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0. Introduction. I t is well known that for much of the mathematics of topos theory, it is in fact sufficient to use a category C whose slice categories C/A are cartesian closed. In such a category, the notion of a 'generalized set', for example an 'Aindexed set', is represented by a morphism B^-A of C, i.e. by an object of C/A. The point about such a(More)
III this paper wc consider &ernIiuistic cwrq~ulation of the esact dct.crIninant. of a tlcusc Inatris Af of iutcgcrs. 11-e present a ucw algorithm wit,h w-orst. caSc comp1wit.T 0 (rl’(log 7I + log IlMll) + 7/” log’ IlMl): where 7,. is die diIneIIsioIi of the matrix aud llA1ll is a I~ou~d 0u the eIIt,rics in Al i lmt with avcritgc~ it.y 0 (71,~ + 2(log II +(More)
The easiest geometric object in affine or projective space is a single rational point. It has no secrets, in particular its defining ideal, i.e. the set of all the polynomials which vanish at the point, is straightforward to describe. Namely, for an affine point with coordinates (a1, . . . , an), the corresponding ideal is p = (x1 − a1, . . . , xn − an);(More)
We present a new algorithm for refining a real interval containing a single real root: the new method combines the robustness of the classical Bisection algorithm with the speed of the Newton-Raphson method; that is, our method exhibits quadratic convergence when refining isolating intervals of simple roots of polynomials (and other well-behaved functions).(More)
A recently introduced, ecologically dominant, exotic ant species, Nylanderia fulva, is invading the Southeastern United States and Texas. We evaluate how this invader impacts diversity and abundance of co-occurring ants and other arthropods in two grasslands. N. fulva rapidly attains densities up to 2 orders of magnitude greater than the combined abundance(More)
Let X be a set of points whose coordinates are known with limited accuracy; our aim is to give a characterization of the vanishing ideal I(X) independent of the data uncertainty. We present a method to compute a polynomial basis B of I(X) which exhibits structural stability, that is, if e X is any set of points differing only slightly from X, there exists a(More)
A growing number of physics teachers are currently turning to instructional technologies such as wireless handheld response systems —colloquially called clickers. Two possible rationales may explain the growing interest in these devices. The first is the presumption that clickers are more effective instructional instruments. The second rationale is somewhat(More)
Bidentate hydroxypyridinones are under active development as orally active iron chelators. With applications for the treatment of general body iron overload, for instance with thalassaemia, the distribution of the chelators should be limited to peripheral tissue and they should not enter the central nervous system. This study compares the predictive(More)
CONTENTS For a real square matrix M, Hadamard's inequality gives an up1 . Introduction p e r bound H for the determinant of M; the bound is sharp if and 2. Distribution only if the rows of M are orthogonal. We study how much we 3. Analysis of |d|/H can expect that H overshoots the determinant of M, when the 4. Analysis of Iog(|d|/H) r o w s °f M are chosen(More)