Uncontrolled intersections are the intersections where there are no external signs or signals to control the movement of vehicles. In mixed traffic conditions priority rules are often violated by the road users. In All-way-stop-controlled intersections (AWSC), the vehicle should stop themselves before they enter the intersection and should check whether any vehicles are present in the other app...

We introduce complex intersection bodies and show that their properties and applications are similar to those of their real counterparts. In particular, we generalize Busemann’s theorem to the complex case by proving that complex intersection bodies of symmetric complex convex bodies are also convex. Other results include stability in the complex Busemann-Petty problem for arbitrary measures an...

Let F be a fixed field and let X simplicial complex on the vertex set V. The Leray number L ( ; ) is minimal d such that for all i ⩾ S ⊂ V , induced [ ] satisfies H ∼ = 0 . numbers play role in formulating proving topological Helly-type theorems. For two complexes Y same V, define relative as ∖ τ ∈ In this paper we extend colorful Helly theorem to setting. Our main tool spectral sequence inters...

The concept of residual intersection, introduced by Artin and Nagata [l] in 1972, is a fruitful generalization of linkage as the following two examples attest. Let I be a strongly Cohen-Macaulay ideal in a CohenMacaulay local ring R. If Z satisfies the condition (G,), then Huneke [6, Proposition 4.31 has proved that the extended Rees algebra R[It, t‘1 is defined by an ideal which is obtained fr...

Helly’s theorem implies that if S is a finite collection of (positive) homothets of a planar convex body B, any three having non-empty intersection, then S has non-empty intersection. We show that for collections S of homothets (including translates) of the boundary ∂B, if any four curves in S have non-empty intersection, then S has non-empty intersection. We prove the following dual version: I...

The special case of an intersection of an algebraic variety with a hyperplane plays an important role in Bézout’s theorem. In this area J. Stückrad and W. Vogel proved the so-called h1-condition in 1971 (see [4]). We think this condition is also important in the multihomogeous case of Bézout’s theorem and so we give here the extension of this condition for this case. We want also look at the ne...