This paper investigates the relationship between housing prices and the quality of public schools in the Australian Capital Territory. To disentangle the effects of schools and other neighbourhood characteristics on the value of residential properties, we compare sale prices of homes on either side of high school attendance boundaries. We find that a 5… (More)
Quantitative bounds on rates of approximation by linear combinations of Heaviside plane waves are obtained for sufficiently differentiable functions f which vanish rapidly enough at infinity: for d odd and f ∈ C d (R d), with lower-order partials vanishing at infinity and dth-order partials vanishing as x −(d+1+ε) , ε > 0, on any domain ⊂ R d with unit… (More)
A b s t r a c t I t i s s h o w n t h a t i n a B a n a c h s p a c e
In Lp-spaces with p an integer from [1, infinity) there exists a best approximation mapping to the set of functions computable by Heaviside perceptron networks with n hidden units; however for p an integer from (1, infinity) such best approximation is not unique and cannot be continuous.
It is shown that for any positive integer n and any function in Lp([0, 1] d) with p ∈ [1, ∞) there exists a best approximation by linear combinations of n characteristic functions of half-spaces. Further, sequences of such linear combinations converging in distance to the best approximation distance have subsequences converging to the best approximation,… (More)