Highest weight Macdonald and Jack Polynomials

Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group. Excited quasiparticle/quasihole states are member of multiplets under the rotation group and generically there is a nontrivial highest weight member of the multiplet from which all states can be constructed. Some of the trial states proposed in the literature belong to classical families of symmetric polynomials. In this paper we study Macdonald and Jack polynomials that are highest weight states. For Macdonald polynomials it is a (q,t)-deformation of the raising angular momentum operator that defines the highest weight condition. By specialization of the parameters we obtain a classification of the highest weight Jack polynomials. Our results are valid in the case of staircase and rectangular partition indexing the polynomials.Comment: 17 pages, published versio

Sub-millimeter images of a dusty Kuiper belt around eta Corvi

We present sub-millimeter and mid-infrared images of the circumstellar disk around the nearby F2V star eta Corvi. The disk is resolved at 850um with a size of ~100AU. At 450um the emission is found to be extended at all position angles, with significant elongation along a position angle of 130+-10deg; at the highest resolution (9.3") this emission is resolved into two peaks which are to within the uncertainties offset symmetrically from the star at 100AU projected separation. Modeling the appearance of emission from a narrow ring in the sub-mm images shows the observed structure cannot be caused by an edge-on or face-on axisymmetric ring; the observations are consistent with a ring of radius 150+-20AU seen at 45+-25deg inclination. More face-on orientations are possible if the dust distribution includes two clumps similar to Vega; we show how such a clumpy structure could arise from the migration over 25Myr of a Neptune mass planet from 80-105AU. The inner 100AU of the system appears relatively empty of sub-mm emitting dust, indicating that this region may have been cleared by the formation of planets, but the disk emission spectrum shows that IRAS detected an additional hot component with a characteristic temperature of 370+-60K (implying a distance of 1-2AU). At 11.9um we found the emission to be unresolved with no background sources which could be contaminating the fluxes measured by IRAS. The age of this star is estimated to be ~1Gyr. It is very unusual for such an old main sequence star to exhibit significant mid-IR emission. The proximity of this source makes it a perfect candidate for further study from optical to mm wavelengths to determine the distribution of its dust.Comment: 22 pages, 4 figures. Scheduled for publication in ApJ 10 February 2005 issu

Identification of nonlinearity in conductivity equation via Dirichlet-to-Neumann map

We prove that the linear term and quadratic nonlinear term entering a nonlinear elliptic equation of divergence type can be uniquely identified by the Dirichlet to Neuman map. The unique identifiability is proved using the complex geometrical optics solutions and singular solutions

The Papoose Flat Pluton of eastern California: a reassessment of its emplacement history in the light of new microstructural and crystallographic fabric observations

One of the most outstanding apparent examples in N America of a forcibly emplaced pluton is the Papoose Flat Pluton of eastern California. Sideways expansion of this granitic pluton, during emplacement into a series of Cambrian shelf strata, has been regarded by early workers as resulting in the observed intense crystal plastic deformation of the pluton's mylonitic border facies and surrounding country rocks. This deformation is evidenced by up to 90% thinning of individual stratigraphic layers within the pluton's metamorphic aureole, although such intense penetrative deformation of the country rocks is not observed outside the aureole. Previously published quartz c-axis fabrics associated with this deformation (and presented on projection planes oriented perpendicular to lineation) were interpreted as being symmetrical with respect to foliation and lineation, implying almost coaxial deformation histories. Such fabrics could be interpreted as indicating that the pluton evolved by "ballooning” as a result of new magma being intruded into its core during emplacement. However, a major problem with applying the strict ballooning model to the Papoose Flat Pluton is that while oblate strains would be expected to develop in association with a ballooning mechanism, the mylonitic rocks of this elongate WNW-ESE-trending pluton and its aureole are characterised by both a strongly developed foliation, which is concordant with the pluton's margin, and an intense, NW-SE trending, shallow plunging stretching lineation. Previously published fabrics from the Papoose Flat Pluton and its metamorphic aureole have been rotated on to a projection plane oriented parallel to lineation and perpendicular to foliation. Examination of the fabrics in this projection plane has revealed that they are in fact dominantly asymmetric, and that a constant sense of asymmetry is detected across the pluton, suggesting a consistent (top-to-the-SE) shear-sense. This new interpretation is strongly supported by microstructural and petrofabric analysis of additional L-S tectonites collected, during recent fieldwork, from both the aureole and quartz veins within the pluton's gneissic border facies. Thus mylonite formation around the Papoose Flat Pluton could have involved large-scale consistently oriented translation and associated shearing, rather than passive "blister-like” coaxial deformation associated with pluton ballooning. It should be noted that mylonitic deformation is restricted to the western half of the pluton, features indicative of a more "permitted” emplacement mechanism being found in the eastern portion of the pluton. The detected top-to-the-SE shear-sense could be interpreted as indicating that the granitic material forming the western part of the pluton was forcibly intruded in a northwestward direction from the pluton source as a nearly solidified wedge beneath a static cover of sedimentary rocks. Alternatively, the detected shear sense could also be interpreted as indicating SE-directed thrusting of the cover rocks over the underlying pluton, the western margin of the pluton suffering intense mylonitic deformation, while the eastern margin was located in a "stress-shadow” region. If this alternative interpretation is correct, then the deformation temperatures indicated by the pattern of quartz c-axis fabrics dictate that thrusting must either be synchronous with pluton emplacement, or at least have commenced during the early stages of pluton coolin

Full-wave invisibility of active devices at all frequencies

There has recently been considerable interest in the possibility, both theoretical and practical, of invisibility (or "cloaking") from observation by electromagnetic (EM) waves. Here, we prove invisibility, with respect to solutions of the Helmholtz and Maxwell's equations, for several constructions of cloaking devices. Previous results have either been on the level of ray tracing [Le,PSS] or at zero frequency [GLU2,GLU3], but recent numerical [CPSSP] and experimental [SMJCPSS] work has provided evidence for invisibility at frequency $k\ne 0$. We give two basic constructions for cloaking a region $D$ contained in a domain $\Omega$ from measurements of Cauchy data of waves at \p \Omega; we pay particular attention to cloaking not just a passive object, but an active device within $D$, interpreted as a collection of sources and sinks or an internal current.Comment: Final revision; to appear in Commun. in Math. Physic

Evidence of reproductive isolation confirms that Apis andreniformis (Smith, 1858) is a separate species from sympatric Apis florea (Fabricius, 1787).

The species Apis andreniformis (Smith, 1858), the small dwarf honey bee of South-east Asia, is recognized as a valid biological species. This recognition is based on distinctive endophallus characteristics in comparison with sympatric Apis florea (Fabricius, 1787). Additionally, scanning electron microscope images of drone basitarsi are presented, as are preliminary comparisons of wing venation

Limiting Carleman weights and anisotropic inverse problems

In this article we consider the anisotropic Calderon problem and related inverse problems. The approach is based on limiting Carleman weights, introduced in Kenig-Sjoestrand-Uhlmann (Ann. of Math. 2007) in the Euclidean case. We characterize those Riemannian manifolds which admit limiting Carleman weights, and give a complex geometrical optics construction for a class of such manifolds. This is used to prove uniqueness results for anisotropic inverse problems, via the attenuated geodesic X-ray transform. Earlier results in dimension $n \geq 3$ were restricted to real-analytic metrics.Comment: 58 page

Formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential

For the Schrodinger equation at fixed energy with a potential supported in a bounded domain we give formulas and equations for finding scattering data from the Dirichlet-to-Neumann map with nonzero background potential. For the case of zero background potential these results were obtained in [R.G.Novikov, Multidimensional inverse spectral problem for the equation -\Delta\psi+(v(x)-Eu(x))\psi=0, Funkt. Anal. i Ego Prilozhen 22(4), pp.11-22, (1988)]

The Detection of Crystalline Silicates in Ultra-Luminous Infrared Galaxies

Silicates are an important component of interstellar dust and the structure of these grains -- amorphous versus crystalline -- is sensitive to the local physical conditions. We have studied the infrared spectra of a sample of ultra-luminous infrared galaxies. Here, we report the discovery of weak, narrow absorption features at 11, 16, 19, 23, and 28 microns, characteristic of crystalline silicates, superimposed on the broad absorption bands at 10 and 18 microns due to amorphous silicates in a subset of this sample. These features betray the presence of forsterite (Mg_2SiO_4), the magnesium-rich end member of the olivines. Previously, crystalline silicates have only been observed in circumstellar environments. The derived fraction of forsterite to amorphous silicates is typically 0.1 in these ULIRGs. This is much larger than the upper limit for this ratio in the interstellar medium of the Milky Way, 0.01. These results suggest that the timescale for injection of crystalline silicates into the ISM is short in a merger-driven starburst environment (e.g., as compared to the total time to dissipate the gas), pointing towards massive stars as a prominent source of crystalline silicates. Furthermore, amorphization due to cosmic rays, which is thought to be of prime importance for the local ISM, lags in vigorous starburst environments.Comment: 7 pages, 5 figures, accepted for publication in Ap