Hamilton begins his criticism by stating that there is a philosophical distinction between the two methods for dating cycles and concludes that the method we use “leaves vague and intuitive exactly what this algorithm is intended to measure”. Nothing is further from the truth. Ask yourself, what is a recession? Common usage suggests that it is a decline in the level of economic activity that la...

The edges of the complete graph Kn are coloured so that no colour appears no more than k times, k = [n/Alnn], for some sufficiently large A. We show that there is always a Hamiltonian cycle in which each edge is a different colour. The proof technique is probabilistic. 'Supported by NSF grant CCR-89000112

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 asy...

The present communication describes three new species of myxosporeans (Myxozoa: Myxosporea: Bivalvulida), Myxobilatus odontamblyopusi sp. n., Myxobolus catmrigalae sp. n. and M. buccoroofus sp. n. from Odontamblyopus rubicundus (HamiltonBuchanan), Catla-Mrigal hybrid carp [male parent fish Catla catla (Hamilton-Buchanan) × female parent fish Cirrhinus mrigala (Hamilton-Buchanan)] and Labeo bata...

We prove that a directed last passage percolation model with discontinuous macroscopic (non-random) inhomogeneities has a continuum limit that corresponds to solving a Hamilton-Jacobi equation in the viscosity sense. This Hamilton-Jacobi equation is closely related to the conservation law for the hydrodynamic limit of the totally asymmetric simple exclusion process. We also prove convergence of...

The Honeycomb toroidal graph is a highly symmetric, vertex-transitive, bipartite graph which has been investigated for certain properties including pan-cyclicity and Hamilton laceability. The main focus of this project was to construct generalised methods for finding Hamilton paths and thus provide a proof of Hamilton laceability for this graph. The resulting proof was successful for a subset o...

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;...