy and particle numbers are diagonal. These quantities satisfy the inequality $S\geq H$. We propose to interprete Shannon's statistical inference as specifying the {\em initial conditions} of the system in terms of $p_{n}$. A definition of macroscopic observables which are characterized by intrinsic time scales is given, and a quantum mechanical condition on the system, which ensures equilibrium, is discussed on the basis of time averaging. An interesting analogy of the change of entroy with the running coupling in renormalization group is noted. A salient feature of our approach is that the distinction between statistical aspects and dynamical aspects of quantum statistical mechanics is very transparent.Comment: 16 pages. Minor refinement in the statements in the previous version. This version has been published in Journal of Phys. Soc. Jpn. 71 (2002) 6

Periodic Chaotic Billiards: Quantum-Classical Correspondence in Energy Space

We investigate the properties of eigenstates and local density of states (LDOS) for a periodic 2D rippled billiard, focusing on their quantum-classical correspondence in energy representation. To construct the classical counterparts of LDOS and the structure of eigenstates (SES), the effects of the boundary are first incorporated (via a canonical transformation) into an effective potential, rendering the one-particle motion in the 2D rippled billiard equivalent to that of two-interacting particles in 1D geometry. We show that classical counterparts of SES and LDOS in the case of strong chaotic motion reveal quite a good correspondence with the quantum quantities. We also show that the main features of the SES and LDOS can be explained in terms of the underlying classical dynamics, in particular of certain periodic orbits. On the other hand, statistical properties of eigenstates and LDOS turn out to be different from those prescribed by random matrix theory. We discuss the quantum effects responsible for the non-ergodic character of the eigenstates and individual LDOS that seem to be generic for this type of billiards with a large number of transverse channels.Comment: 13 pages, 18 figure

Herschelobservations of the W3 GMC (II): clues to the formation of clusters of high-mass stars

The W3 giant molecular cloud is a prime target for investigating the formation of high-mass stars and clusters. This second study of W3 within the HOBYS Key Program provides a comparative analysis of subfields within W3 to further constrain the processes leading to the observed structures and stellar population. Probability density functions (PDFs) and cumulative mass distributions (CMDs) were created from dust column density maps, quantified as extinction AV. The shape of the PDF, typically represented with a lognormal function at low Av “breaking” to a power-law tail at high Av, is influenced by various processes including turbulence and selfgravity. The breaks can also be identified, often more readily, in the CMDs. The PDF break from lognormal (Av(SF)» 6–10 mag) appears to shift to higher Av by stellar feedback, so that high-mass star-forming regions tend to have higher PDF breaks. A second break at Av> 50 mag traces structures formed or influenced by a dynamic process. Because such a process has been suggested to drive high-mass star formation in W3, this second break might then identify regions with potential for hosting high-mass stars/clusters. Stellar feedback appears to be a major mechanism driving the local evolution and state of regions within W3. A high initial star formation efficiency in a dense medium could result in a self-enhancing process, leading to more compression and favorable star formation conditions (e.g., colliding flows), a richer stellar content, and massive stars. This scenario would be compatible with the “convergent constructive feedback” model introduced in our previous Herschel study

Constraints on the architecture of the HD 95086 planetary system with the Gemini Planet Imager

We present astrometric monitoring of the young exoplanet HD 95086 b obtained with the Gemini Planet Imager between 2013 and 2016. A small but significant position angle change is detected at constant separation; the orbital motion is confirmed with literature measurements. Efficient Monte Carlo techniques place preliminary constraints on the orbital parameters of HD 95086 b. With 68% confidence, a semimajor axis of 61.7^{+20.7}_{-8.4} au and an inclination of 153.0^{+9.7}_{-13.5} deg are favored, with eccentricity less than 0.21. Under the assumption of a co-planar planet-disk system, the periastron of HD 95086 b is beyond 51 au with 68% confidence. Therefore HD 95086 b cannot carve the entire gap inferred from the measured infrared excess in the SED of HD 95086. We use our sensitivity to additional planets to discuss specific scenarios presented in the literature to explain the geometry of the debris belts. We suggest that either two planets on moderately eccentric orbits or three to four planets with inhomogeneous masses and orbital properties are possible. The sensitivity to additional planetary companions within the observations presented in this study can be used to help further constrain future dynamical simulations of the planet-disk system.Comment: Accepted for publication in ApJ