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971.
The Laplacian and Dirac operators on critical planar graphs 总被引:6,自引:0,他引:6
R. Kenyon 《Inventiones Mathematicae》2002,150(2):409-439
On a periodic planar graph whose edge weights satisfy a certain simple geometric condition, the discrete Laplacian and Dirac
operators have the property that their determinants and inverses only depend on the local geometry of the graph. We obtain
explicit expressions for the logarithms of the (normalized) determinants, as well as the inverses of these operators. We relate
the logarithm of the determinants to the volume plus mean curvature of an associated hyperbolic ideal polyhedron. In the associated
dimer and spanning tree models, for which the determinants of the Dirac operator and the Laplacian respectively play the role
of the partition function, this allows us to compute the entropy and correlations in terms of the local geometry. In addition,
we define a continuous family of special discrete holomorphic functions which, via convolutions, gives a general process for
constructing discrete holomorphic functions and discrete harmonic functions on critical planar graphs.
Oblatum 6-III-2002 & 12-VI-2002?Published online: 6 August 2002 相似文献
972.
Roger M. Hill 《The Journal of the Operational Research Society》1989,40(11):983-992
The context is that of a retail chain where stock is purchased into a central warehouse from which branch stocks are replenished. This paper considers possible methods of allocating limited warehouse stock to branches, and uses simulation to quantify the resulting benefits. 相似文献
973.
974.
975.
976.
977.
Let G=(V,E) be a undirected k-edge connected graph with weights ce on edges and wv on nodes. The minimum 2-edge connected subgraph problem, 2ECSP for short, is to find a 2-edge connected subgraph of G, of minimum total weight. The 2ECSP generalizes the well-known Steiner 2-edge connected subgraph problem. In this paper we study the convex hull of the incidence vectors corresponding to feasible solutions of 2ECSP. First, a natural integer programming formulation is given and it is shown that its linear relaxation is not sufficient to describe the polytope associated with 2ECSP even when G is series-parallel. Then, we introduce two families of new valid inequalities and we give sufficient conditions for them to be facet-defining. Later, we concentrate on the separation problem. We find polynomial time algorithms to solve the separation of important subclasses of the introduced inequalities, concluding that the separation of the new inequalities, when G is series-parallel, is polynomially solvable. 相似文献
978.
979.
S.N. Abdulmadjid M.M. Suliyanti K.H. Kurniawan T.J. Lie M. Pardede R. Hedwig K. Kagawa M.O. Tjia 《Applied physics. B, Lasers and optics》2006,82(1):161-166
We report in this paper the results of an experimental study on hydrogen analysis of solid samples in high pressure helium
ambient gas employing the basic scheme of laser induced breakdown spectroscopy (LIBS). It is shown that the metastable excited
state of helium atom can be utilized to induce delayed excitation of the ablated hydrogen atoms, and thereby avoid the Stark
broadening effect as well as overcoming the undesirable mismatch effect, which are responsible for inefficient excitation
respectively. It is further demonstrated that for samples of high boiling-point materials such as zircaloy, successful hydrogen
analysis can be achieved by a newly introduced double excitation technique employing single laser realized in a modified configuration
of the conventional LIBS method.
PACS 51-52 相似文献
980.
The magnetocrystalline anisotropy of thin magnetic wires of iron and cobalt is quite different from the bulk phases. The spin moment of monatomic Fe wire may be as high as 3.4 μB, while the orbital moment as high as 0.5 μB. The magnetocrystalline anisotropy energy (MAE) was calculated for wires up to 0.6 nm in diameter starting from monatomic wire and adding consecutive shells for thicker wires. I observe that Fe wires exhibit the change sign with the stress applied along the wire. It means that easy axis may change from the direction along the wire to perpendicular to the wire. We find that ballistic conductance of the wire depends on the direction of the applied magnetic field, i.e. shows anisotropic ballistic magnetoresistance. This effect occurs due to the symmetry dependence of the splitting of degenerate bands in the applied field which changes the number of bands crossing the Fermi level. We find that the ballistic conductance changes with applied stress. Even for thicker wires the ballistic conductance changes by factor 2 on moderate tensile stain in our 5×4 model wire. Thus, the ballistic conductance of magnetic wires changes in the applied field due to the magnetostriction. This effect can be observed as large anisotropic BMR in the experiment. 相似文献