The intersection shadow theorem of Katona is an important tool in extremal set theory. The original proof is purely combinatorial. The aim of the present paper is to show how it is using linear independence latently.

In this note we use the deep BBDG decomposition theorem in order to give a new proof of the so-called “stratified multiplicative property” for certain intersection cohomology invariants of complex algebraic varieties.

Generalizing the two-commodity ow theorem of Rothschild and Whinston and the multiiow theorem of Lovv asz and Cherkasskij, Karzanov and Lomonosov proved a min-max theorem on maximum multiiows in the seventies. Their original proof is quite long and technical and relies on earlier investigations on metrics. The main purpose of the present paper is to provide a relatively simple proof of this the...

This paper addresses the problem of obtaining a consistent estimate (or upper bound) of the covariance matrix when combining two quantities with unknown correlation. The combination is defined linearly with two gains. When the gains are chosen a priori, a family of consistent estimates is presented in the paper. The member in this family having minimal trace is said to be “family-optimal”. When...

Let X be a nonempty, compact, convex set in R and let f be an upper semicontinuous mapping from X to the collection of nonempty, compact, convex subsets of R. It is well known that such a mapping has a stationary point on X; i.e., there exists a point X such that its image under f has a nonempty intersection with the normal cone of X at the point. In the case where, for every point in X, it hol...

The subject of this paper is a special class of configurations, or patterns, of intersecting circles in constant curvature surfaces. The combinatorial aspect of such a pattern is described by a cellular decomposition of the surface. The faces of the cellular decomposition correspond to circles and the vertices correspond to points where circles intersect. (See figures 1 and 2.) In the most gene...

Note that the intersection property in Theorem A is equivalent to saying that NL(P ) is a p-group. Also, since this property is clearly independent of the choice of P in Sylp(G), it is clear that L is characteristic in G. Our interest in this characteristic subgroup was motivated by the following. Theorem B. Suppose that G is p-solvable and let L be the largest normal subgroup of G such that L∩...

In 1982 (see [1]) Imre Bárány observed that some of the classical theorems in convexity admit interesting and mysterious generalizations which he called “colorful theorems”. For example, the Colorful Helly Theorem says that if a family (repetitions of the same sets are allowed) of compact convex sets in Rk is colored (properly) with k+1 colors and it has the property that any choice of k+1 diff...

Two classical problems in economics, the existence of a market equilibrium and the existence of social choice functions, are formalized here by the properties of a family of cones associated with the economy. It was recently established that a necessary and sufficient condition for solving the former is the nonempty intersection of the family of cones, and one such condition for solving the lat...

The Chow Moving Lemma is a theorem which asserts that a given algebraic s-cycle on a smooth algebraic variety X can be moved within its rational equivalence class to intersect properly a given r-cycle on X provided that r + s ≥ dim(X) (cf. [Chow], [S2]). In the past few years, there has been considerable interest in studying spaces of algebraic cycles rather than simply cycles modulo an equival...