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  • OPTICS  (5)
  • mixed integer programming  (1)
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  • 1
    Electronic Resource
    Electronic Resource
    Marginal values in mixed integer linear programming (1989)
    Springer
    Mathematical programming 44 (1989), S. 67-75 
    Details
    ISSN: 1436-4646
    Keywords: Marginal values ; mixed integer programming
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Mathematics
    Notes: Abstract For a given optimization problem, P, considered as a function of the data, its marginal values are defined as the directional partial derivatives of the value of P with respect to perturbations in that data. For linear programs, formulas for the marginal values were given by Mills, [10], and further developed by the current author [16]. In this paper, the marginal value formulas are extended to the case of mixed integer linear programming (MIP). As in ordinary linear programming, discontinuities in the value can occur, and the analysis here identifies them. This latter aspect extends previous work on continuity by the current author, [18], Geoffrion and Nauss, [5], Nauss, [11], and Radke, [12], and work on the value function of Blair and Jeroslow, [2]. Application is made to model formulation and to post-optimal analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01587077
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    Paper (German National Licenses)
    Fulltext
  • 2
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    The study of X-ray scattering to determine surface topography of smooth surfaces (1982)
    In:  Other Sources
    Details
    Publication Date: 2016-06-07
    Description: The scattering of X-rays from state-of-the-art polished mirrors is discussed with reference to the requirements of the Advanced X-ray Astrophysics Facility telescope. An experimental set-up is described which allows information to be obtained with subarcsecond resolution. A sample of the data obtained is presented along with a possible theoretical model for its interpretation.
    Keywords: OPTICS
    Type: NASA. Marshall Space Flight Center The 1982 NASA(ASEE Summer Fac. Fellowship Program; 24 p
    Format: text
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    NASA TECHNICAL REPORTS
  • 3
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    The AXAF technology program: The optical flats tests (1984)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: The results of a technology program aimed at determining the limits of surface polishing for reflecting X-ray telescopes is presented. This program is part of the major task of developing the Advanced X-ray Astrophysical Facility (AXAF). By studying the optical properties of state-of-the-art polished flat surfaces, conclusions were drawn as to the potential capability of AXAF. Surface microtopography of the flats as well as their figure are studied by X-ray, visual, and mechanical techniques. These techniques and their results are described. The employed polishing techniques are more than adequate for the specifications of the AXAF mirrors.
    Keywords: OPTICS
    Type: NASA-TM-82570 , NAS 1.15:82570
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 4
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    Reduction of the one-dimensional X-ray scattering data on mirror flats at NASA/Marshall Space Flight Center (1981)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: Data on the scattering of X-rays from various mirror flats obtained from different vendors. The scattering data discussed in this section is obtained by a one dimensional proportional counter at X-ray energies of 8.06, 6.4 and 2.99 keV. X-rays are generated at one end of a 312.4m long tube which is under vacuum. This long tube provides a parallel beam of X-rays which is then collimated by a slit and allowed to scatter from a pair of mirror flats at small grazing angles of incidence. The slit and mirrors assembly is placed 182.4 meters from the other end of the tube where the proportional counter detector is located. The detector is sitting on an optical table which is pivoted so that it can rotate to intercept X-rays at a range of spatial locations. The optical table pivot is located 2.78 meters in front of the detector, and has an operational angular range of 350 arc minutes. Measured from the position of the mirror, this total angular range of the data is (350) (2.78/182.4) = 5.33 arcminutes.
    Keywords: OPTICS
    Type: NASA-CR-170749 , NAS 1.26:170749 , TR-1
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 5
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    Relations between mirror flats geometry and X-ray data (1982)
    In:  CASI
    Details
    Publication Date: 2019-06-28
    Description: The X-ray data is used to determine the position where the mirror flats are properly aligned. The zero angle of incidence position of the mirrors is determined with the data. The mirrors are in the periscope geometry. However, the value of S sub T, the distance from the slit to the plane of the short mirror, is not fixed nor known a priori. This parameter plays a very important role in the zero position of the mirrors. As a further complicating factor, it is possible that the mirrors are not parallel. That is, they may be cocked by some angles alpha and beta, respectively. The relation between the X-ray data and the geometry of the mirrors is given. The experimental errors are given in terms of known or measured parameters.
    Keywords: OPTICS
    Type: NASA-CR-170750 , NAS 1.26:170750 , TR-2
    Format: application/pdf
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    NASA TECHNICAL REPORTS
  • 6
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    Experimental results for the scattering of X-rays from smooth surfaces (1984)
    In:  Other Sources
    Details
    Publication Date: 2019-06-28
    Description: By utilizing the unique X-ray test facility at NASA's Marshall Space Flight Center, high resolution data have been obtained for the scattering of X-rays from smooth optical flats. Using X-rays with energies in the range from 2.99 keV to 8.06 keV, the resulting reflected images from five state-of-the-art polished mirror flats with various substrate and coating materials are presented and analyzed. Evidence for large angle scattering is shown to exist for some energies and is discussed in terms of theoretical models for surface defects.
    Keywords: OPTICS
    Type: Optical Engineering (ISSN 0091-3286); 23; 177-186
    Format: text
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    NASA TECHNICAL REPORTS
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