228 research outputs found
Cauchy's functional equation and extensions: Goldie's equation and inequality, the Go{\l}\k{a}b-Schinzel equation and Beurling's equation
The Cauchy functional equation is not only the most important single
functional equation, it is also central to regular variation. Classical
Karamata regular variation involves a functional equation and inequality due to
Goldie; we study this, and its counterpart in Beurling regular variation,
together with the related Go{\l}\k{a}b-Schinzel equation.Comment: Companion paper to: Additivity, subadditivity and linearity:
automatic continuity and quantifier weakenin
Additivity, subadditivity and linearity: automatic continuity and quantifier weakening
We study the interplay between additivity (as in the Cauchy functional
equation), subadditivity and linearity. We obtain automatic continuity results
in which additive or subadditive functions, under minimal regularity
conditions, are continuous and so linear. We apply our results in the context
of quantifier weakening in the theory of regular variation completing our
programme of reducing the number of hard proofs there to zero.Comment: Companion paper to: Cauchy's functional equation and extensions:
Goldie's equation and inequality, the Go{\l}\k{a}b-Schinzel equation and
Beurling's equation Updated to refer to other developments and their
publication detail
Pointing/roll mechanism for the ultraviolet coronagraph spectrometer
A pointing/roll mechanism for the Ultraviolet Coronagraph Spectrometer (UVCS) is presented along with a description of the mechanism control algorithm. The mechanism, operating in space, will position the 2.1 meter long, 0.7 meter diameter UVCS instrument in pitch and yaw, within a 54 arc-minute half angle cone, and will also allow it to rotate + or - 179.75 deg. After considerable design effort, an optimum mechanical solution was achieved, which meets all scientific requirements as well as weight, volume, and power budgets. Evolution of the mechanism is presented along with the design status
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