in this paper, construction properties of branches in the root locus of a positive feedback system whose loop transfer function is not strictly proper have been investigated. we have introduced and proved the formulations for calculating the number of branches passing through infinity, point of intersection of the asymptotes on the real axis, and angle of these asymptotes with positive directio...

In this paper we examine spectral properties of random intersection graphs when the number of vertices is equal to the number of labels. We call this class symmetric random intersection graphs. We examine symmetric random intersection graphs when the probability that a vertex selects a label is close to the connectivity threshold τc. In particular, we examine the size of the second eigenvalue o...

We prove that for two germs of analytic mappings $$f,g:({\mathbb {C}}^n,0) \rightarrow ({\mathbb {C}}^p,0)$$ with the same Newton polyhedra which are (Khovanskii) non-degenerate and their zero sets complete intersections isolated singularity at origin, there is a piecewise family $$\{f_t\}$$ maps $$f_0=f, f_1=g$$ has so-called uniform stable radius Milnor fibration. As corollary, we show number...

Polygon-circle graphs are intersection graphs of polygons inscribed in a circle. This class of graphs includes circle graphs (intersection graphs of chords of a circle), circular arc graphs (intersection graphs of arcs on a circle), chordal graphs and outerplanar graphs. We investigate binding functions for chromatic number and clique covering number of polygon-circle graphs in terms of their c...

Bezout’s theorem gives us the degree of intersection of two properly intersecting projective varieties. As two curves in P never intersect properly, Bezout’s theorem cannot be directly used to bound the number of intersection points of such curves. In this work, we bound the maximum number of intersection points of two integral ACM curves in P. The bound that we give is in many cases optimal as...

A family of sets in the plane is simple if the intersection of its any subfamily is arc-connected, and it is pierced by a line L if the intersection of its any member with L is a nonempty segment. It is proved that the intersection graphs of simple families of compact arc-connected sets in the plane pierced by a common line have chromatic number bounded by a function of their clique number.