Sarbazi-Azad, Ould-Khaoua, and Mackenzie proved in 2001 that there exists a Hamiltonian cycle in a pyramid network and they also constructed a Hamiltonian path between apex and each of 4 frontiers of a pyramid network. The fault tolerance is a crucial matter for parallel computing, especially in a large network. This work improves Sarbazi-Azad et al.’s result and considers other relative proble...

It is a simple fact that cubic Hamiltonian graphs have at least two Hamiltonian cycles. Finding such a cycle is NP -hard in general, and no polynomial time algorithm is known for the problem of finding a second Hamiltonian cycle when one such cycle is given as part of the input. We investigate the complexity of approximating this problem where by a feasible solution we mean a(nother) cycle in t...

New approach in classification of integrable hydrodynamic chains is established. This is the method of the Hamiltonian hydrodynamic reductions. Simultaneously, this approach yields explicit Hamiltonian hydrodynamic reductions of the Hamiltonian hydrodynamic chains. The concept of reducible Poisson brackets is established. Also this approach is useful for non-Hamiltonian hydrodynamic chains. The...

We develop a combinatorial method to show that the dodecahedron graph has, up to rotation and reflection, a unique Hamiltonian cycle. Platonic graphs with this property are called topologically uniquely Hamiltonian. The same method is used to demonstrate topologically distinct Hamiltonian cycles on the icosahedron graph and to show that a regular graph embeddable on the 2-holed torus is topolog...

In this paper we generalize constructions of non-commutative integrable systems to the context of weakly Hamiltonian actions on Poisson manifolds. In particular we prove that abelian weakly Hamiltonian actions on symplectic manifolds split into Hamiltonian and non-Hamiltonian factors, and explore generalizations in the Poisson setting.

We consider the fault hamiltonian properties of m×n meshes with two wraparound edges in the first row and the last row, denoted by M2(m, n), m ≥ 2, n ≥ 3. M2(m, n) is a spanning subgraph of Pm × Cn which has interesting fault hamiltonian properties. We show that M2(m, n) with odd n is hamiltonian-connected and 1-fault hamiltonian. For even n, M2(m, n), which is bipartite, with a single faulty e...

Theoretically, in order to describe the behavior of a spectrum, a mathematical model whichcould predict the spectrum characteristics is needed. Since in this study a Two-state system has beenused like models which was introduced previously past and could couple with the environment, theformer ideas have been extended in this study. we use the second quantized version for writing thisHamiltonian...

We discuss the numerical solution of structured generalized eigenvalue problems that arise from linear-quadratic optimal control problems, H∞ optimization, multibody systems, and many other areas of applied mathematics, physics, and chemistry. The classical approach for these problems requires computing invariant and deflating subspaces of matrices and matrix pencils with Hamiltonian and/or ske...

The Hamiltonian cycle problem in digraph is mapped into a matching cover bipartite graph. Based on this mapping, it is proved that determining existence a Hamiltonian cycle in graph is O(n). Abstract. Hamiltonian Cycle, Z-mapping graph, complexity, decision, matching covered, optimization Hamiltonian Cycle, Z-mapping graph, complexity, decision, matching covered, optimization

considering a temperature dependent two-level quantum system, we have numerically solved the landau-zener transition problem. the method includes the incorporation of temperature effect as a thermal noise added schrödinger equation for the construction of the hamiltonian. here, the obtained results which describe the changes in the system including the quantum states and the transition probabil...