Multivariable link invariants arising from sl(2|1) and the Alexander polynomial

In this paper we construct a multivariable link invariant arising from the quantum group associated to the special linear Lie superalgebra sl(2|1). The usual quantum group invariant of links associated to (generic) representations of sl(2|1) is trivial. However, we modify this construction and define a nontrivial link invariant. This new invariant can be thought of as a multivariable version of the Links-Gould invariant. We also show that after a variable reduction our invariant specializes to the Conway potential function, which is a version of the multivariable Alexander polynomial.Comment: 19 pages, to appear in Journal of Pure and Applied Algebra. Several changes and a proof added. (see math.GT/0609034 for other Lie superalgebras

Automatic Construction of Explicit R Matrices for the One-Parameter Families of Irreducible Typical Highest Weight (0|\alpha) Representations of U_q[gl(m|n)]

We detail the automatic construction of R matrices corresponding to (the tensor products of) the (0|\alpha) families of highest-weight representations of the quantum superalgebras U_q[gl(m|n)]. These representations are irreducible, contain a free complex parameter \alpha, and are 2^{mn} dimensional. Our R matrices are actually (sparse) rank 4 tensors, containing a total of 2^{4mn} components, each of which is in general an algebraic expression in the two complex variables q and \alpha. Although the constructions are straightforward, we describe them in full here, to fill a perceived gap in the literature. As the algorithms are generally impracticable for manual calculation, we have implemented the entire process in Mathematica; illustrating our results with U_q[gl(3|1)].Comment: 65 pages, 6 tables. David De Wit: <http://www.kurims.kyoto-u.ac.jp/~ddw

A Spline LR Test for Goodness-of-Fit

Goodness-of-Fit tests, nuisance parameters, cubic spline, Neyman smooth test, Lagrange Multiplier test, stable distributions, student t distributions

Survey of Army/NASA rotorcraft aeroelastic stability research

Theoretical and experimental developments in the aeroelastic and aeromechanical stability of helicopters and tilt-rotor aircraft are addressed. Included are the underlying nonlinear structural mechanics of slender rotating beams, necessary for accurate modeling of elastic cantilever rotor blades, and the development of dynamic inflow, an unsteady aerodynamic theory for low frequency aeroelastic stability applications. Analytical treatment of isolated rotor stability in hover and forward flight, coupled rotor-fuselage stability are considered. Results of parametric investigations of system behavior are presented, and correlations between theoretical results and experimental data from small- and large-scale wind tunnel and flight testing are discussed

Analysis of the astroclimate parameters associated with the tropospheric conditions and their time evolution at Roque de Los Muchachos Observatory

The early 1970's saw the start of a new era in astronomy with the rst approach to building large telescopes (2 to 5 meters class telescope) and locating them in the right places. The astronomical community started to evaluate these sites using the sky quality "seeing" parameters as one the major constraints to decide where to place the observatory in the world and where is the best location in the observatory. Taking a few words from one of the rst site testing works by Merle Walker (Walker,1971) that considered the Islands like as: Canary Islands, Hawaiian islands or Crete, a possible ideal place for Astronomy. "The best seeing occurs at sites on peaks near sea coasts having cold ocean currents oshore that reduce the height of the [temperature] inversion layer, and where the laminar air-flow set up over the ocean still persists". (....) "Mountain peaks on (small) islands in warm oceans may be good sites, provided that the peaks are suciently high to place the observer above the inversion layer". It is in this new era when many engineers, physicist, meteorologists and astronomers started to search for new places and to develop new instruments to measure the sky quality. Please see the site testing report for La Palma from Mcinees (Mcinnes,1973). Astronomy is now becoming more sophisticated, with new observatories and new adaptive optics instruments that can compensate the atmosphere to the difraction limit of the telescopes. The newer Adaptive Optics require more information about the optical parameters that aect image quality and it is also becoming more important to manage the technical and human resources in the observatory for high resolution observations. To obtain the information needed, a new set of instruments have been developed and used, such as: MASS-DIMM, DIMM, SCIDAR, SLODAR,Lusci, etc to mention only a few. They have been the main contributor to analyzing potential new sites for the future extremely large telescopes. They also provide new data for the analysis of the expected performances of the new generation of AO instruments for the TMT or E-ELT. The purpose of this thesis is to establish the influence of the upper atmosphere, monitored using tropospheric wind speed and temperature, on the local sky conditions, measured by the refractive index parameter C2n and the astroclimate parameters (seeing, isoplanatic angle and coherence time), and their evolution through the years. The meteorological data used come from a launch site located about 150 km away from the observatory and which provides data for meterological forecasting agencies. It has been determined that the best yearly period for the seeing was the year 2005, which corresponds with the year with lower upper wind speed periods. The use of these meteorological data and the good agreement found with the local sky conditions, provide the rst step to constructing a simple parametric optical turbulence model (Trinquet model) of the Observatory Roque de Los Muchachos. This in turn opens the way to performing a nowcast of the astroclimate parameters and the refractive index parameter C2n using the meteorological forecasting data. It can also be used to help design the AO instrumentation capabilities at the ORM (and perhaps by extension elsewhere). Due to the importance of the knowledge of the vertical C2n distribution and how this aacts the Laser Guide Star (LGS) AO observations, an instrument was proposed based on the DIMM technique and using a range-gated CCD detector to measure the backscattered laser light at dierent altitudes. This can then produce a vertical distribution of the Fried parameter r0 and the seeing. A simple prototype was built but due to the lack of time and various faults the rst experiments could not full the proposed requirements. The preliminary prototype design and the initial on-sky results are provided in appendices of this thesis in order to suggest and support future work

Fast methods for inverse wave scattering problems

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2008.Includes bibliographical references (p. 125-137).Inverse wave scattering problems arise in many applications including computerized/diffraction tomography, seismology, diffraction/holographic grating design, object identification from radar singals, and semiconductor quality control. Efficient algorithms exist for some inverse wave scattering problems in the low- and high-frequency regime or with weak scatterers. However, inverse wave scattering problems in the resonance regime with strong scatterers still pose many challenges. This thesis proposes algorithms for inverse wave scattering problems in the resonance regime with strong scatterers. These problems are part of, for instance, grating design, object identification, and semiconductor quality control. The proposed methods are (a) a spectrally convergent Nyström method for periodic structures in 2-D; (b) a fast Jacobian approximation method accompanying a Nyström method; (c) a fast and accurate method for evaluating the potential integrals in the 3-D mixed-potential integral operator with the Rao-Wilton-Glisson basis function; and (d) optimization with parameterized reduced-order models. The Nyström method and the method to evaluate the potential integrals accelerate scattered field evaluations by solving integral equations efficiently. The Jacobian approximation method and optimization with parameterized reduced-order models efficiently couple algorithms to evaluate scattered fields due to a guess of the scatterer and optimization methods to improve the guess. The Nyström and the Jacobian approximation methods are used to identify the parameters characterizing a periodic dielectric grating in 2-D. The method to evaluate the potential integrals and optimization with parameterized reduced-order models are applied to the problem of identifying simple discrete geometries in 3-D.by Jung Hoon Lee.Ph.D