A modification of the kuhn-tucker theorem technical report no. 1, 1 jun. - 31 dec. 1964
Modification of Kuhn-Tucker theorem for maximizing set of concave functions
MAXIMUM PRINCIPLE↗
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Some extensions of the Kuhn-Tucker results in concave programming
Some extensions of Kuhn-Tucker results in concave programming
Moore, J. C.↗
Kuhn-Tucker optimization based reliability analysis for probabilistic finite elements
The fusion of probability finite element method (PFEM) and reliability analysis for fracture mechanics is considered. Reliability analysis with specific application to fracture mechanics is presented, and computational procedures are discussed. Explicit expressions for the optimization procedure with regard to fracture mechanics are given. The results show the PFEM is a very powerful tool in determining the second-moment statistics. The method can determine the probability of failure or fracture subject to randomness in load, material properties and crack length, orientation, and location.
Liu, W. K.↗
Embedding impedance approximations in the analysis of SIS mixers
Future millimeter-wave radio astronomy instruments will use arrays of many SIS receivers, either as focal plane arrays on individual radio telescopes, or as individual receivers on the many antennas of radio interferometers. Such applications will require broadband integrated mixers without mechanical tuners. To produce such mixers, it will be necessary to improve present mixer design techniques, most of which use the three-frequency approximation to Tucker's quantum mixer theory. This paper examines the adequacy of three approximations to Tucker's theory: (1) the usual three-frequency approximation which assumes a sinusoidal LO voltage at the junction, and a short-circuit at all frequencies above the upper sideband; (2) a five-frequency approximation which allows two LO voltage harmonics and five small-signal sidebands; and (3) a quasi five-frequency approximation in which five small-signal sidebands are allowed, but the LO voltage is assumed sinusoidal. These are compared with a full harmonic-Newton solution of Tucker's equations, including eight LO harmonics and their corresponding sidebands, for realistic SIS mixer circuits. It is shown that the accuracy of the three approximations depends strongly on the value of omega R(sub N)C for the SIS junctions used. For large omega R(sub N)C, all three approximations approach the eight-harmonic solution. For omega R(sub N)C values in the range 0.5 to 10, the range of most practical interest, the quasi five-frequency approximation is a considerable improvement over the three-frequency approximation, and should be suitable for much design work. For the realistic SIS mixers considered here, the five-frequency approximation gives results very close to those of the eight-harmonic solution. Use of these approximations, where appropriate, considerably reduces the computational effort needed to analyze an SIS mixer, and allows the design and optimization of mixers using a personal computer.
Kerr, A. R.↗
Proof Test Diagrams for a Lithia-Alumina-Silica Glass-Ceramic
The glass-ceramic (Zerodur, Schott Glaswerke, Mainz, Germany) contains 70% to 78% by weight crystalline phase of high-quartz structure with a mean crystal size of 50-55 nm. The vitreous phase has a positive thermal expansion coefficient which is practically balanced by the negative coefficient of the crystalline phase. This results in a material which can maintain longitudinal stability during thermal cycling. This was one of the reasons for its choice as the material for the grazing incidence mirrors for the Chandra X-Ray Facility. Brittle materials such as glass and glass-ceramics which exhibit slow crack growth and subsequent fast fracture to failure exhibit a time dependence in strength. The decrease in strength for a constant applied load is known as static fatigue. In many cases, environment plays a major role in the material lifetime. It has been shown for silicate glasses that crack velocity will increase as the amount of water vapor in the environment surface finish and rate of loading. A rough surface finish leads to a lower tensile strength than for an optically polished surface. The strength of glass is observed in general to increase with increasing load rate. This phenomena is known as dynamic fatigue. This was observed for Zerodur by Tucker and Gent and Tucker in previous dynamic fatigue studies, in which lifetimes were obtained. All of the above named factors need to be considered when glass is to be used in load bearing applications.
Tucker, Dennis S.↗
Using White Dish CMB Anisotropy Data to Probe Open and Flat-A CDM Cosmogonies
In this paper we present a similar analysis of the Tucker at al. (1993, hereafter T93) White Dish CMB anisotropy data collected at the South Pole. The white dish detector and telescope are described in Tucker et al. (1994).
Cosmic Microwave background Beamwidth Calibration↗
Space Archeology Overview at Gordion: 2010 to 2012
In fiscal years 2010, 2011, and 2012, Compton Tucker was the principal investigator of a NASA Space Archaeology project that worked at Gordion, in Central Turkey. Tucker was assisted by an excellent team of co-workers including Joseph Nigro and Daniel Slayback of Science Systems Applications Incorporated, Jenny Strum of the University of New Mexico, and Karina Yager, a post doctoral fellow at NASA/GSFC. This report summaries their research activities at Gordion for the field seasons of 2010, 2011, and 2012. Because of the possible use of our findings at Gordion for tomb robbing there and/or the encouragement of potential tomb robbers using our geophysical survey methods to locate areas to loot, we have not published any of our survey results in the open literature nor placed any of these results on any web sites. These 2010- 2012 survey results remain in the confidential archives of the University of Pennsylvania's University Museum of Archaeology and Anthropology, the group that leads the Gordion Excavation and Research Project. Excavations are planned for 2013 at Gordion, including several that will be based upon the research results in this report. The site of Gordion in central Turkey, famous as the home of King Midas, whose father's intricately tied knot gave the site its name, also served as the center of the Phrygian kingdom that ruled much of Central Anatolia in Asia Minor during the early first millennium B.C. Gordion has been a University of Pennsylvania Museum of Archaeology and Anthropology excavation project since 1950, yet the site is incompletely published despite six decades of research. The primary obstacles related to the site and its preservation were two problems that NASA technology could address: (1) critical survey errors in the hundreds of maps and plans produced by the earlier excavators, most of which used mutually incompatible geospatial referencing systems, that prevented any systematic understanding of the site; and (2) agricultural encroachment upon the site that was compromising its archaeological integrity. Our NASA Space Archaeology proposal was written to address both of these problems. When we started working at Gordion in 2010, we added a third objective, (3) ground penetrating radar and magnetic geophysical surveys of threatened areas. The first objective our NASA Space Archaeology Project was to provide the University of Pennsylvania's Museum of Archaeology and Anthropology a system to rectify and incorporate all existing survey data from Gordion, including previous aerial photographs of the site, detailed site surveys, maps, and excavation plans, into a common mapping system. This was accomplished with a Geographic Information System (GIS) based upon a 60 cm Quickbird satellite image ortho-rectified using Shuttle Radar Topographic Mission (SRTM) 30 m digital elevation data and tied to a known datum at Gordion. This enabled the first accurate, multi-layer plan of this complex site, occupied almost continuously from the Bronze Age to the 1st millennium CE, and made possible Gordion's three-dimensional development for the first time.
Gordion↗
A superconducting tunnel junction receiver for millimeter-wave astronomy
The development and construction of an ultralow noise heterodyne receiver for millimeter wave astronomy is described along with its use for 115.3 GHz Co line observations. The receiver uses a Superconductor-Insulator-Superconductor (SIS) quasiparticle tunnel junction mixer to convert the millimeter wave signal to a microwave intermediate frequency. Experiments aimed at quantitative verification of J. R. Tucker's quantum mixer theory are studied, to see whether it could be used as the basis for the design of a practical receiver. The experimental results were in excellent agreement with the theory, assuming the three frequency approximation. Infinite available gain and negative output resistance were observed for the first time, nonclassical effects which are not seen in conventional diode mixers. Using Tucker's theory, an SIS receiver was then designed and constructed. At 115 GHz, the single sideband receiver noise temperature is 83K, the lowest ever reported in this frequency range. A CO survey toward Cygnus-X region, using this SIS receiver on the Columbia-GISS 4 ft. telescope, is also described.
Pan, S. K.↗
Accurate experimental and theoretical comparisons between superconductor-insulator-superconductor mixers showing weak and strong quantum effects
A systematic study of the gain and noise in superconductor-insulator-superconductor mixers employing Ta based, Nb based, and Pb-alloy based tunnel junctions was made. These junctions displayed both weak and strong quantum effects at a signal frequency of 33 GHz. The effects of energy gap sharpness and subgap current were investigated and are quantitatively related to mixer performance. Detailed comparisons are made of the mixing results with the predictions of a three-port model approximation to the Tucker theory. Mixer performance was measured with a novel test apparatus which is accurate enough to allow for the first quantitative tests of theoretical noise predictions. It is found that the three-port model of the Tucker theory underestimates the mixer noise temperature by a factor of about 2 for all of the mixers. In addition, predicted values of available mixer gain are in reasonable agreement with experiment when quantum effects are weak. However, as quantum effects become strong, the predicted available gain diverges to infinity, which is in sharp contrast to the experimental results. Predictions of coupled gain do not always show such divergences.
Mcgrath, W. R.↗
Investigating the Relationship Between Liquid Water and Leaf Area in Clonal Populus
Leaf Area Index (LAI) is one of the most commonly employed biophysical parameters used to characterize vegetation canopies and scale leaf physiological processes to larger scales. For example, LAI is a critical parameter used in regional scale estimates of evapotranspiration, photosynthesis, primary productivity, and carbon cycling (Running et al., 1989; Dorman and Sellers, 1989; Potter et al., 1993). LAI is typically estimated using ratio-based techniques, such as the Normalized Difference Vegetation Index (NDVI: e.g. Tucker 1979; Asrar et al., 1989; Sellers 1985, 1987). The physical basis behind this relationship depends on the high spectral contrast between scattered near-infrared (NIR) and absorbed red radiation in canopies. As the number of leaves present in a canopy increases over a unit area, NIR reflectance increases, while red reflectance decreases, resulting in an increase in the ratio. Through time series and image compositing, NDVI provides an additional temporal measure of how these parameters change, providing a means to monitor fluxes and productivity (Tucker et al., 1983). NDVI, while highly successful for agriculture and grassland ecosystems has been found to be less successful in evergreen chaparral and forested ecosystems (Badhwar et al., 1986; Gamon et al., 1993; Hall et al., 1995). Typically, the relationship between NDVI and LAI becomes progressively more asymptotic at LAI values above three (Sellers, 1985), although linear relationships have been observed in conifers at LAis as high as 13 (Spanner et al., 1990). In this paper, we explore an alternative approach for estimating LAI for remotely sensed data from AVIRIS based on estimates of canopy liquid water. Our primary objective is to test the hypothesis that the depth of the liquid water bands expressed in canopy reflectance spectra at 960, 1200, 1400 and 1900 nm increases with increasing LAI in canopies. This study builds from work by Roberts et al. (1997), in which liquid water was shown to increase following a gradient of increasing LAI ranging from grasslands to coniferous forests. In that study, it was observed that forests, which showed little variation in NDVI, showed significant variation in liquid water. In order to test this hypothesis, we analyzed field spectra measured over Populus resprouts of known LAI and monitored changes in liquid water in young Populus stands as they aged over a 4-year time span. The study was conducted in south-central Washington, in a clonal Populus fiber farm owned and operated by Boise-Cascade near the town of Wallula.
Roberts, Dar↗
The X-ray spectra of the Vela and Puppis supernova remnants and the shock-wave model of supernova remnants
The structure and spectrum of the Vela and Puppis supernova remnants (SNRs) were observed in soft (0.1 to 1.5 keV) X rays from a rocket. The spectral data of both objects below 1.5 keV are consistent with thermal radiation from a hot plasma and are not consistent with a simple power-law function. Fitting the data to a Tucker-Koren model results in values of T = (4.3 plus or minus 0.3) x 1,000,000 K for Vela and T = (7 plus or minus 1) x 1,000,000 K for Puppis. The present data, earlier data from the Cygnus Loop, and results on Cas A and Tycho reported by others are considered within the context of a simple model in which X rays are thermally produced as a result of a shock wave expanding into the interstellar medium. X-ray data on the temperature, intrinsic diameter, and intrinsic luminosity of the five SNRs are used to compute the age, energy release, and initial interstellar density for each one. From measurements of X-ray absorption along the line of sight, and also from shock-wave model interpretations of temperature-diameter-luminosity relations, it is concluded that the average density of interstellar material is about 0.1 per cu cm between the sun and the nearest X-ray emitting SNR, Vela.
Gorenstein, P.↗
Temporal relationships between spectral response and agronomic variables of a corn canopy
Attention is given to an experiment in which spectral radiance data collected in three spectral regions are related to corn canopy variables. The study extends the work of Tucker et al. (1979) in that more detailed measurements of corn canopy variables were made using quantitative techniques. Wet and dry green leaf biomass is considered along with the green leaf area index, chlorotic leaf biomass, chlorotic leaf area, and leaf water content. In addition, spectral data were collected with a hand-held radiometer having Landsat-D Thematic Mapper (TM) bands TM3 (0.63-0.69 micrometers), TM4 (0.76-0.90 micrometers), and TM5 (1.55-1.75 micrometers). TM3, TM4, and TM5 seem to be well situated spectrally for making remotely sensed measurements related to chlorophyll concentration, leaf density, and leaf water content.
Kimes, D. S.↗
The onset of galactic winds in early-type galaxies
Researchers report on a program using Einstein x ray observations of the x ray spectra and surface brightness profiles (or extents) of a large sample of early-type (elliptical and SO) galaxies for which the goal is to determine the critical optical luminosity for which galactic winds are important. For galaxies in which the x ray emission is dominated by hydrostatic coronae, the x ray spectra will be relatively soft (characterized by a temperature of approx. 10 to the 7th power K), while for galaxies with a galactic wind, the emission will be dominated by the spectrally harder discrete sources (since the x ray emission from the wind is essentially negligible). In this new sample of 180 galaxies, there are 28 early type galaxies with sufficient counts to obtain a spectrum with the Einstein Image Proportional Counter (IPC). This sample more than doubles the total number of early-type galaxies in earlier compilations (Forman, Jones, and Tucker 1985; Canizares et al. 1987). The new spectral observations will help determine the critical optical luminosity for the onset of galactic winds which is important for understanding the chemical evolution of galaxies and of the intergalactic medium. The implications of galactic winds for the heavy element enrichment and energy content of the intracluster medium are discussed.
Forman, W.↗
The Eclipse Project
The Eclipse Project by Tom Tucker provides a readable narrative and a number of documents that record an important flight research effort at NASA's Dryden Flight Research Center. Carried out by Kelly Space and Technology, Inc., in partnership with the Air Force and Dryden at Edwards Air Force Base in the Mojave Desert of California, this project tested and gathered data about a potential newer and less expensive way to launch satellites into space. Whether the new technology comes into actual use will depend on funding, market forces, and other factors at least partly beyond the control of the participants in the project. This is a familiar situation in the history of flight research.
Tucker, Tom↗
Optimal filter design subject to output delobe constraints
The design of filters for detection and estimation in radar and communications systems is considered, with inequality constraints on the maximum output sidelobe levels. A constrained optimization problem in Hilbert space is formulated, incorporating the sidelobe constraints via a partial ordering of continuous functions. Generalized versions (in Hilbert space) of the Kuhn-Tucker and Duality Theorems allow the reduction of this problem to an unconstrained one in the dual space of regular Borel measures. A convergent algorithm is presented for computational solution of the dual problem.
Fortmann, T. E.↗
The attenuation of X-rays emitted by supernovae
The attenuation of X-rays in Arnett's C-12 detonation supernova model is computed. The attenuation of X-rays in the filaments of the Crab Nebula is computed using a model for the filaments by Woltjer and a model by Davidson and Tucker. An empirical expression by Gorenstein, Kellogg, and Gursky for the optical thickness of the interstellar medium for three supernova remnants is analyzed.
Schocken, K.↗
Complementary variational principle and duality in mathematical programming.
The relationship between the complementary variational principle and duality in mathematical programming is demonstrated through a geometric approach in a Hilbert space setting. A necessary and sufficient condition for the existence of such a principle is given in the case of a convex functional constrained by linear dynamics. Its relationship to the Kuhn-Tucker saddle point theory is indicated. Applications to various programming and control problems are discussed.
Chan, W. L.↗
X-ray spectrum of the Tycho supernova
Uhuru satellite data combined with Wisconsin rocket data suggest that the X-ray spectrum of the Tycho supernova remnant is composite and includes a thermal as well as a nonthermal component, the latter being an extension of the radio spectrum. Attempts have been made to fit the low-energy observations (thermal component) with the Tucker and Koren calculations for the solar corona.
Coleman, P. L.↗