In this paper, we are interested in solving the so-called norm equation NL/K(x) = a, where L/K is a given arbitrary extension of number fields and a a given algebraic number of K. By considering S-units and relative class groups, we show that if there exists at least one solution (in L, but not necessarily in ZL), then there exists a solution for which we can describe precisely its prime ideal ...

The objective of this study was to test the hypothesis that high-intensity hypoxic training improves sea-level performances more than equivalent training in normoxia. Sixteen well-trained collegiate and Masters swimmers (10 women, 6 men) completed a 5-wk training program, consisting of three high-intensity training sessions in a flume and supplemental low- or moderate-intensity sessions in a po...

Resum Moderation in virtual communities should not be a private privilege. This paper proposes a method for participants in a social network to decide their own rules for accepting (or not) contents. With the norm argument map, participants are able to argue about norms and voice their opinions about other people?s arguments. This structure, equipped with a method to fuse all the data introduce...

Resum Moderation in virtual communities should not be a private privilege. This paper proposes a method for participants in a social network to decide their own rules for accepting (or not) contents. With the norm argument map, participants are able to argue about norms and voice their opinions about other people?s arguments. This structure, equipped with a method to fuse all the data introduce...

We define S to be the set of those φ ∈ C∞(R,C) such that pn(φ) < ∞ for all n ≥ 0. S is a complex vector space and each pn is a norm, and because each pn is a norm, a fortiori {pn : n ≥ 0} is a separating family of seminorms. With the topology induced by this family of seminorms, S is a Fréchet space. As well, D : S → S defined by (Dφ)(x) = φ′(x), x ∈ R 1http://individual.utoronto.ca/jordanbell/...

Let ω \omega be a weight on right cancellative semigroup alttext="upper S"> S encoding="application/x-tex">S</...

This paper investigates convergence of the discontinuous finite volume method (DFVM) underminimal regularity assumptions on solutions of second order elliptic boundary value problems. Conventional analysis requires the solutions to be in Sobolev spacesH1+s, s > 1 2 . Here we assume the solutions are in H1+s, s > 0 and employ the techniques developed in Gudi (2010) [18,20] to derive error estima...

We study the Cauchy problem for the modified KdV equation ut + uxxx + (u )x = 0, u(0) = u0 for data u0 in the space Ĥr s defined by the norm ‖u0‖Ĥr s := ‖〈ξ〉 sû0‖Lr′ ξ . Local well-posedness of this problem is established in the parameter range 2 ≥ r > 1, s ≥ 1 2 − 1 2r , so the case (s, r) = (0, 1), which is critical in view of scaling considerations, is almost reached. To show this result, we...

We prove additivity of the minimal conditional entropy associated with a quantum channel Φ, represent by a completely positive (CP), trace-preserving map, when the infimum of S(γ12)−S(γ1) is restricted to states of the form (I ⊗Φ) ( |ψ〉〈ψ| ) We show that this follows from multiplicativity of the completely bounded norm of Φ considered as a map from L1 → Lp for Lp spaces defined by the Schatten ...