That this estimate of the order of magnitude at infinity cannot be essentially improved is shown by examples of the form z=f(x) —g(y), /">0, g">0, where/ and g can be chosen such that the order is just 0(r). A still open question is whether z(x, y) can or cannot be o(r) along a special sequence of radii r —>». In proving the theorem we shall, essentially, follow Bernstein's original arguments. ...

M.A. Lone, W.J. Edwards and R. Collins AECL Research, Chalk River Laboratories Chalk River, Ontario, Canada. KOJ lJO (613)-584-3311 Thermal neutron capture cross section of the 9%r(n,y)91 Sr reaction was measured in a D20 moderated neutron flux with an activation technique. The sensitivity of the measurement was improved by using chemical separation of 90Y from 91 Sr for reduction of the intens...

Does massless (λΦ)4 theory exhibit spontaneous symmetry breaking (SSB)? The raw 1loop result implies that it does, but the “RG-improved” result implies the opposite. I argue that the appropriate “low-energy effective theory” is a nonlocal field theory involving an attractive, long-range interaction Φ2(x)Φ2(y)/z4, where z =|x−y |. RG improvement then requires running couplings for both this inte...

The aim of this paper is to explain how, starting from a Goppa code C(X,G, P1, ..., Pn) and a cyclic covering π : Y → X of degree m, one can twist the initial code to another one C(X,G + Dχ, P1, ..., Pn), where Dχ is a non-principal degree 0 divisor on X associated to a character χ of Gal(Y/X), in the hope that `X(G + Dχ) > `X(G). We give, using a MAGMA program, several examples where this occu...

Let G be a group. We say that G has spread r if for any set of distinct elements {x1, . . . , xr} ⊂ G there exists an element y ∈ G with the property that 〈xi, y〉 = G for every 1 ≤ i ≤ r. Few bounds on the spread of finite simple groups are known. In this paper we present improved upper bounds for the spread of many of the sporadic simple groups, in some cases improving on the best known upper ...

This is the second in a series of papers where we combine the classical approach to exponential Diophantine equations (linear forms in logarithms, Thue equations, etc.) with a modular approach based on some of the ideas of the proof of Fermat’s Last Theorem. In this paper we use a general and powerful new lower bound for linear forms in three logarithms, together with a combination of classical...

We present algorithms for testing the satisfiability and finding the tightened transitive closure of conjunctions of addition constraints of the form ±x ± y ≤ d and bound constraints of the form ±x ≤ d where x and y are integer variables and d is an integer constrant. The running time of these algorithms is a cubic polynomial in the number of input constraints. We also describe an efficient mat...

Sa longue carrière sera universitaire. De 1955 à la fin de son existence, il n’aura jamais cessé de soigner, de chercher, d’enseigner. C’est en 1955, en effet, qu’il devient assistant dans le département d’orthodontie de l’Université d’Indiana à Indianapolis où il vient de terminer sa Maîtrise en orthodontie. Il en assumera la responsabilité de 1956 à 1970 après avoir gravi tous les échelons de...

S 7 WADT'06, 1-3 June 2006 La Roche en Ardenne, Belgium