Center and representations of infinitesimal Hecke algebras of sl_2

In this paper, we compute the center of the infinitesimal Hecke algebras Hz associated to sl_2 ; then using nontriviality of the center, we study representations of these algebras in the framework of the BGG category O. We also discuss central elements in infinitesimal Hecke algebras over gl(n) and sp(2n) for all n. We end by proving an analogue of the theorem of Duflo for Hz.Comment: Final form, to appear in "Communications in Algebra"; 35 pages, laTe

A Dense Reference Network for Mass-Market Centimeter-Accurate Positioning

The quality of atmospheric corrections provided by a dense reference network for centimeter-accurate carrierphase differential GNSS (CDGNSS) positioning is investigated. A dense reference network (less than 20 km inter-station distance) offers significant benefits for mass-market users, enabling lowcost (including single-frequency) CDGNSS positioning with rapid integer ambiguity resolution. Precise positioning on a massmarket platform would significantly influence the world economy, ushering in a host of consumer-focused applications such as globally-registered augmented and virtual reality and improved all-weather safety and efficiency for intelligent transportation systems, applications which have so far been hampered by the several-meter-level errors in standard GNSS positioning. This contribution examines CDGNSS integer ambiguity resolution performance in terms of network correction uncertainty, and network correction uncertainty, in turn, in terms of network density. It considers the total error in network corrections: a sum of ionospheric, tropospheric, and reference station multipath components. The paper’s primary goal is to identify the network density beyond which mass-market users would see no further significant improvement in ambiguity resolution performance. It finishes by describing development and deployment of a low-cost dense reference network in Austin, Texas.Aerospace Engineering and Engineering Mechanic

Unveiling Sources of Heating in the Vicinity of the Orion BN/KL Hot Core as Traced by Highly Excited Inversion Transitions of Ammonia

Using the Expanded Very Large Array, we have mapped the vicinity of the Orion BN/KL Hot Core with sub-arcsecond angular resolution in seven metastable inversion transitions of ammonia: (J,K)=(6,6) to (12,12). This emission comes from levels up to 1500 K above the ground state, enabling identification of source(s) responsible for heating the region. We used this multi-transition dataset to produce images of the rotational/kinetic temperature and the column density of ammonia for ortho and para species separately and on a position-by-position basis. We find rotational temperature and column density in the range 160-490 K and (1-4)x10^17 cm^-2, respectively. Our spatially-resolved images show that the highest (column) density and hottest gas is found in a northeast-southwest elongated ridge to the southeast of Source I. We have also measured the ortho-para ratio of ammonia, estimated to vary in the range 0.9-1.6. Enhancement of ortho with respect to para and the offset of hot ammonia emission peaks from known (proto)stellar sources provide evidence that the ammonia molecules have been released from dust grains into the gas-phase through the passage of shocks and not by stellar radiation. We propose that the combined effect of Source I's proper motion and its low-velocity outflow impinging on a pre-existing dense medium is responsible for the excitation of ammonia and the Orion Hot Core. Finally, we found for the first time evidence of a slow (5 km/s) and compact (1000 AU) outflow towards IRc7.Comment: To appear in Astrophysical Journal Letters Special Issue on the EVLA. 8 pages, 4 figure

When a Mechanical Model Goes Nonlinear

This paper had its origin in a curious discovery by the first author in research performed with an undergraduate student. The following odd fact was noticed: when a mechanical model of a suspension bridge (linear near equilibrium but allowed to slacken at large distance in one direction) is shaken with a low-frequency periodic force, several different periodic responses can result, many with high-frequency components

Carrier localization mechanisms in InGaN/GaN quantum wells

Localization lengths of the electrons and holes in InGaN/GaN quantum wells have been calculated using numerical solutions of the effective mass Schr\"odinger equation. We have treated the distribution of indium atoms as random and found that the resultant fluctuations in alloy concentration can localize the carriers. By using a locally varying indium concentration function we have calculated the contribution to the potential energy of the carriers from band gap fluctuations, the deformation potential and the spontaneous and piezoelectric fields. We have considered the effect of well width fluctuations and found that these contribute to electron localization, but not to hole localization. We also simulate low temperature photoluminescence spectra and find good agreement with experiment.Comment: 7 pages, 7 figure

A Documentary of High-Mass Star Formation: Probing the Dynamical Evolution of Orion Source I on 10-100 AU Scales using SiO Masers

A comprehensive picture of high-mass star formation has remained elusive, in part because examples of high-mass YSOs tend to be relatively distant, deeply embedded, and confused with other emission sources. These factors have impeded dynamical investigations within tens of AU of high-mass YSOs--scales that are critical for probing the interfaces where outflows from accretion disks are launched and collimated. Using observations of SiO masers obtained with the VLA and the VLBA, the KaLYPSO project is overcoming these limitations by mapping the structure and dynamical/temporal evolution of the material 10-1000 AU from the nearest high-mass YSO: Radio Source I in the Orion BN/KL region. Our data include ~40 epochs of VLBA observations over a several-year period, allowing us to track the proper motions of individual SiO maser spots and to monitor changes in the physical conditions of the emitting material with time. Ultimately these data will provide 3-D maps of the outflow structure over approximately 30% of the outflow crossing time. Here we summarize recent results from the KaLYPSO project, including evidence that high-mass star formation is occurring via disk-mediated accretion.Comment: 5 pages; to appear in the proceedings of IAU Symposium 242, Astrophysical Masers and their Environments, ed. J. Chapman & W. Baa