Casimir invariants and characteristic identities for gl(∞)gl(\infty )

A full set of (higher order) Casimir invariants for the Lie algebra $gl(\infty )$ is constructed and shown to be well defined in the category $O_{FS}$ generated by the highest weight (unitarizable) irreducible representations with only a finite number of non-zero weight components. Moreover the eigenvalues of these Casimir invariants are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from $gl(\infty )$ are also determined and generalize those previously obtained for $gl(n)$ by Bracken and Green.$^{1,2}$Comment: 10 pages, PlainTe

Eigenvalues of Casimir operators for gl(m/∞)gl(m/\infty)

A full set of Casimir operators for the Lie superalgebra $gl(m/\infty)$ is constructed and shown to be well defined in the category $O_{FS}$ generated by the highest weight irreducible representations with only a finite number of non-zero weight components. The eigenvalues of these Casimir operators are determined explicitly in terms of the highest weight. Characteristic identities satisfied by certain (infinite) matrices with entries from $gl(m/\infty)$ are also determined.Comment: 10 pages, Te

Early-type Stars: Most Favorable Targets for Astrometrically Detectable Planets in the Habitable Zone

Early-type stars appear to be a difficult place to look for planets astrometrically. First, they are relatively heavy, and for fixed planetary mass the astrometric signal falls inversely as the stellar mass. Second, they are relatively rare (and so tend to be more distant), and for fixed orbital separation the astrometric signal falls inversely as the distance. Nevertheless, because early-type stars are relatively more luminous, their habitable zones are at larger semi-major axis. Since astrometric signal scales directly as orbital size, this gives early-type stars a strong advantage, which more than compensates for the other two factors. Using the Hipparcos catalog, we show that early-type stars constitute the majority of viable targets for astrometric searches for planets in the habitable zone. We contrast this characteristic to transit searches, which are primarily sensitive to habitable planets around late-type stars.Comment: Submitted to ApJ Letters, 8 pages including 2 figure

M Dwarfs from Hubble Space Telescope Star Counts. IV

We study a sample of about 1400 disk M dwarfs that are found in 148 fields observed with the Wide Field Camera 2 (WFC2) on the Hubble Space Telescope and 162 fields observed with pre-repair Planetary Camera 1 (PC1), of which 95 of the WFC2 fields are newly analyzed. The method of maximum likelihood is applied to derive the luminosity function and the Galactic disk parameters. At first, we use a local color-magnitude relation and a locally determined mass-luminosity relation in our analysis. The results are consistent with those of previous work but with considerably reduced statistical errors. These small statistical errors motivate us to investigate the systematic uncertainties. Considering the metallicity gradient above the Galactic plane, we introduce a modified color-magnitude relation that is a function of Galactic height. The resultant M dwarf luminosity function has a shape similar to that derived using the local color-magnitude relation but with a higher peak value. The peak occurs at $M_V \sim 12$ and the luminosity function drops sharply toward $M_V \sim 14$. We then apply a height-dependent mass-luminosity function interpolated from theoretical models with different metallicities to calculate the mass function. Unlike the mass function obtained using local relations, which has a power-law index $\alpha = 0.47$, the one derived from the height-dependent relations tends to be flat ($\alpha = -0.10$). The resultant local surface density of disk M dwarfs (12.2 +/- 1.6 M_sun pc^{-2}) is somewhat smaller than the one obtained using local relations (14.3 +/- 1.3 M_sun pc^{-2}). Our measurement favors a short disk scale length, H = 2.75 +/- 0.16 (statistical) +/- 0.25 (systematic) kpc.Comment: 20 pages, 10 ps figures, accepted for publication in Ap

Derivatives of spin dynamics simulations

We report analytical equations for the derivatives of spin dynamics simulations with respect to pulse sequence and spin system parameters. The methods described are significantly faster, more accurate and more reliable than the finite difference approximations typically employed. The resulting derivatives may be used in fitting, optimization, performance evaluation and stability analysis of spin dynamics simulations and experiments. Keywords: NMR, EPR, simulation, analytical derivatives, optimal control, spin chemistry, radical pair.Comment: Accepted by The Journal of Chemical Physic

Dilemmas in doing insider research in professional education

This article explores the dilemmas I encountered when researching social work education in England as an insider researcher who was simultaneously employed as an educator in the host institution. This was an ethnographic project deploying multiple methods and generating rich case study material which informed the student textbook Becoming a Social Worker the four-year period of the project. First, ethical dilemmas emerged around informed consent and confidentiality when conducting surveys of students and reading their portfolios. Second, professional dilemmas stemmed from the ways in which my roles as a researcher, academic tutor, social worker and former practice educator converged and collided. Third, political dilemmas pertained to the potential for the project to crystallize and convey conflicts among stakeholders in the university and community. Since the majority of research in social work education is conducted by insiders, we have a vital interest in making sense of such complexity

The Extreme Microlensing Event OGLE-2007-BLG-224: Terrestrial Parallax Observation of a Thick-Disk Brown Dwarf

Parallax is the most fundamental technique to measure distances to astronomical objects. Although terrestrial parallax was pioneered over 2000 years ago by Hipparchus (ca. 140 BCE) to measure the distance to the Moon, the baseline of the Earth is so small that terrestrial parallax can generally only be applied to objects in the Solar System. However, there exists a class of extreme gravitational microlensing events in which the effects of terrestrial parallax can be readily detected and so permit the measurement of the distance, mass, and transverse velocity of the lens. Here we report observations of the first such extreme microlensing event OGLE-2007-BLG-224, from which we infer that the lens is a brown dwarf of mass M=0.056 +- 0.004 Msun, with a distance of 525 +- 40 pc and a transverse velocity of 113 +- 21 km/s. The velocity places the lens in the thick disk, making this the lowest-mass thick-disk brown dwarf detected so far. Follow-up observations may allow one to observe the light from the brown dwarf itself, thus serving as an important constraint for evolutionary models of these objects and potentially opening a new window on sub-stellar objects. The low a priori probability of detecting a thick-disk brown dwarf in this event, when combined with additional evidence from other observations, suggests that old substellar objects may be more common than previously assumed.Comment: ApJ Letters, in press, 15 pages including 2 figure