‎for a set of non-negative integers~$l$‎, ‎the $l$-intersection number of a graph is the smallest number~$l$ for which there is an assignment of subsets $a_v subseteq {1,dots‎, ‎l}$ to vertices $v$‎, ‎such that every two vertices $u,v$ are adjacent if and only if $|a_u cap a_v|in l$‎. ‎the bipartite $l$-intersection number is defined similarly when the conditions are considered only for the ver...

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...

We explore the geometry linking the shape of a curved mirror surface to the distortions it produces on a scene it reflects. Our analysis is local and differential. We assume a simple calibrated scene composed of lines passing through a point. We demonstrate that local information about the geometry of the surface may be recovered up to the second order from either the orientation and curvature ...

‎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. ...

A proper non-empty subset C of the points of a linear space S = (P; L) is called line-closed if any two intersecting lines of S , each meeting C at least twice, have their intersection in C. We show that when every line has k points and every point lies on r lines the maximum size for such sets is r + k ? 2. In addition it is shown that this cannot happen for projective spaces PG(n; q) unless q...

The station location problem consists of placing new stations along the railway tracks of an existing network in order to increase the number of users. In this paper we consider the problem for a railway network consisting of two intersecting lines forming an angle α. An approach for solving the problem in polynomial time for sufficiently large angles α is presented.

let $g$ be a finite group with the identity $e$‎. ‎the subgroup intersection graph $gamma_{si}(g)$ of $g$ is the graph with vertex set $v(gamma_{si}(g)) = g-e$ and two distinct vertices $x$ and $y$ are adjacent in $gamma_{si}(g)$ if and only if $|leftlangle xrightrangle capleftlangle yrightrangle|>1$‎, ‎where $leftlangle xrightrangle $ is the cyclic subgroup of $g$ generated by $xin g$‎. ‎in th...

‎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. ...

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 ...

Article history: Received 14 November 2009 Received in revised form 29 April 2010 Accepted 6 May 2010