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	Hamiltonian path - Wikipedia, the free encyclopedia
		A Hamiltonian cycle is a cycle in an undirected graph which visits each vertex exactly once and also returns to the starting vertex.
		Hamiltonian paths and cycles are named after William Rowan Hamilton who invented the icosian game, now also known as Hamilton's puzzle, which involves finding a Hamiltonian cycle in the edge graph of the dodecahedron.
		The best characterization of hamiltonian graphs was given in 1972 by the Bondy-Chvátal theorem which generalizes earlier results by G.
	en.wikipedia.org /wiki/Hamiltonian_path (573 words)

	Hamiltonian - Wikipedia, the free encyclopedia
		In classical mechanics, the Hamiltonian is a function describing the state of a mechanical system in terms of position and momentum variables.
		Both the Hamiltonian operator in physics and Hamiltonian cycles in graph theory are named after Sir William Rowan Hamilton.
		Hamiltonian also refers to those who are supporters of views expressed by Alexander Hamilton.
	en.wikipedia.org /wiki/Hamiltonian (141 words)

	Hamiltonian path - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-11-05)
		In the mathematical field of graph theory, a Hamiltonian path is a path in an undirected graph which visits each vertex exactly once.
		A Hamiltonian cycle, Hamiltonian circuit, vertex tour or graph cycle is a cycle that visits each vertex exactly once (excluding the start/end vertex).
		Similar notions may be defined for directed graphs, where edges (arcs) of a path or a cycle are required to point in the same direction, i.e., connected tail-to-head.
	www.butte-silverbow.us /project/wikipedia/index.php/Hamiltonian_path (589 words)

	Hamiltonian Cycles in the Vertex-Adjacency Dual
		A Hamiltonian cycle is a walk in a graph G that starts from a vertex v of G and ends at v after visiting all the vertices of G exactly once.
		The Hamiltonian cycle is a special case of the Traveling Salesman Problem (known as the TSP problem), where given a number of cities and the costs of travelling from one to the other, a salesman needs to find the cheapest roundtrip route that visits each city and returns to the starting point.
		Hamiltonian cycles in triangulations are studied when adjacency is defined as vertex-adjacency, where two triangles are considered to be adjacent if they share exactly at least one vertex.
	cgm.cs.mcgill.ca /~athens/cs507/Projects/2004/Perouz-Taslakian/introduction.htm (1100 words)

	The Hamiltonian Page
		A sufficient condition for a semicomplete multipartite digraph to be Hamiltonian, by J. Bang-Jensen, G. Gutin and J. Huang.
		Sufficient conditions for semicomplete multipartite digraphs to be Hamiltonian, by Y. Guo, M. Tewes, L. Volkmann, and A. Yeo.
		Hamiltonian paths and cycles in hypertournaments, by G. Gutin and A.
	www.ing.unlp.edu.ar /cetad/mos/Hamilton.html (1335 words)

	Hamiltonian Path Problem
		Hamiltonian Path is defined to be a single path that visits every node in the given graph, or a permutation of nodes in such a way that for every adjacent node in the permutation there is an edge defined in the graph.
		Simple way of solving the Hamiltonian Path problem would be to permutate all possible paths and see if edges exist on all the adjacent nodes in the permutation.
		If the graph is a complete graph, then naturally all generated permutations would quality as a Hamiltonian path.
	www.cs.toronto.edu /~arnold/492/ParallelAlgorithms/commentedReport/node12.html (218 words)

	Markov Chain Monte Carlo - Hamiltonian Method
		Hamiltonian trajectories for a two-dimensional asymmetric uncorrelated Gaussian pdf, demonstrating the ability of the Hamiltonian trajectories to readily transverse the length of the target pdf.
		The efficiency of the algorithm is calculated as the ratio of the mean square deviation from the mean of the parameter variance expected for ideal independent sampling method to that observed for the 1000 runs.
		As with it any MCMC method, it is also possible to improve the performance of the Hamiltonian method for correlated and asymmetric pdfs through the usual means of adapting the algorithm to include estimates of the covariance structure of the target pdf [2].
	public.lanl.gov /kmh/publications/samo01a.html (1456 words)

	Hamiltonian Cycles (Site not responding. Last check: 2007-11-05)
		The Hamiltonian cycle problem is one of the most famous in graph theory.
		If G does not have a Hamiltonian cycle, then there can be no such TSP tour in G', because the only way to get a tour of cost n in G would be to use only edges of weight 1, which implies a Hamiltonian cycle in G.
		Since the latter is the case, this reduction shows that TSP is hard, at least as hard as Hamiltonian cycle.
	www.cs.toronto.edu /~yuana/AlgorithmManual/BOOK/BOOK3/NODE107.HTM (335 words)

	Improved scaling of hybrid Monte Carlo by using shadow Hamiltonian
		A cheap approximation to the modified Hamiltonian has been introduced recently.
		Using the shadow Hamiltonian for the MD trajectory and the acceptance rule, the computational effort moving from one configuration to an approximately independent configuration is proportional to
		There is an additional memory requirement to form the shadow Hamiltonian.
	www.nd.edu /~izaguirr/Career2001/node23.html (256 words)

	Hamiltonian function -- Encyclopædia Britannica
		also called Hamiltonian, mathematical definition introduced in 1835 by Sir William Rowan Hamilton to express the rate of change in time of the condition of a dynamic physical system—one regarded as a set of moving particles.
		The Hamiltonian of a system specifies its total energy—i.e., the sum of its kinetic energy (that of motion) and its potential energy (that of position)—in terms of the Lagrangian…;
		The Hamiltonian of a system specifies its total energy—i.e., the sum of its kinetic energy (that of motion) and its potential energy (that of position)—in terms of the...
	www.britannica.com /eb/article-9039044?tocId=9039044 (922 words)

	PlanetMath: Hamiltonian cycle
		If there's a cycle visiting all vertices exactly once, we say that the cycle is a hamiltonian cycle.
		See Also: Hamiltonian graph, Hamiltonian path, graph theory, traceable
		This is version 2 of Hamiltonian cycle, born on 2001-10-24, modified 2002-02-03.
	planetmath.org /encyclopedia/HamiltonianCycle.html (56 words)

	Hamiltonian Functions (Site not responding. Last check: 2007-11-05)
		The function H0 is used to obtain the Dipolar Hamiltonian as a first order perturbation to the Zeeman Hamiltonian.
		If the input arguments heta and phi are given the returned Hamiltonian is for the orientation at theta degrees down from the interaction PAS z-axis and phi degrees over from the interaction PAS x-axis.
		The function H is used to obtain the Dipolar Hamiltonian.
	gamma.magnet.fsu.edu /html/modules/rank2/intdipa8.htm (788 words)

	Hamiltonian
		The Hamiltonian equations assert, firstly, that the speed component is the partial derivative of the Hamiltonian with respect to the corresponding momentum component.
		We start in the Hamiltonian picture and define finite "canonical transformations" as new positions (Q) and their canonical momenta (P) that are each functions of both old positions (q) and their canonical momenta (p) in such a way that the Hamiltonian equations retain the same form under the transformation.
		The old momenta (p) inside the old Hamiltonian are partial derivatives of S with respect to the corresponding position components (q).
	www.qedcorp.com /pcr/pcr/hamilton.html (1214 words)

	JoeUser.com - blogs from an average joe
		Because it is the President that sets the tone of foreign policy and that position is independently elected every 4 years, the foreign policy of the United States can be very inconsistent depending on the leader.
		Hamiltonians supported the first Gulf War because of the need to protect a vital natural resource (oil).
		I am probably equal parts Hamiltonian and Jacksonian with a few touches of Jeffersonian (in the sense that I believe the US should be more self sufficient).
	www.joeuser.com /Articles/The4SchoolsofUSForeignPol.html (657 words)

	The Interaction Hamiltonian
		Unfortunately, this form of the Hamiltonian is not the most useful in optical physics since it is expressed in terms of the vector potential and needs to be evaluated at all charge positions.
		Before we manipulate the Hamiltonian further, we digress a bit to get a better fix on what we are really look for.
		From the most basic notions of electrostatics, the energy of interaction with an external transverse field should be expressible as the "energy of assembly" [2]-- viz.
	people.deas.harvard.edu /~jones/ap216/lectures/ls_3/ls3_u4/ls3_unit_4.html (680 words)

	The Hamiltonian Page
		Hamiltonian Path Problems in the Online-Optimization of flexible manufacturing systems, by N. Ascheuer, Ph.D.Thesis, University of Technology Berlin, Germany, 1995.
		Optimal Parallel Construction of Hamiltonian Cycles and Spanning Trees in Random Graphs, by Philip D. MacKenzie and Quentin F. Stout, (preliminary version), In Proc.
		Hamiltonian cycles avoiding the arcs of prescribed subtournaments, by J. Bang-Jensen, G. Gutin, and A. Yeo.
	www.densis.fee.unicamp.br /~moscato/Hamilton.html (1318 words)

	Fordy -- Hamiltonian Theory
		In a series of papers [2,4-8] we constructed a large class of coupled KdV (and related) equations, which are isospectral to an energy-dependent Schrödinger operator and which possess N+1 compatible, local Hamiltonian structures (in the N-component case).
		In [23,24] we generalised these results to a class of non-homogeneous hydrodynamic systems which can be associated with a pair of quadratic Hamiltonians with terms which are linear in momenta.
		Q.P. Liu, Hamiltonian structures for integrable nonlinear evolution equations, Ph.D. Thesis, University of Leeds, 1991.
	www.amsta.leeds.ac.uk /CNLS/research/fordy/hamilton.html (853 words)

	Heisenberg Hamiltonian
		This is the reason why the exchange Hamiltonian that was derived for the hydrogen molecule is introduced.
		One may note that this Hamiltonian was derived from the exchange Hamiltonian for the hydrogen molecule i.e.
		One may note that in the case of ferromagnets the above Heisenberg Hamiltonian predicts the parallel alignment of atomic spins, but dosen't specify a preferential direction of alignment.
	phycomp.technion.ac.il /~riki/Heisenberg.html (606 words)

	Hamiltonian Dynamics, Variational Principles and Symplectic Invariants by Helmut H.W. Hofer
		For example, the problem of finding periodic orbits on a prescribed energy surface is closely related to the problem of designing an energy-efficient transport for open sets in phase space.
		The second concept is concerned with the notion of energy of a symplectic map.
		Autonomous Hamiltonian flows are geodesics for this metric (but not the unique ones) and periodic orbits are related to conjugate points.
	www.ima.umn.edu /PI/abstracts/hofer1.html (268 words)

	IP2 A Second Hamiltonian Cycle (Site not responding. Last check: 2007-11-05)
		The problem of finding a Hamiltonian cycle in a graph is NP-complete.
		Moreover, in a bipartite Hamiltonian graph, the number of Hamiltonian cycles increases (at least) exponentially as a function of the minimum degree.
		And in the cubic case, that number increases (at least) exponentially as a function of the girth.
	www.siam.org /meetings/da99/ip2.htm (177 words)

	Amazon.ca: Books: Morse Theory for Hamiltonian Systems (Site not responding. Last check: 2007-11-05)
		Within six succinct chapters, Morse Theory for Hamiltonian Systems provides a detailed description of the Maslov index, introduces the notion of relative Morse index, and describes the functional setup for the variational theory of Hamiltonian systems, including a new proof of the equivalence between the Hamiltonian and the Lagrangian index.
		The purely abstract functional aspects have been clearly separated from the applications to Hamiltonian systems, so many of the results can be applied in and other areas of current research, such as wave equations, Chern-Simon functionals, and Lorentzian geometry.
		Morse Theory for Hamiltonian Systems not only offers clear, well-written prose and a unified account of results and techniques, but it also stimulates curiosity by leading readers into the fascinating world of symplectic topology.
	www.amazon.ca /exec/obidos/ASIN/1584882026 (342 words)

	Hamiltonian mechanics (Site not responding. Last check: 2007-11-05)
		It may seem excessive to have so many ways of doing the same thing, but each formulation has its own advantages: for example, the Lagrangian and Hamiltonian formulations are very powerful in bringing out conservation laws in dynamical systems, and relating them to symmetries.
		If the Lagrangian does not depend explicitly on time, the Hamiltonian is a constant of the motion, as the following calculation shows.
		Thus the Hamiltonian can be identified with the total energy of the system.
	www.orcero.org /irbis/md/node20.html (258 words)

	The Hamiltonian Cycle Problem.
		A Hamiltonian cycle c of G is a cycle that goes through every vertex exactly once.
		This experiment is performed for a graph for which we know a Hamiltonian cycle exists.
		The blue strand indicated with a dotted line is a circular single-stranded molecule that encodes the Hamiltonian Cycle.
	www.math.usf.edu /~jonoska/bio-comp/node3.html (893 words)

	A Hamiltonian-Jacobi Algorithm - Byers (ResearchIndex) (Site not responding. Last check: 2007-11-05)
		It preserves Hamiltonian structure without using a l c condensed form.
		Although it converges too slowly for use on conventional seria omputers, it may be attractive for some highly parallel architectures.
		0.4: Lagrangian Invariant Subspaces of Hamiltonian Matrices - Mehrmann, Xu (1998)
	citeseer.ist.psu.edu /byers90hamiltonianjacobi.html (342 words)

	Amazon.ca: Books: Hamiltonian Systems with Three or More Degrees of Freedom (Site not responding. Last check: 2007-11-05)
		A survey of current knowledge about Hamiltonian systems with three or more degrees of freedom and related topics.
		The Hamiltonian systems appearing in most of the applications are non-integrable.
		Hence methods to prove non-integrability results are presented and the different meaning attributed to non-integrability are discussed.
	www.amazon.ca /exec/obidos/ASIN/0792357108 (391 words)

	Graph Theory Lecture Notes 12
		Each vertex of the dodecahedron was labeled with the name of a city, and one was to find a circuit using the edges of the dodecahedron which visited each city once and only once.
		Corollary: G is Hamiltonian iff c(G) is Hamiltonian.
		If there is more than one Hamiltonian path in a tournament, the vertices do not have a unique ranking.
	www-math.cudenver.edu /~wcherowi/courses/m4408/gtln12.html (723 words)

	GENERALIZED HAMILTONIAN FORMALISM FOR FIELD THEORY
		In the framework of the geometric formulation of field theory, classical fields are represented by sections of fibred manifolds, and their dynamics is phrased in jet manifold terms.
		The Hamiltonian formalism in fibred manifolds is the multisymplectic generalization of the Hamiltonian formalism in mechanics when canonical momenta correspond to derivatives of fields with respect to all world coordinates, not only to time.
		In the Hamiltonian formalism, these conditions appear automatically as a part of the Hamilton equations, corresponding to different Hamiltonian forms associated with a degenerate Lagrangian density.
	www.worldscibooks.com /physics/2550.html (200 words)

	Some intriguing open problems in Hamiltonian dynamics
		For a discrete mass distribution, the Hamiltonian system is finite dimensional and there is Poincaré recurrence.
		Call the "good set" the maximal invariant subset in the phase space of a Hamiltonian systems for which the invariant Liouville measure is almost periodic.
		Yes, the dynamics should exist for any smooth initial measure in the phase space and the motion is conjugated to an isospectral deformation of a Calderon-Zygmund operator.
	www.math.harvard.edu /~knill/seminars/intr (1532 words)

	hamiltonian
		The idea was to quantize these, making them into operators acting on wavefunctions on the space of 3-metrics, and then to quantize the Hamiltonian and diffeomorphism constraints and seek wavefunctions annihilated by these quantized constraints.
		It is often difficult to quantize non-polynomial expressions in the canonically conjugate variables and their derivatives.
		In terms of these new variables the Hamiltonian constraint appears polynomial in form, reviving hopes for canonical quantum gravity.
	math.ucr.edu /home/baez/hamiltonian (1284 words)

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