27,789 research outputs found
Approximate min-max relations on plane graphs
Let G be a plane graph, let τ(G) (resp. τ′(G)) be the minimum number of vertices (resp. edges) that meet all cycles of G, and let ν(G) (resp. ν′(G)) be the maximum number of vertex-disjoint (resp. edge-disjoint) cycles in G. In this note we show that τ(G)≤3 ν(G) and τ′(G)≤4 ν′(G)-1; our proofs are constructive, which yield polynomial-time algorithms for finding corresponding objects with the desired properties. © 2011 The Author(s).published_or_final_versionSpringer Open Choice, 28 May 201
Phase Diagrams and Crossover in Spatially Anisotropic d=3 Ising, XY Magnetic and Percolation Systems: Exact Renormalization-Group Solutions of Hierarchical Models
Hierarchical lattices that constitute spatially anisotropic systems are
introduced. These lattices provide exact solutions for hierarchical models and,
simultaneously, approximate solutions for uniaxially or fully anisotropic d=3
physical models. The global phase diagrams, with d=2 and d=1 to d=3 crossovers,
are obtained for Ising, XY magnetic models and percolation systems, including
crossovers from algebraic order to true long-range order.Comment: 7 pages, 12 figures. Corrected typos, added publication informatio
3nj Morphogenesis and Semiclassical Disentangling
Recoupling coefficients (3nj symbols) are unitary transformations between
binary coupled eigenstates of N=(n+1) mutually commuting SU(2) angular momentum
operators. They have been used in a variety of applications in spectroscopy,
quantum chemistry and nuclear physics and quite recently also in quantum
gravity and quantum computing. These coefficients, naturally associated to
cubic Yutsis graphs, share a number of intriguing combinatorial, algebraic, and
analytical features that make them fashinating objects to be studied on their
own. In this paper we develop a bottom--up, systematic procedure for the
generation of 3nj from 3(n-1)j diagrams by resorting to diagrammatical and
algebraic methods. We provide also a novel approach to the problem of
classifying various regimes of semiclassical expansions of 3nj coefficients
(asymptotic disentangling of 3nj diagrams) for n > 2 by means of combinatorial,
analytical and numerical tools
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