Boundedness Theorems for the Relaxation Method

Boundedness Theorems for the Relaxation Method

Boundedness Theorems for Dilators and Ptykes

Kechris, A.S., Boundedness theorems for dilators and ptykes, Annals of Pure and Applied Logic 52 (1991) 79-92. The main theorem of this paper is: If f is a partial function from K, to X, which is Pi-bounded, then there is a weakly finite primitive recursive dilator D such that for all infinite a E domu), f(a) s D(a). The proof involves only elementary combinatorial constructions of trees. A gen...

Lagrangian Relaxation Method for the Step fixed-charge Transportation Problem

In this paper, a step fixed charge transportation problem is developed where the products are sent from the sources to the destinations in existence of both unit and step fixed-charges. The proposed model determines the amount of products in the existing routes with the aim of minimizing the total cost (sum of unit and step fixed-charges) to satisfy the demand of each customer. As the problem i...

Weak Boundedness Theorems for Canonically Fibered Gorenstein Minimal Threefolds

Let X be a Gorenstein minimal projective 3-fold with at worst locally factorial terminal singularities. Suppose the canonical map is of fiber type. Denote by F a smooth model of a generic irreducible element in fibers of φ1 and so F is a curve or a smooth surface. The main result is that there is a computable constant K independent of X such that g(F ) ≤ 647 or pg(F ) ≤ 38 whenever pg(X) ≥ K.

Weak Boundedness Theorems for Canonically Fibered Gorenstein Minimal 3-folds

Let X be a Gorenstein minimal projective 3-fold with at worst locally factorial terminal singularities. Suppose the canonical map is of fiber type. Denote by F a smooth model of a generic irreducible element in fibers of φ1 and so F is a curve or a smooth surface. The main result is that there is a computable constant K independent of X such that g(F ) ≤ 647 or pg(F ) ≤ 38 whenever pg(X) ≥ K.