With an optimal design one wants to determine the ideal allocation of observations for the estimation of the unknown parameter vector θ of a given model ( ) ( ) θ ; i i x f y E = , with [ ] p T θ θ θ L 1 = , ( ) n T x x X ,..., 1 = , the xi from a given experimental region ER.. Let ( ) X V ; θ be the asymptotical variance-covariance matrix of the least squares estimatorθ̂ of θ . We consider the ...

Using the theory of Newton Polygons, we formulate a simple criterion for the Galois group of a polynomial to be “large.” For a fixed α ∈ Q−Z<0, Filaseta and Lam have shown that the nth degree Generalized Laguerre Polynomial L (α) n (x) = ∑n j=0 ( n+α n−j ) (−x)/j! is irreducible for all large enough n. We use our criterion to show that, under these conditions, the Galois group of L (α) n (x) is...

In this work, we present a modification of an algorithm for solving the permutation ambiguity in convolutive blind source separation. A well known approach for separation of convolutive mixtures is the transformation to the time-frequency domain, where the convolution becomes a multiplication. With this approach it is possible to use well known instantaneous ICA algorithms independently in each...

This paper is devoted to graded algebras A having a single homogeneous relation. We give a criterion for A to be N-Koszul where N is the degree of the relation. This criterion uses a theorem due to Gerasimov. As a consequence of the criterion, some new examples of N-Koszul algebras are presented. We give an alternative proof of Gerasimov’s theorem for N = 2, which is related to Dubois-Violette’...

The results from classical asymptotic theory typically require assumptions of pointwise differentiability of a criterion function with respect an unknown parameter. Taylor expansion about some " true " value in the parameter space then gives a quadratic approximation to the criterion function, within error terms that can be bounded using the remainder from the Taylor expansion. With appropriate...

The effects of increasing work (force) requirements on energy expenditure and response topography were examined in 7 rats pressing a beam to earn food. For the 1st 16 days, the force requirement was 5.52 x 10(-2) N (5.625 g). This increased by 4.91 x 10(-2) N (5 g) every 7th session until Ss had experienced 10 upward shifts. Following the 54.57 x 10(-2) N (55.625 g) condition, the original crit...

For two subsetsW and V of a normed space X. The relative Kolmogorov n-width ofW relative to V in X is defined by Kn(W,V )X := inf Ln sup f∈W inf g∈V∩Ln ‖f − g‖X , where the infimum is taken over all n-dimensional subspaces Ln of X. For ∈ R+, defineW p (1 p ∞) to be the collection of 2 -periodic and continuous functions f representable as a convolution f (t)= c + (B ∗ g)(t), where g ∈ Lp(T ), T ...