In this paper we prove that given a generalized dihedral group DH and a generating subset S, if S∩H 6= ∅ then the Cayley digraph → Cay(DH , S) is Hamiltonian. The proof we provide is via a recursive algorithm that produces a Hamilton circuit in the digraph.

1 Intestinal Disease Research Program, Department of Pathology and Molecular Medicine, Faculty of Health Science, McMaster University, Hamilton, ON, Canada 2 Current address: Unité Mixte de Recherche Systèmes d’Elevage, Nutrition Animale et Humaine, Institut National de la Recherche Agronomique/Agrocampus, St-Gilles, France 3 Membrane Protein Research Group, Department of Physiology, Faculty of...

Background: Attention deficit hyperactivity disorder (ADHD) affects 5% of children. In addition to pharmacotherapy, non-drug treatments such as appropriate parenting are also very important in the treatment of these children. Diagnosis and treatment of parents with psychiatric disorders and substance abuse and evaluation of the frequency of these disorders in parents is critical. Methods: In th...

Little research has been done on the effects of hyperbaric oxygen (HBO) on depression and anxiety after spinal cord injury (SCI). The aim of this study was to investigate the effects of HBO on psychological problems and never function, especially on depression and anxiety in the patients with incomplete SCI (ISCI).Sixty patients with ISCI combined with depression and anxiety were randomly divid...

Y. Le Manach1,* and G. S. Collins2 Departments of Anesthesia & Clinical Epidemiology and Biostatistics, Michael DeGroote School of Medicine, Faculty of Health Sciences, McMaster University and the Perioperative Research Group, Population Health Research Institute, Hamilton, Canada, and Centre for Statistics in Medicine, Nuffield Department of Orthopaedics, Rheumatology and Musculoskeletal Scien...

76 Identification of genes for the ethylene-forming enzyme and inhibition of ethylene synthesis in transgenic plants using antisense genes Mondher Bouzayen,t Andrew Hamilton,* Steve Picton,* Sarah Barton* and Don Grierson* *A.F.R.C. Research Group in Plant Gene Regulation, University of Nottingham, School of Agriculture, Sutton Bonington, Loughborough LE 12 5RD, U.K. and fE.N.S.A. Toulouse, 145...

A typical left-invariant optimal control problem on the rotation group SO (3) is investigated. The reduced Hamilton equations associated with an extremal curve are derived in a simple and elegant manner. These equations are then explicitly integrated by Jacobi elliptic functions.

Canonical formalism for SO(2) is developed. This group can be seen as a toy model of the Hamilton-Dirac mechanics with constraints. The Lagrangian and Hamiltonian are explicitly constructed and their physical interpretation are given. The Euler-Lagrange and Hamiltonian canonical equations coincide with the Lie equations. It is shown that the constraints satisfy CCR. Consistency of the constrain...

We study M-alternating Hamilton paths, and M-alternating Hamilton cycles in a simple connected graph G on ν vertices with a perfect matchingM . Let G be a bipartite graph, we prove that if for any two vertices x and y in different parts of G, d(x)+d(y) ≥ ν/2+2, then G has an M-alternating Hamilton cycle. For general graphs, a condition for the existence of an M-alternating Hamilton path startin...

A bent Hamilton cycle in a grid graph is one in which each edge in a successive pair of edges lies in a different dimension. We show that the d-dimensional grid graph has a bent Hamilton cycle if some dimension is even and d ≥ 3, and does not have a bent Hamilton cycle if all dimensions are odd. In the latter case, we determine the conditions for when a bent Hamilton path exists. For the d-dime...