Quantum canonical transformations have attracted interest since the beginning of quantum theory. Based on their classical analogues, one would expect them to provide a powerful quantum tool. However, the difficulty of solving a nonlinear operator partial differential equation such as the quantum Hamilton-Jacobi equation (QHJE) has hindered progress along this otherwise promising avenue. We over...

We investigate minimum vertex degree conditions for 3-uniform hypergraphs which ensure the existence of loose Hamilton cycles. A loose Hamilton cycle is a spanning cycle in which consecutive edges intersect in a single vertex. We prove that every 3-uniform n-vertex (n even) hypergraph H with minimum vertex degree δ1(H) ≥ ( 7 16 + o(1) ) (n 2 ) contains a loose Hamilton cycle. This bound is asym...

McMaster University; Hamilton, Canada; Hamilton Regional Laboratory Medicine Program; Hamilton, Canada; Universitaetsklinikum; Freiburg, Germany; National Center for Rare Diseases; Istituto Superiore di Sanit a; Rome, Italy; National Research Council; Institute for Research on Population and Social Policies; Rome, Italy; National Research Council; Institute of Clinical Physiology; Lecce, Italy;...

Karen M. Cogliati,a Allison F. Mistakidis,a Julie R. Marentette,a Adrienne Lau,b Benjamin M. Bolker,c,d Bryan D. Neff,b and Sigal Balshinea aDepartment of Psychology, Neuroscience & Behaviour, McMaster University, Hamilton, ON L8S 4K1, Canada, bDepartment of Biology, Western University, London, ON N6A 5B7, Canada cDepartment of Mathematics & Statistics, McMaster University, Hamilton, ON L8S 4K1...

A graph G is k-Hamilton-connected (k-hamiltonian) if G−X is Hamilton-connected (hamiltonian) for every setX ⊂ V (G) with |X| = k. In the paper, we prove that (i) every 5-connected claw-free graph with minimum degree at least 6 is 1Hamilton-connected, (ii) every 4-connected claw-free hourglass-free graph is 1-Hamilton-connected. As a byproduct, we also show that every 5-connected line graph with...

1Department of Medicine, University of Western Ontario, 339 Windermere Road, London, ON, Canada N6A 5A5 2Division of Endocrinology and Metabolism, St. Joseph’s Hospital, 268 Grosvenor Street, London, ON, Canada N6A 4V2 3Department of Epidemiology and Biostatistics, McMaster University, 1280 Main Street West, Hamilton, ON, Canada L8S 4K1 4Department of Medicine, McMaster University, 1280 Main St...

Let m ≥ 2 and k ≥ 2 be integers. We show that K k×m has a decomposition into Hamilton cycles of Kierstead-Katona type if k | m. We also show that K (3) 3×m − T has a decomposition into Hamilton cycles where T is a 1-factor if and only if 3 m and m = 4. We introduce a notion of symmetry and comment on the existence of symmetric Hamilton cycle decompositions of K (k) k×m.

Mi hael Albert, Alan Frieze and Bru e Reed Department of Mathemati s, Carnegie-Mellon University, Pittsburgh, U.S.A.y Submitted: April 25th,1995 A epted May 9th, 1995 Abstra t The edges of the omplete graph Kn are oloured so that no olour appears more than d ne times, where < 1=32 is a onstant. We show that if n is suÆ iently large then there is a Hamiltonian y le in whi h ea h edge is a di ere...

Let us suppose Σ ⊃ −1. Recent developments in formal potential theory [22] have raised the question of whether M ′′ = σ. We show that ∆F ∈ ∞. In future work, we plan to address questions of splitting as well as compactness. It would be interesting to apply the techniques of [22] to smoothly co-tangential lines.

The eikonal equation and variants of it are of significant interest for problems in computer vision and image processing. It is the basis for continuous versions of mathematical morphology, stereo, shape-from-shading and for recent dynamic theories of shape. Its numerical simulation can be delicate, owing to the formation of singularities in the evolving front, and is typically based on level s...