Best linear unbiased estimators for properties of digitized straight lines

This paper considers the problem of measuring properties of digitized straight lines from the viewpoint of measurement methodology. The measurement and estimation process is described in detail, revealing the importance of a step called ``characterization' which was not recognized explicitly before. Using this new concept, BLUE (Best Linear Unbiased) estimators are found. These are calculated for various properties of digitized straight lines, and are briefly compared to previous work.     

An analytical and numerical study of the two-dimensional Bratu equation

Bratu's problem, which is the nonlinear eigenvalue equationu+ exp(u)=0 withu=0 on the walls of the unit square and as the eigenvalue, is used to develop several themes on applications of Chebyshev pseudospectral methods. The first is the importance ofsymmetry: because of invariance under the C₄ rotation group and parity in bothx andy, one can slash the size of the basis set by a factor of eight and reduce the CPU time by three orders of magnitude. Second, the pseudospectral method is ananalytical as well as a numerical tool: the simple approximation3.2A exp(–0.64A), whereA is the maximum value ofu(x, y), is derived via collocation with but a single interpolation point, but is quantitatively accurate for small and moderateA. Third, the Newton-Kantorovich/Chebyshev pseudospectral algorithm is so efficient that it is possible to compute good numerical solutions—five decimal places—on amicrocomputer inbasic. Fourth, asymptotic estimates of the Chebyshev coefficients can be very misleading: the coefficients for moderately or strongly nonlinear solutions to Bratu's equations fall off exponentially rather than algebraically withv untilv is so large that one has already obtained several decimal places of accuracy. The corner singularities, which dominate the behavior of the Chebyshev coefficients in thelimit v, are so weak as to be irrelevant, and replacing Bratu's problem by a more complicated and realistic equation would merely exaggerate the unimportance of the corner branch points even more.     

Comparison of M. longissimus dorsi pigment concentration from implanted and control Angus and Limousin bulls and steers

M. longissimus dorsi total pigment concentration, visual color score and 24-h pH values were evaluated in a 2(3) factorial design that included bulls versus steers, Zeranol implants versus control and Angus versus Limousin comparisons. Bulls had greater total pigment concentration than steers (3.25 versus 2·90 mg/g; P < 0·01) and darker colored lean (P < 0·01). Twenty-four hour pH values did not differ between bulls and steers. Zeranol implanting and breed had no effect on total pigment concentration or visual color score; however, Limousin had higher (P < 0·05) 24-h pH values than Angus. The initial slaughter group (N = 10; average age = 256 days) had 34% less total pigment than the final slaughter group (N = 48; average age = 458 days). The correlation between visual color score and total pigment concentration was -0·65. These results indicate that the darker colored lean from bulls is due in part to an increase in pigment concentration.     

Experimental results of the erosion of molybdenum due to blistering by He+ bombardment

We report some preliminary measurement of the erosion rate of plasma dumps when bombarded with 100 keV He⁺ ions at high power density ( 1 MW/m²). The expected erosion rates, based on measurements of He blistering that were made at lower power density ( 0.3 MW/m²), indicate a potentially serious problem for fusion reactors. Our tests use a reactorlike power density and produce He blisters at a rate that is slower than predicted by 2 to 4 orders of magnitude, depending on the temperature of the molybdenum target.