A syllabus of line geometry

In the study of advanced geometry, we shall deal with a certain important relation between pairs of figures in space, and also between their properties. There are two distinct parts to analytic geometry, the analytic work and the geometric interpretation. Two systems of geometry, depending upon different elements with the same number of coordinates, will have the same analytic expressions and will differ only in the interpretation of the analysis. In such a case it is often sufficient to know the meaning of the coordination and the interpretation of a few fundamental relations in each system in order to find for a theorem in one geometry a corresponding theorem in the other. The nature of this relation is explained by the theorem of duality which assets that a dual, or reciprocal, statement can be derived from a given statement

Respondent Consistency in a Tournament-Style Contingent Choice Survey

We present the results of an internet-based contingent choice survey about management options at North Cascades National Park, focusing on respondent consistency. A tournament-style contingent ranking design followed by a contingent rating exercise allows for tests of different kinds of consistency in survey responses. Many respondents give inconsistent responses, but these inconsistencies do not create large differences in estimated tradeoffs between scenario attributes

Space-Time Correlations and Spectra of Wall Pressure in a Turbulent Boundary Layer

Measurements of the statistical properties of the fluctuating wall pressure produced by a subsonic turbulent boundary layer are described. The measurements provide additional information about the structure of the turbulent boundary layer; they are applicable to the problems of boundary-layer induced noise inside an airplane fuselage and to the generation of waves-on water. The spectrum of the wall pressure is presented in dimensionless form. The ratio of the root-mean-square wall pressure to the free-stream dynamic pressure is found to be a constant square root of bar P(sup 2)/q(sub infinity) = 0.006 independent of Mach number and Reynolds number. In addition, space- time correlation measurements in the stream direction show that pressure fluctuations whose scale is greater than or equal to 0.3 times the boundary-layer thickness are convected with the convection speed U(sub c) = 0.82U(sub infinity) where U(infinity) is the free-stream velocity and have lost their identity in a distance approximately equal to 10 boundary-layer thicknesses

Collision of a vortex pair with a contaminated free surface

Collision of a viscous, two‐dimensional vortex pair with a contaminated, free surface is studied numerically. The Froude number is assumed to be small, so the surface remains flat. The full Navier–Stokes equations and a conservation equation for the surface contaminant are solved numerically by a finite difference method. The shear stress at the free surface is proportional to the contamination gradient, and simulations for several values of the proportionality constant (W), as well as Reynolds numbers, have been performed. The evolution is also compared with full‐slip and no‐slip boundaries. As the vortices approach the surface, the upwelling between them pushes the contaminant outward, reducing the amount directly above the vortices, and leading to a clean region for low W. As W is increased the clean region becomes smaller, and eventually no clean region is formed. Except for very low W, the contaminant layer leads to the creation of secondary vortices, causing the original vortices to rebound in a similar way as vortices colliding with a no‐slip boundary. For one case, the numerical results are compared with experimental measurements with satisfactory results. Computations of a vortex pair colliding obliquely with a contaminated surface and head‐on collision of axisymmetric vortex rings are also presented.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/70265/2/PFADEB-4-6-1215-1.pd

Spectroscopic Orbits for 15 Late-Type Stars

Spectroscopic orbital elements are determined for 15 stars with periods from 8 to 6528 days with six orbits computed for the first time. Improved astrometric orbits are computed for two stars and one new orbit is derived. Visual orbits were previously determined for four stars, four stars are members of multiple systems, and five stars have Hipparcos G designations or have been resolved by speckle interferometry. For the nine binaries with previous spectroscopic orbits, we determine improved or comparable elements. For HD 28271 and HD 200790, our spectroscopic results support the conclusions of previous authors that the large values of their mass functions and lack of detectable secondary spectrum argue for the secondary in each case being a pair of low-mass dwarfs. The orbits given here may be useful in combination with future interferometric and Gaia satellite observations

Spectroscopic Orbits for 15 Late-Type Stars

Spectroscopic orbital elements are determined for 15 stars with periods from 8 to 6528 days with six orbits computed for the first time. Improved astrometric orbits are computed for two stars and one new orbit is derived. Visual orbits were previously determined for four stars, four stars are members of multiple systems, and five stars have Hipparcos G designations or have been resolved by speckle interferometry. For the nine binaries with previous spectroscopic orbits, we determine improved or comparable elements. For HD 28271 and HD 200790, our spectroscopic results support the conclusions of previous authors that the large values of their mass functions and lack of detectable secondary spectrum argue for the secondary in each case being a pair of low-mass dwarfs. The orbits given here may be useful in combination with future interferometric and Gaia satellite observations

Spectroscopic Orbits for Late-type Stars. II

We have determined spectroscopic orbital elements for 13 systems—10 single-lined binaries and three double-lined binaries. For the three binaries with previously published spectroscopic orbits, we have computed improved or comparable elements. While two systems have relatively short periods between 10 and 19 days, the remaining systems have much longer periods ranging from 604 to 9669 days. One of the single-lined systems, HD 142640, shows both short-period and long-period velocity variations and so is triple. For three systems—HD 59380, HD 160933, and HD 161163—we have combined our spectroscopic results with Hipparcos astrometric observations to obtain astrometric orbits. For HD 14802 we have determined a joint orbital solution from spectroscopic velocities and interferometric observations. The orbits given here will be useful in combination with future interferometric and Gaia satellite observations