‎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...

Two elements $g$ and $h$ of a permutation group $G$ acting on set $V$ are said to be intersecting if $g(v) = h(v)$ for some $v \in V$. More generally, subset ${\cal F}$ is an every pair intersecting. The intersection density $\rho(G)$ transitive the maximum value quotient $|{\cal F}|/|G_v|$ where runs over all sets in $G_v$ stabilizer $v\in In this paper groups degree twice prime determined, pr...

In this paper we contribute to the investigation of the fractal nature of the intersection local time measure on the intersection of independent Brownian paths. We particularly point out the difference in the small scale behaviour of the intersection local times in three-dimensional space and in the plane by studying almost sure limit theorems motivated by the notion of average densities introd...

Traffic flow systems are nonlinear and uncertain, so it is very difficult to find their optimal points. In traditional traffic control systems, the traffic lights of crossings change in a fixed time period that is not optimal. On the other hand, most proposed systems are sufficiently capable of coping with the uncertainties of traffic flow. To solve this problem, there is a need to develop expe...

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 ...