Opening nodes on horosphere packings

Opening infinitely many nodes

we develop a theory of holomorphic differentials on a certain class of non-compact Riemann surfaces obtained by opening infinitely many nodes.

On Mixed Sphere Packings

Balls of two diierent radii r 1 < r 2 can trivially be packed in E 3 with density better than the classical packing density 3 L = 0:74048. .. , if r 1 =r 2 0:41::. We show that this even holds for r 1 =r 2 = 0:623. .. Further we show, under strong restrictions, that r 1 =r 2 close to 1 does not yield a density > 3 L. These results correspond to similar results on circle packings in the plane

On sequences of lattice packings

ON DEGREES OF END NODES AND CUT NODES IN FUZZY GRAPHS

The notion of strong arcs in a fuzzy graph was introduced byBhutani and Rosenfeld in [1] and fuzzy end nodes in the subsequent paper[2] using the concept of strong arcs. In Mordeson and Yao [7], the notion of“degrees” for concepts fuzzified from graph theory were defined and studied.In this note, we discuss degrees for fuzzy end nodes and study further someproperties of fuzzy end nodes and fuzz...

Generation of Optimal Packings from Optimal Packings

We define two notions of generation between the various optimal packings Qm of m congruent disks in a subset K of R2. The first one that we call weak generation consists in getting Qn by removing m − n disks from Qm and by displacing the n remaining congruent disks which grow continuously and do not overlap. During a weak generation of Qn from Qm, we consider the contact graphs G(t) of the inte...