In [7], Tits classified spherical buildings of rank at least three. In the addenda of [7], he introduced the Moufang property for buildings and observed that with only the results of Chapter 4 of [7] one could show that an irreducible spherical building of rank at least three and all of its irreducible residues of rank at least two must satisfy the Moufang property. Tits and the author have rec...

Given a convex n-gon P , a Fagnano periodic orbit of the respective dual billiard map is an n-gon Q whose sides are bisected by the vertices of P . For which polygons P does the ratio Area Q/AreaP have the minimal value? The answer is shown to be: for affine-regular polygons. Mathematics Subject Classification (1991): 52-XX.

In this paper, we introduce a technique to find the cyclic path covering number of Euler graphs, by using the t-hypohamiltonian graphs. Also a special type of Euler graph in the name n-gon is also being introduced and a general result of cpcn of n-gon is also found. Finally an algorithm to find the cyclic path covering number of any Euler graph is being developed. AMS subject classification: 54...

A connected plane graph taken with its interior faces forms an (r, q)-polycycle if the interior faces are all r-gons (where r = const > 3), while all interior vertices are of the maximal possible degree, denoted by q (where q = const > 3); see [1]. Any finite (r, q)-polycycle is homeomorphic to a disc and its boundary is homeomorphic to a circle. The cyclic sequence q1q2 . . . qm formed by the ...

This Article is brought to you for free and open access by the Electrical & Computer Engineering at ODU Digital Commons. It has been accepted for inclusion in Electrical & Computer Engineering Faculty Publications by an authorized administrator of ODU Digital Commons. For more information, please contact [email protected]. Repository Citation Namkoong, Gon; Boland, Patrick; Lee, Keejoo; an...

We introduce and study an infinite random triangulation of the unit disk that arises as the limit of several recursive models. This triangulation is generated by throwing chords uniformly at random in the unit disk and keeping only those chords that do not intersect the previous ones. After throwing infinitely many chords and taking the closure of the resulting set, one gets a random compact su...

We study the farthest-point distance function, which measures the distance from z ∈ C to the farthest point or points of a given compact set E in the plane. The logarithm of this distance is subharmonic as a function of z, and equals the logarithmic potential of a unique probability measure with unbounded support. This measure σE has many interesting properties that reflect the topology and geo...

We single out the polygonal paths of order that solve each of the 1 odd n  2 odd n       different longest non-cyclic Euclidean Hamiltonian path problems in      iπ e 1 , odd n n n ij n n K d     networks by an arithmetic algorithm. As by product, the procedure determines the winding index of cyclic Hamiltonian polygonals on the vertices of a regular polygon.

Through many researches on modeling and analyzing biological pathways, Petri net has recognized as a promising method for representing biological pathways. Recently, Matsuno et. al. (2003) introduced hybrid functional Petri net (HFPN) for giving more intuitive and natural biological pathway modeling method than existing Petri nets. They also developed Genomic Object Net (GON) which employs the ...