To motivate our result, consider Newton’s method N for solving the equationf(z) = 0, wheref is a complex polynomial, f(z) = X$0 aizi. We write N: 5$ X S + S, where Z& is the space of polynomials of degree %d and S is the Riemann sphere C U ~0. Then N(f, z) = Nf(z) = z f(z)/f’(z) is rational over C inf and z; that is, N can be formed from the complex rational operations (+ , , x , +) from the co...

Logics for ‘generally’ are intended to express some vague notions, such as ‘generally’, ‘several’, ‘many’, ‘most’, etc., by means of the new generalized quantifier ∇ and to reason about assertions with ‘generally’ (important issues in qualitative reasoning). We introduce the idea of functional interpretation for ‘generally’ and show that representative functions (akin to Skolem functions) enabl...


 The Fathers of the Second Vatican Council, via constitution Sacrosanctum Concilium, postulated a reform marriage ceremony. As result, rites contained in Rituale Romanum 1952 were abolished by promulgation Ordo celebrandi matrimonium 1969. Until 1988, apart from Society Saint Pius X, was generally not celebrated according to earlier Ritual. After institution Pontifical Commission Ecclesia...