Contracting an element from a cocircuit

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An extension to GUM methodology: degrees-of-freedom calculations for correlated multidimensional estimates

The Guide to the Expression of Uncertainty in Measurement advocates the use of an 'effective number of degrees of freedom' for the calculation of an interval of measurement uncertainty. However, it does not describe how this number is to be calculated when (i) the measurand is a vector quantity or (ii) when the errors in the estimates of the quantities defining the measurand (the 'input quantities') are not incurred independently. An appropriate analysis for a vector-valued measurand has been described (Metrologia 39 (2002) 361-9), and a method for a one-dimensional measurand with dependent errors has also been given (Metrologia 44 (2007) 340-9). This paper builds on those analyses to present a method for the situation where the problem is multidimensional and involves correlated errors. The result is an explicit general procedure that reduces to simpler procedures where appropriate. The example studied is from the field of radio-frequency metrology, where measured quantities are often complex-valued and can be regarded as vectors of two elements.Comment: 30 pages with 2 embedded figure

Misregistration's effects on classification and proportion estimation accuracy

The estimates of crop type and acreage are undertaken in the AgRISTARS program by registering multiple date acquisitions of small subareas of LANDSAT scenes (termed segments), and applying multispectral analysis to them. An important contribution to errors in classification and acreage estimates is misregistration between multiple acquisitions. The formula used to express this relationship is given and the operations applied are so shown in diagrams. The taking of a LANDSAT feature vector and the derivation of the brightness and greeness are illustrated. It is shown that for any given sensor IFOV geometry, typical populations of fields can be derived and histograms can be plotted of the number of fields against field size according to ground truth. As a function of the resolution element, the IFOV of the sensor can draw the proportion of pure pixels in a given crop. Because the thematic mapper has a smaller resolution, the proportion of pixels that are pure in any given area will be larger

Extended analytical study of the free-wing/free-trimmer concept

The free wing/free trimmer concept was analytically studied in order to: (1) compare the fore and aft trimmer configurations on the basis of equal lift capability, rather than equal area; (2) assess the influence of tip mounted aft trimmers, both free and fixed, on the lateral directional modes and turbulence responses; (3) examine the feasibility of using differential tip mounted trimmer deflection for lateral control; (4) determine the effects of independent fuselage attitude on the lateral directional behavior; and (5) estimate the influence of wing sweep on dynamic behavior and structural weight. Results indicate that the forward trimmer concept is feasible with the reduced size examined, but it remains inferior to the aft trimmer in every respect except structural weight. Differential motion of the aft trimmer is found to provide powerful lateral control; while the effect of fuselage deck angle is a reduction of the dutch roll damping ratio for nose-down attitudes

Coulomb plus power-law potentials in quantum mechanics

We study the discrete spectrum of the Hamiltonian H = -Delta + V(r) for the Coulomb plus power-law potential V(r)=-1/r+ beta sgn(q)r^q, where beta > 0, q > -2 and q \ne 0. We show by envelope theory that the discrete eigenvalues E_{n\ell} of H may be approximated by the semiclassical expression E_{n\ell}(q) \approx min_{r>0}\{1/r^2-1/(mu r)+ sgn(q) beta(nu r)^q}. Values of mu and nu are prescribed which yield upper and lower bounds. Accurate upper bounds are also obtained by use of a trial function of the form, psi(r)= r^{\ell+1}e^{-(xr)^{q}}. We give detailed results for V(r) = -1/r + beta r^q, q = 0.5, 1, 2 for n=1, \ell=0,1,2, along with comparison eigenvalues found by direct numerical methods.Comment: 11 pages, 3 figure

Mission analysis of solar powered aircraft

The effect of a real mission scenario on a solar powered airplane configuration which had been developed in previous work were assessed. The mission used was surveillance of crop conditions over a route from Phoenix to Tucson to Tombstone, Arizona. Appendices are attached which address the applicability of existing platforms and payloads to do this mission

Chiral extrapolations for nucleon magnetic moments

Lattice QCD simulations have made significant progress in the calculation of nucleon electromagnetic form factors in the chiral regime in recent years. With simulation results achieving pion masses of order ~180 MeV, there is an apparent challenge as to how the physical regime is approached. By using contemporary methods in chiral effective field theory, both the quark-mass and finite-volume dependence of the isovector nucleon magnetic moment are carefully examined. The extrapolation to the physical point yields a result that is compatible with experiment, albeit with a combined statistical and systematic uncertainty of 10%. The extrapolation shows a strong finite-volume dependence; lattice sizes of L > 5 fm must be used to simulate results within 2% of the infinite-volume result for the magnetic moment at the physical pion mass.Comment: 7 pages, 12 figures, 1 tabl

Orbit/attitude estimation for the GOES spacecraft using VAS landmark data

A software system is described which provides for batch least squares estimation of spacecraft orbit, attitude, and camera bias parameters using image data from the Geostationary Operational Environmental Satellites (GOES). The image data are obtained by the Visible and Infrared Spin Scan Radiometer (VISSR) Atmospheric Sounder (VAS). The resulting estimated parameters are used for absolute image registration. Operating in the Digital Equipment Corporation (DEC) PDP-11/70 computer, the FORTRAN system also includes the capabilities of image display and manipulations. An overview of the system is presented as well as some numerical results obtained from observations taken by the SMS-2 satellite over a 3 day interval in August 1975

Power Counting Regime of Chiral Effective Field Theory and Beyond

Chiral effective field theory complements numerical simulations of quantum chromodynamics (QCD) on a space-time lattice. It provides a model-independent formalism for connecting lattice simulation results at finite volume and a variety of quark masses to the physical world. The asymptotic nature of the chiral expansion places the focus on the first few terms of the expansion. Thus, knowledge of the power-counting regime (PCR) of chiral effective field theory, where higher-order terms of the expansion may be regarded as negligible, is as important as knowledge of the expansion itself. Through the consideration of a variety of renormalization schemes and associated parameters, techniques to identify the PCR where results are independent of the renormalization scheme are established. The nucleon mass is considered as a benchmark for illustrating this general approach. Because the PCR is small, the numerical simulation results are also examined to search for the possible presence of an intrinsic scale which may be used in a nonperturbative manner to describe lattice simulation results outside of the PCR. Positive results that improve on the current optimistic application of chiral perturbation theory beyond the PCR are reported.Comment: 18 pages, 55 figure