Regular Maps on Surfaces with Large Planar Width

The minimal polynomial of 2cos(π/p) and its application to regular maps of large planar width

Realization of Regular Maps of Large Genus

Regular map is an algebraic concept to describe most symmetric tilings of closed surfaces of arbitrary genus. All regular maps resp. symmetric tilings of surfaces up to genus 302 are algebraically known in the form of symmetry groups acting on their universal covering spaces. But still little is known about geometric realizations, i.e. finding most symmetric embeddings of closed surfaces and a ...

Almost All Rooted Maps Have Large Representativity

Let M be a map on a surface S. The edge-width of M is the length of a shortest non-contractible cycle of M . The face-width (or, representativity) of M is the smallest number of intersections a noncontractible curve in S has with M . (The edge-width and face-width of a planar map may be de ned to be in nity.) A map is an LEW-embedding if its maximum face valency is less than its edge-width. For...

Effect of Heat Treatment Time on the Characteristics of Coating Formed on Nanocrystalline Finemet Foils

In the present research, amorphous Fe73.5Si13.5B9Nb3Cu1 Finemet foils, 21-26µm in thickness and 5mm in width, were prepared by Planar Flow Casting (PFC) process. Wound cores of amorphous Finemet foils were simultaneously annealed and heat treated at 540°C for 60, 120 and 240 minutes in steam and air flow to form oxide insulating coating layer on both surfaces of the foils. The structure of nano...

Counting 2-Connected 4-Regular Maps on the Projective Plane

In this paper the number of rooted (near-) 4-regular maps on the projective plane are investigated with respect to the root-valency, the number of edges, the number of inner faces, the number of nonroot-vertex-loops, the number of nonroot-vertexblocks. As special cases, formulae for several types of rooted 4-regular maps such as 2-connected 4-regular projective planar maps, rooted 2-connected (...