We express the Segre class of a monomial scheme—or, more generally, a scheme monomially supported on a set of divisors cutting out complete intersections— in terms of an integral computed over an associated body in euclidean space. The formula is in the spirit of the classical Bernstein-Kouchnirenko theorem computing intersection numbers of equivariant divisors in a torus in terms of mixed volu...

In this paper we establish the Aleksandrov-Fenchel type inequality for volume differences function of convex bodies and the Aleksandrov-Fenchel inequality for Quermassintegral differences of mixed projection bodies, respectively. As applications, we give positive solutions of two open problems. M.S.C. 2000: 52A40.

A new kinematic formula for the support measures of convex bodies is proved. The underlying operation is the convex hull operation for pairs of convex bodies. Further, the concept of mixed support measures is introduced and kinematic relations for these new functionals are indicated.

This paper presents a central station controlling the traffic flow of an intersection. In the proposed scenario autonomously driven and manually driven vehicles are mixed. The objective is to regulate both types of vehicles. Autonomously driven ones are controlled via wireless LAN communications; the autonomous vehicles send their positions and wait for the permission to traverse the intersecti...

In integer programming, the elementary closure associated with a family of cuts is the convex set de ned by the intersection of all the cuts in the family. In this paper, we compare the elementary closures arising from several classical families of cuts: three versions of Gomory’s fractional cuts, three versions of Gomory’s mixed integer cuts, two versions of intersection cuts and their strengt...

Let A be a regular local ring containing 1/2, which is either equicharacteristic, or is smooth over a d.v.r. of mixed characteristic. We prove that the product maps on derived Grothendieck-Witt groups of A satisfy the following property: given two elements with supports which do not intersect properly, their product vanishes. This gives an analogue for “oriented intersection multiplicities” of ...

Let A be a regular local ring containing 1/2, which is either equicharacteristic, or is smooth over a d.v.r. of mixed characteristic. We prove that the product maps on derived Grothendieck-Witt groups of A satisfy the following property: given two elements with supports which do not intersect properly, their product vanishes. This gives an analogue for “oriented intersection multiplicites” of S...

‎Let $R$ be a commutative ring with non-zero identity. ‎We describe all $C_3$‎- ‎and $C_4$-free intersection graph of non-trivial ideals of $R$ as well as $C_n$-free intersection graph when $R$ is a reduced ring. ‎Also, ‎we shall describe all complete, ‎regular and $n$-claw-free intersection graphs. ‎Finally, ‎we shall prove that almost all Artin rings $R$ have Hamiltonian intersection graphs. ...

Some Orlicz-Brunn-Minkowski type inequalities for (dual) quermassintegrals of polar bodies and star dual have been introduced. In this paper, we generalize the results establish some mixed bodies.

PM**£(*') f° r h£rS$2 where h ( < ^ ) is the point nearest to s* at which €(li)«<r(4j). If $(52)==<r(52), then let h~$%. For r<t2 let p(r) =p(^)+log log log fc — log log log r for Ui^r^h where #1 (<*2) is the point of intersection of y—p with y = p (£2) + log log log fe—log log log r. Let p(r)~p for r i^ rgwi . It is always possible to choose H SO large that r\<ti\. We repeat the procedure and ...