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971.
972.
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
973.
Recently, the theory of sortability of partition property has been shown to be an effective tool to prove the existence of an optimal partition with that property. In this paper, we extend the theory to multi-partition where the partition is on t types of components. We apply our results to settle an optimal assignment problem whose proof was incomplete as given in the literature. 相似文献
974.
Héctor J. Sussmann 《Set-Valued Analysis》2002,10(2-3):233-285
It is shown that the construction of needle variations can be carried out for almost lower semicontinuous differential inclusions rather than for the case of ordinary single-valued continuously differentiable vector fields usually considered in the literature. The construction leads to needle variations whose flows are in general set-valued but still have good differentiability properties. The variations are constructed by using single-valued selections that are not necessarily continuous with respect to the state variable, but have instead a much weaker 'integral continuity' property, somewhat more general that the 'directional continuity' considered in previous work by A. Cambini and S. Querci, A. Pucci, and A. Bressan. The existence of many such selections is proved by slightly adapting an argument due to Bressan, extending it from the lower semicontinuous to the almost lower semicontinuous case, and strengthening it to yield not only directional continuity at all points but also full continuity at a specified point. 相似文献
975.
J. W. Barrett 《International Journal of Theoretical Physics》1991,30(9):1171-1215
This article is about a different representation of the geometry of the gravitational field, one in which the paths of test bodies play a crucial role. The primary concept is the geometry of the motion of a test body, and the relation between different such possible motions. Space-time as a Lorentzian manifold is regarded as a secondary construct, and it is shown how to construct it from the primary data. Some technical problems remain. Yang-Mills fields are defined by their holonomy in an analogous construction. I detail the development of this idea in the literature, and give a new version of the construction of a bundle and connection from holonomy data. The field equations of general relativity are discussed briefly in this context. 相似文献
976.
Robert J. Rubin 《Journal of statistical physics》1991,65(5-6):1207-1216
A one-dimensional lattice random walk in the presence ofm equally spaced traps is considered. The step length distribution is a symmetric exponential. An explicit analytic expression is obtained for the probability that the random walk will be trapped at thejth trapping site. 相似文献
977.
978.
Lerner E.J. 《IEEE transactions on plasma science. IEEE Nuclear and Plasma Sciences Society》1989,17(2):259-263
A cosmological model is presented that produces He, C, O, D, Li, Be, and B in their observed abundances without a Big Bang. The elements are produced during the 1.5-Gy formation period of a galaxy, with C, O, and other heavy elements produced by stars of M >12 M3 , He by stars of 6 Ms<M <12 Ms, and D, Li, Be, and B by cosmic-ray reactions in a nearly pure H plasma halo. Thus, the model shows that the major elements used in astrophysical studies can be produced during galactic formation by exactly the same processes known to function today at much lower rates 相似文献
979.
S. J. Montgomery-Smith 《Israel Journal of Mathematics》1989,67(1):123-128
We show that the canonical embeddingC(K) →L
Φ(μ) has Gaussian cotypep, where μ is a Radon probability measure onK, and Φ is an Orlicz function equivalent tot
p(logt)
p/2 for larget. 相似文献
980.
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