We consider the analytic continuation of the transfer function for a 2 × 2 matrix Hamiltonian into the unphysical sheets of the energy Riemann surface. We construct a family of non-selfadjoint operators which reproduce certain parts of the transfer-function spectrum including resonances situated on the unphysical sheets neighboring the physical sheet. On this basis, completeness and basis prope...

A perfectly one-factorable (P1F) regular graph G is a graph admitting a partition of the edge-set into one-factors such that the union of any two of them is a Hamiltonian cycle. We consider the case in which G is a cubic graph. The existence of a P1F cubic graph is guaranteed for each admissible value of the number of vertices. We give conditions for determining P1F graphs within a subfamily of...

In the present paper we outline the stochastic limit approach to superfluidity. The Hamiltonian describing the interaction between the Bose condensate and the normal phase is introduced. Sufficient in the stochastic limit condition of superfluidity is proposed. Existence of superfluidity in the stochastic limit of this system is proved and the non– linear (quadratic) equation of motion describi...

In a previous paper the authors showed that almost all labelled cubic graphs are hamiltonian. In the present paper, this result is used to show that almost all r-regular graphs are hamiltonian for any fixed r ≥ 3, by an analysis of the distribution of 1-factors in random regular graphs. Moreover, almost all such graphs are r-edge-colourable if they have an even number of vertices. Similarly, al...

The use of sub-Riemannian geometry on the Heisenberg group H(n) provides a compact picture of symplectic geometry. Any Hamiltonian diffeomorphism on R lifts to a volume preserving bi-Lipschitz homeomorphisms of H(n), with the use of its generating function. Any curve of a flow of such homeomorphisms deviates from horizontality by the Hamiltonian of the flow. From the metric point of view this m...

The quasi-regular patterns generated from hamiltonian has unique balanced symmetry. The patterns are quite suitable for the textile fabric. However the number of patterns just generated from hamiltonian are limited. Therefore in this paper a 110 of functions built by the methods of hamiltonian of superposition, nesting, combination and parameter variations, and it can increase the type and quan...

When a Hamiltonian system is subject to constraints which depend explicitly on time, difficulties can arise in attempting to reduce the system to its physical phase space. Specifically, it is non-trivial to restrict the system in such a way that one can find a Hamiltonian time-evolution equation involving the Dirac bracket. Using a geometrical formulation, we derive an explicit condition which ...

The Weinstein conjecture, as the general existence problem for periodic orbits of Hamiltonian or Reeb flows, has been among the central questions in symplectic topology for over two decades and its investigation has led to understanding of some fundamental properties of Hamiltonian flows. In this paper we survey some recently developed and well-known methods of proving various particular cases ...

A comparison of the eigenvalues of the Dirac and Laplace operator on the two-dimensional torus. Abstract We compare the eigenvalues of the Dirac and Laplace operator on a two-dimensional torus with respect to the trivial spin structure. In particular, we compute their variation up to order 4 upon deformation of the flat metric, study the corresponding Hamiltonian and discuss several families of...

In this paper we propose a family of cubic bipartite planar graphs, brother trees, denoted by BT(n) with n 2. Any BT(n) is hamiltonian. It remains hamiltonian if any edge is deleted. Moreover, it remains hamiltonian when a pair of nodes (one from each partite set) is deleted. These properties are optimal. Furthermore, the number of nodes in BT(n) is 6 · 2n − 4 and the diameter is 2n+ 1.  2003 ...