From a security standpoint, it is preferable to implement least privilege network security policies in which only the bare minimum of TCP/UDP ports on internal hosts are accessible from outside the perimeter. Unfortunately, organizations with such policies can no longer communicate using common multiport protocols that require randomly chosen ports for auxiliary connections. This paper introduc...

The covariogram of a measurable set A ⊂ R is the function gA which to each y ∈ R associates the Lebesgue measure of A ∩ (y + A). This paper proves two formulas. The first equates the directional derivatives at the origin of gA to the directional variations of A. The second equates the average directional derivative at the origin of gA to the perimeter of A. These formulas, previously known with...

The proofs and applications are based on a Riemannian version of Gromov’s non-squeezing theorem and classical integral geometry. Given a convex surface Σ ⊂ R and a point q in the unit sphere S we denote by UΣ(q) the perimeter of the orthogonal projection of Σ onto a plane perpendicular to q. We obtain a function UΣ on the sphere which is clearly continuous, even, and positive. Let us denote the...

We give analytic inclusion-exclusion formulas for the area and perimeter derivatives of a union of finitely many disks in the plane.

Convexity estimators are commonly used in the analysis of shape. In this paper we define and evaluate a new easily computable measure of convexity for polygons. Let be an arbitrary polygon. If denotes the perimeter in the sense of metrics of the polygon obtained by the rotation of by angle with the origin as the center of the applied rotation, and if is the Euclidean perimeter of the minimal re...

Given a set of points in 2 or 3 dimensions, the problem of computing a geometric structure enclosing the point set while optimizing some criteria of the enclosing structure such as area, perimeter, surface area or volume has been widely studied in the literature [1, 2, 9, 7, 11, 16, 3, 5, 4, 6, 17, 14, 18]. In this paper, we are particularly interested in the 2 dimensional setting where the enc...

in the present research necessities of instream flow needs (ifn) assessment in the rivers with focusing on delichai river as case study is investigated using the hydro-ecological methods. at first, ifn is assessed using two common approaches of the tennant and wetted perimeter. then considering that rainbow trout is the most important and dominant species in this river, ecological condition of ...