We provide a different axiomatization of the core interpreted as a reasonable set (Milnor, 1952) and introduce a new property, called max-intersection, related with the vector lattice structure of cooperative games with transferable utility. In particular, it is shown that the core is the only solution satisfying projection consistency, reasonability, max-intersection and modularity.

Bounded linear regularity, the strong conical hull intersection property (strong CHIP), and the conical hull intersection property (CHIP) are properties of a collection of finitely many closed convex intersecting sets in Euclidean space. It was shown recently that these properties are fundamental in several branches of convex optimization, including convex feasibility problems, error bounds, Fe...

Due to the orbifold singularities, the intersection numbers on the moduli space of curves Mg,n are in general rational numbers rather than integers. We study the properties of the denominators of these intersection numbers and their relationship with the orders of automorphism groups of stable curves. We also present a conjecture about the numerical property for a general class of Hodge integrals.

An intersection representation of a graph G is a function f : V…G† ! 2 (where S is any set) with the property that uv A E…G† if and only if f …u†V f …v†0h. The size of the representation is jSj. The intersection number of G is the smallest size of an intersection representation of G. The intersection number can be expressed as an integer program, and the value of the linear relaxation of that p...

We define the typed lambda calculus Fω ∧ , a natural generalization of Girard’s system F with intersection types and bounded polymorphism. A novel aspect of our presentation is the use of term rewriting techniques to present intersection types, which clearly splits the computational semantics (reduction rules) from the syntax (inference rules) of the system. We establish properties such as Chur...

A hollow axis-aligned box is the boundary of the cartesian product of d compact intervals in Rd. We show that for d ≥ 3, if any 2d of a collection of hollow axis-aligned boxes have non-empty intersection, then the whole collection has non-empty intersection; and if any 5 of a collection of hollow axis-aligned rectangles in R2 have non-empty intersection, then the whole collection has non-empty ...

We work in the stable homotopy category of p–complete connective spectra having mod p homology of finite type. H∗(X) means cohomology with Z/p coefficients, and is a left module over the Steenrod algebra A. A spectrum Z is called spacelike if it is a wedge summand of a suspension spectrum, and a spectrum X satisfies the Brown–Gitler property if the natural map [X,Z] −→HomA(H∗(Z), H∗(X)) is onto...

The aim of this paper is to investigate strong notion strongly ⨁-supplemented modules in module theory, namely ⨁-locally artinian supplemented modules. We call a M if it locally and its supplement submodules are direct summand. In study, we provide the basic properties particular, show that every summand supplemented. Moreover, prove ring R semiperfect with radical only projective R-module