A fundamental question of graph theory lies in counting the number of graphs which satisfy certain properties. In particular, the structure of intersection graphs of planar curves is unknown, and Schaefer, Sedgwick, and Štefankovič have shown that recognizing such graphs is NP-complete. As such, the number of intersection graphs of planar curves poses an interesting problem. Pach and Tóth have ...

In this paper we will determine the multiple point manifolds of certain self-transverse immersions in Euclidean spaces. Following the triple points, these immersions have a double point self-intersection set which is the image of an immersion of a smooth 5-dimensional manifold, cobordant to Dold manifold $V^5$ or a boundary. We will show there is an immersion of $S^7times P^2$ in $mathbb{R}^{1...

Emissions from motor vehicles, one of the most important air pollution sources in city, is emerging as a growing problem large-scale cities. The amounts emissions are affected by number vehicles traffic, vehicle technology, geometric and traffic conditions highways intersections, environmental factors. Traffic flow mostly interrupted at Intersections local especially city centers. these points,...

We consider vector spaces Hn,l and Fn,l spanned by the degree n coefficients of suitable power series forms of the Homfly and Kauffman polynomials of links with l components. The intersection Hn,l ∩ Fn,l contains two Vassiliev invariants, one coming from the Jones polynomial and the second one belonging to another skein theoretically defined polynomial. We show that the whole intersection is sp...