Due to the complexity of the required numerical codes, many of the new formulations for the evolution of gravitational fields in numerical relativity are not tested on binary evolutions. We introduce in this paper a new testing ground for numerical methods based on the simulation of binary neutron stars. This numerical set-up is used to develop a new technique, the Hamiltonian relaxation (HR), ...

A Hamiltonian path (cycle) of a graph is a simple path (cycle) which visits each vertex of the graph exactly once. The Hamiltonian path (cycle) problem is to determine whether a graph contains a Hamiltonian path (cycle). A graph is called Hamiltonian connected if there exists a Hamiltonian path between any two distinct vertices. Supergrid graphs were first introduced by us and include grid grap...

Pauli’s well known theorem (W. Pauli, Hanbuch der Physik vol. 5/1, ed. S. Flugge, (1926) p.60) asserts that the existence of a self-adjoint time operator canonically conjugate to a given Hamiltonian implies that the time operator and the Hamiltonian posses completely continuous spectra spanning the entire real line. Thus the conclusion that there exists no self-adjoint time operator conjugate t...

A hamiltonian graph G of order n is k-ordered, 2 ≤ k ≤ n, if for every sequence v1, v2, . . . , vk of k distinct vertices of G, there exists a hamiltonian cycle that encounters v1, v2, . . . , vk in this order. Theorems by Dirac and Ore, presenting sufficient conditions for a graph to be hamiltonian, are generalized to k-ordered hamiltonian graphs. The existence of k-ordered graphs with small m...

Two hamiltonian paths P1 = 〈u1,u2, . . . ,un(G)〉 and P2 = 〈v1,v2, . . . ,vn(G)〉 of G from u to v are independent if u = u1 = v1, v = vn(G) = un(G), and vi = ui for every 1 < i < n(G). A set of hamiltonian paths, {P1,P2, . . . ,Pk }, of G from u to v are mutually independent if any two different hamiltonian paths are independent from u to v . A bipartite graph G is hamiltonian laceable if there ...

Random s = 1/2 XY chains and the theory of quasi-one-dimensional ferroelectrics with hydrogen bonds L'viv-1994

Bi-Hamiltonian formulation is significant for investigating integrable properties of nonlinear systems of differential equations [1] [2] [3]. Many mathematical and physical systems have been found to possess such kind of bi-Hamiltonian formulation. There are two important problems related to bi-Hamiltonian theory. The one is which kind of systems can possess bi-Hamiltonian formulation and the o...

Let a and b be nonnegative integers with 2 ≤ a < b, and let G be a Hamiltonian graph of order n with n ≥ (a+b−4)(a+b−2) b−2 . An [a, b]-factor F of G is called a Hamiltonian [a, b]-factor if F contains a Hamiltonian cycle. In this paper, it is proved that G has a Hamiltonian [a, b]-factor if |NG(X)| > (a−1)n+|X|−1 a+b−3 for every nonempty independent subset X of V (G) and δ(G) > (a−1)n+a+b−4 a+...

The prism over a graph G is the Cartesian product G2K2 of G with the complete graph K2. If G is hamiltonian, then G2K2 is also hamiltonian but the converse does not hold in general. Having a hamiltonian prism is shown to be an interesting relaxation of being hamiltonian. In this paper, we examine classical problems on hamiltonicity of graphs in the context of having a hamiltonian prism. c © ???...

We construct a Hamiltonian suspension for a given symplectomorphism which is the perturbation of a Poincaré map. This is especially useful for the conversion of perturbative results between symplectomorphisms and Hamiltonian flows in any dimension 2d. As an application, using known properties of area-preserving maps, we prove that for any Hamiltonian defined on a symplectic 4-manifold M and any...