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Topology of definable Hausdorff limits
Let be a set definable in an o-minimal expansion of the
real field, be its projection, and assume that the non-empty
fibers are compact for all and uniformly bounded,
{\em i.e.} all fibers are contained in a ball of fixed radius If
is the Hausdorff limit of a sequence of fibers we give an
upper-bound for the Betti numbers in terms of definable sets
explicitly constructed from a fiber In particular, this allows to
establish effective complexity bounds in the semialgebraic case and in the
Pfaffian case. In the Pfaffian setting, Gabrielov introduced the {\em relative
closure} to construct the o-minimal structure \S_\pfaff generated by Pfaffian
functions in a way that is adapted to complexity problems. Our results can be
used to estimate the Betti numbers of a relative closure in the
special case where is empty.Comment: Latex, 23 pages, no figures. v2: Many changes in the exposition and
notations in an attempt to be clearer, references adde
Performance and test section flow characteristics of the National Full-Scale Aerodynamics Complex 80- by 120-Foot Wind Tunnel
Results from the performance and test section flow calibration of the 80- by 120-Foot Wind Tunnel are presented. Measurements indicating the 80- by 120-ft test section flow quality were obtained throughout the tunnel operational envelope and for atmospheric wind speeds up to approximately 20 knots. Tunnel performance characteristics and a dynamic pressure system calibration were also documented during the process of mapping the test section flow field. Experimental results indicate that the test section flow quality is relatively insensitive to dynamic pressure and the level of atmospheric winds experienced during the calibration. The dynamic pressure variation in the test section is within +/-75 percent of the average. The axial turbulence intensity is less than 0.5 percent up to the maximum test section speed of 100 knots, and the vertical and lateral flow angle variations are within +/-5 deg and +/-7 deg, respectively. Atmospheric winds were found to affect the pressure distribution in the test section only at high ratios of wind speed to test section speed
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