Digoxin did not reduce overall mortality, but it reduced the rate of hospitalization both overall and for worsening heart failure. These findings define more precisely the role of digoxin in the management of chronic heart failure.
In the early post-AMI period, the QOL of patients admitted at sites with angiography was higher than that of patients admitted at sites without angiography. However, by 1 year, the QOL and functional status of patients was similar in both groups. Differences in QOL were greatest when differences in treatment were greatest, lending support to a positive albeit small association between an early invasive approach to post-AMI care and improved QOL.
To each non totally real cubic extension K of Q and to each generator α of the cubic field K, we attach a family of cubic Thue equations, indexed by the units of K, and we prove that this family of cubic Thue equations has only a finite number of integer solutions, by giving an effective upper bound for these solutions.
StatementsLet us consider an irreductible binary cubic form having rational integers coefficientswith the property that the polynomial F(X, 1) has exactly one real root α and two complex imaginary roots, namely α ′ and α ′ . Hence α ∈ Q, α ′ = α ′ andLet K be the cubic number field Q(α) which we view as a subfield of R. Define σ : K → C to be one of the two complex embeddings, the other one being the conjugate σ . Hence α ′ = σ (α) and α ′ = σ (α). If τ is defined to be the complex conjugation, we have σ = τ • σ and σ • τ = σ .
Let K be a number field, let S be a finite set of places of K containing the archimedean places and let µ, α1, α2, α3 be non-zero elements in K. Denote by OS the ring of S-integers in K and by O × S the group of S-units. Then the set of equivalence classes (namely, up to multiplication by S-units) of the solutions (x, y, z, ε1, ε2, ε3, ε) satisfying Card{α1ε1, α2ε2, α3ε3} = 3, is finite. With the help of this last result, we exhibit, for every integer n > 2, new families of Thue-Mahler equations of degreee n having only trivial solutions. Furthermore, we produce an effective upper bound for the number of these solutions. The proofs of this paper rest heavily on Schmidt's subspace theorem.
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