The ring loading problem with integer demand splitting is that of routing κ traffic requirements on an undirected ring network. We present a compact polyhedral description of the set of feasible solutions to the problem, whose number of variables and constraints is O(κ). © 2009 Elsevier B.V. All rights reserved.

Abstract In dimensions n ≥ 4 {n\geq 4} , an ancient κ-solution is a nonflat, complete, solution of the Ricci flow that uniformly PIC and weakly PIC2; has bounded curvature; κ-noncollapsed. this paper, we study classification κ-solutions to n -dimensional on S<...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...

The Main Theorem is the equiconsistency of the following two statements: (1) κ is a measurable cardinal and the tree property holds at κ; (2) κ is a weakly compact hypermeasurable cardinal. From the proof of the Main Theorem, two internal consistency results follow: If there is a weakly compact hypermeasurable cardinal and a measurable cardinal far enough above it, then there is an inner model ...

Every nontrivial countably productive coreflective subcategory of topological linear spaces is κ-productive for a large cardinal κ (see [10]). Unlike that case, in uniform spaces for every infinite regular cardinal κ, there are coreflective subcategories that are κ-productive and not κ-productive (see [8]). From certain points of view, the category of topological groups lies in between those ca...

Now it is obvious from the usual definitions that an inaccessible κ is subtle iff every κ-tree T satisfies STP(T ), for which we shall just write κ-STP, iff the complete binary tree 2<κ satisfies STP(2<κ), and similarly for ineffability (and one can take this as a definition if unfamiliar with the concepts). By [Mit73] one can collapse a weakly compact (a Mahlo) cardinal onto ω2 such that in th...

We study the determinacy of the game Gκ(A) introduced in [FuKoShe] for uncountable regular κ and several classes of partial orderings A. Among trees or Boolean algebras, we can always find an A such that Gκ(A) is undetermined. For the class of linear orders, the existence of such A depends on the size of κ. In particular we obtain a characterization of κ = κ in terms of determinacy of the game ...

We study the determinacy of the game Gκ(A) introduced in [FuKoShe] for uncountable regular κ and several classes of partial orderings A. Among trees or Boolean algebras, we can always find an A such that Gκ(A) is undetermined. For the class of linear orders, the existence of such A depends on the size of κ. In particular we obtain a characterization of κ = κ in terms of determinacy of the game ...