Convergence in a multidimensional randomized Keynesian beauty contest

We study the asymptotics of a Markovian system of $N \geq 3$ particles in $[0,1]^d$ in which, at each step in discrete time, the particle farthest from the current centre of mass is removed and replaced by an independent $U [0,1]^d$ random particle. We show that the limiting configuration contains $N-1$ coincident particles at a random location $\xi_N \in [0,1]^d$. A key tool in the analysis is a Lyapunov function based on the squared radius of gyration (sum of squared distances) of the points. For d=1 we give additional results on the distribution of the limit $\xi_N$, showing, among other things, that it gives positive probability to any nonempty interval subset of $[0,1]$, and giving a reasonably explicit description in the smallest nontrivial case, N=3.Comment: 26 pages, 4 figure

The Douglas-Peucker line simplification algorithm : an introduction with programs

CISRG discussion paper ;

Centralisers of Dehn twist automorphisms of free groups

AbstractWe refine Cohen and Lustig's description of centralisers of Dehn twists of free groups. We show that the centraliser of a Dehn twist of a free group has a subgroup of finite index that has a finite classifying space. We describe an algorithm to find a presentation of the centraliser. We use this algorithm to give an explicit presentation for the centraliser of a Nielsen automorphism in Aut(Fn). This gives restrictions to actions of Aut(Fn) on CAT(0) spaces.</jats:p

Effects of a simulated space environment on thermal radiation characteristics of selected black coatings

Simulated space environment effects on thermal radiation characteristics of black coating

Vacuum and ultraviolet radiation effects on binders and pigments for spacecraft thermal control coatings

An evaluation of several silicone resin binders and powdered inorganic pigments for potential use in spacecraft thermal-control paint formulations is presented. The pigments were selected on the basis of a hypothesis relating the heat of formation of a compound to the compound's resistance to ultra-radiation-induced degradation. Reflectance measurements were made in situ to determine degradation rates due to ultraviolet radiation. The tested polydimethylsiloxane resins were not significantly affected by long exposures to ultraviolet radiation. All the pigments, which were dispersed in a polydimethylsiloxane resin, were degraded by ultraviolet radiation as determined by an increase of solar absorptance. For the materials evaluated in this study, no evidence was found to indicate that pigments with high heats of formation were resistant to ultraviolet degradation

A Method for Measuring the Spectral Normal Emittance in Air of A Variety of Materials Having Stable Emittance Characteristics

A method and apparatus is described for the measurement of spectral normal emittance in air of a variety of materials. The system permits measurements to be performed over a wavelength region of 1.0 through 15.0 microns and over a temperature range of 600F to 1,8000F with an accuracy of 5.0 percent. The advantages of this system are described. Results obtained by this system are compared with results reported by another observer using a different technique

Monterey Bay study

The multispectral scanner capabilities of LANDSAT 1 were tested over California's Monterey Bay area and portions of the San Joaquin Valley. Using both computer aided and image interpretive processing techniques, the LANDSAT 1 data were analyzed to determine their potential application in terms of land use and agriculture. Utilizing LANDSAT 1 data, analysts were able to provide the identifications and areal extent of the individual land use categories ranging from very general to highly specific levels (e.g., from agricultural lands to specific field crop types and even the different stages of growth). It is shown that the LANDSAT system is useful in the identification of major crop species and the delineation of numerous land use categories on a global basis and that repeated surveillance would permit the monitoring of changes in seasonal growth characteristics of crops as well as the assessment of various cultivation practices with a minimum of onsite observation. The LANDSAT system is demonstrated to be useful in the planning and development of resource programs on earth