The presence of edge-disjoint Hamiltonian cycles provides an advantage when implementing algorithms that require a ring structure by allowing message traffic to be spread evenly across the network. Edge-disjoint Hamiltonian cycles also provide the edge-fault tolerant hamiltonicity of an interconnection network. In this paper, we first study the property of edge-disjoint Hamiltonian cycles in tr...

1.1. The steps. The Kepler conjecture asserts that no packing of spheres in three dimensions has density greater than π/ √ 18 ≈ 0.74048. This paper is one of a series of papers devoted to the Kepler conjecture. This series began with [I], which proposed a line of research to prove the conjecture, and broke the conjecture into smaller conjectural steps which imply the Kepler conjecture. The step...

(1992). 12 approach should be combined with precise designing tools. Adding the ability to merge curves using Boolean operations will allow one to merge a circle with the tip of the wing, making it feasible to precisely design the cross-section of the missile. The techniques presented herein with the aid of the NUBS representation can be easily enhanced to support these features. The method pre...

The primary decomposition theorem due to Krohn and Rhodes KR which has been considered as one of the fundamental results in the theory of automata and semigroups states that every automaton is homomorphic to a cascaded de composition wreath product of simpler automata of two kinds reset automata and permutation automata If the automaton is non counting and correspond ingly its transformation se...

1.1. The steps. The Kepler conjecture asserts that no packing of spheres in three dimensions has density greater than π/ √ 18 ≈ 0.74078. This paper is one of a series of papers devoted to the Kepler conjecture. This series began with [I], which proposed a line of research to prove the conjecture, and broke the conjecture into smaller conjectural steps which imply the Kepler conjecture. The step...