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941.
942.
K. V. Storozhuk 《Proceedings of the American Mathematical Society》2007,135(6):1861-1863
We give a short proof of a generalization of the Rolewicz theorem based on the uniform boundedness principle.
943.
944.
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
945.
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
946.
947.
Summary In the present paper we study truncated projections for the fanbeam geometry in computerized tomography. First we derive consistency conditions for the divergent beam transform. Then we study a singular value decomposition for the case where only the interior rays in the fan are provided, as for example in region-of-interest tomography. We show that the high angular frequency components of the searched-for densities are well determined and we present reconstructions from real data where the missing information is approximated based on the singular value decomposition.The work of the authors was supported by the Deutsche Forschungsgemeinschaft under grant Lo 310/2-4 相似文献
948.
Summary We consider a class of infinite delay equations of neutral type which includes Volterrra type integral und integrodifferential equations. Using abstract approximation results (cf. Trotter-Kato-type) for strongly continuous semigroups we develop an approximation scheme which is based on approximation of the system state by Laguerre (and Legendre) polynomials. Numerical examples demonstrate the feasibility of the scheme and show infinite order convergence for smooth data.Supported in part by the Air Force Office of Scientific Research under Contracts AFORS-84-0398 and AFORS-85-0303 and the National Aeronautics and Space Administration under NASA Grant NAG-1-517 and by NSF under Grant UINT-8521208Supported in part by the Air Force Office of Scientific Research under Contract AFORS-84-0398 and in part by the Fonds zur Förderung der wissenschaftlichen Forschung, Austria, under project No. S3206 相似文献
949.
950.