In this paper, we present new Hamiltonian operators for the integrable couplings of Ablowitz–Kaup–Newell–Segur hierarchy and Kaup–Newell hierarchy. The corresponding Hamiltonians allow nontrivial degeneration. Multi-Hamiltonian structures are investigated. involutive property is proven known with respect to two Poisson brackets defined by operators.

A symbol is a pattern (of physical marks, electromagnetic energy, etc.) which denotes, designates, or otherwise has meaning. The notion that intelligence requires the use and manipulation of symbols, and that humans are therefore symbol systems, has been extremely in uential in arti cial intelligence. keywords: symbol, reasoning, intelligence, representation, logic This article has two parts. W...

The Newell Highway is the longest highway in NSW, stretching over 1,000 kilometres from the Victorian border to the Queensland border. It is a major freight route from Melbourne to Brisbane, as well as being popular with interstate travellers and tourists. This route was reviewed using a multi-disciplinary method developed by the NSW Centre for Road Safety based on Safe System principles. The r...

A coupled AKNS-Kaup-Newell hierarchy of systems of soliton equations is proposed in terms of hereditary symmetry operators resulted from Hamiltonian pairs. Zero curvature representations and tri-Hamiltonian structures are established for all coupled AKNS-Kaup-Newell systems in the hierarchy. Therefore all systems have infinitely many commuting symmetries and conservation laws. Two reductions of...

Brandon Newell, MD, is Assistant Professor; and Kimberly A. Horii, MD, is Associate Professor, University of Missouri-Kansas City, Children’s Mercy Hospitals and Clinics. Address correspondence to: Brandon D. Newell, MD, of Missouri-Kansas City, Children’s Mercy Hospitals and Clinics, 2401 Gilham Road, Kansas City, MO 64108; fax: 816-983-6710; or e-mail: [email protected]. Dr. Newell and Dr. Hori...