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2004 | 2 | 4 | 660-686
Tytuł artykułu

Covering group and graph of discretized volumes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We consider a discretized volume V consisting of finite, congruent and attached copies of a tile t. We find a group L V the orbit of which, when applied to t, is just V. We show the connection between the structural matrixQ in the formal solution of a boundary value problem formulated for volume V and the so called auxiliary matrix of the graph Γv associated with V. We show boundary value problems to be isomorphic if the graphs associated with the volumes are isomorphic, or, if the covering groups are Sunada pairs.
Wydawca

Czasopismo
Rocznik
Tom
2
Numer
4
Strony
660-686
Opis fizyczny
Daty
wydano
2004-12-01
online
2004-12-01
Twórcy
autor
  • Nuclear Regulatory Commission, 11555 Rockville Pike, 20852, Rockville, MD, USA, yxo@nrc.gov
Bibliografia
  • [1] L. Babai: “Automorphism groups, isomorphism, reconstruction”, In: R.L. Graham, M. Grötsel and L. Lovász (Eds.): Handbook of Combinatorics, North Holland-Elsevier, 1995, pp. 1447–1540.
  • [2] M. Bolla and G. Tusnády: “Spectra and optimal partitions of weighted graphs”, Discrete Mathematics, Vol. 128, (1994), pp. 1–20. http://dx.doi.org/10.1016/0012-365X(94)90100-7[Crossref]
  • [3] J.A. Bondy: “Basic Graph Theory: Paths and Circuits”, In: R.L. Graham, M. Grötschel and L, Lovaśz (Eds.): Handbook of Combinatorics, Vol. I, Elsevier, Amsterdam, 1995, pp. 3–110.
  • [4] R. Brooks: “Constructing isospectral manifolds”, Am. Math. Mon., Vol. 95, (1988). pp. 823–839. http://dx.doi.org/10.2307/2322897[Crossref]
  • [5] P. Buser: “Cayley graphs and planar Isospectral domains”, In: T. Sunada (Ed.): Geometry and Analysis on Manifolds, Lect. Notes Math., Vol. 1339, Springer, Berlin, 1988, pp. 64–79.
  • [6] P. Buser, J. Conway, P. Doyle and K.-D. Semmler: “Some planar isospectral domains”, International Mathematics Research Notices, Vol. 1994, (1994), pp. 391–400. http://dx.doi.org/10.1155/S1073792894000437[Crossref]
  • [7] J. Callaway: Electron Band Theory, Academic Press, New York, 1964.
  • [8] A. Chatterjee and W.R. Holley: “A General Theory of DNA Strand Break Production by Direct and Indirect Effects”, Radiation Protection and Dosimetry, Vol. 31, (1990), pp. 241–246.
  • [9] C. Gordon, D. Webb and S. Wolpert: “Isospectral plane domains and surfaces via Riemannian orbifolds”, Invent. math., Vol. 110, (1992), pp. 1–22. http://dx.doi.org/10.1007/BF01231320[Crossref]
  • [10] C. Gordon and D. Webb: “You can’t Hear the Shape of a Drum”, American Scientist, Vol. 84, (1996), pp. 46–56.
  • [11] G.J. Habetler and M.A. Martino: “Existence Theorems and Spectral Theory for the Multigroup Diffusion Model”, In: Proc. of the Eleventh Symposium in Applied Mathematics of the American Mathematical Society, Vol. XI, Nuclear Reactor Theory, AMS, Providence, RI(USA), 1961.
  • [12] J. Hersch: “Erweiterte Symmetrieeigenschaften von Lösungen gewisser linearer Rand- und Eigenwertprobleme”, J. reine angew. Math., Vol. 218, (1965), pp. 143–158.
  • [13] B. Kawohl: “Symmetry or Not?”, The Mathematical Intelligencer, Vol. 20, (1998), pp. 16–23. http://dx.doi.org/10.1007/BF03025292[Crossref]
  • [14] W. Ludwig and C. Falter: Symmetries in Physics, Springer, 1988.
  • [15] M. Makai and Y. Orechwa: “Symmetries of boundary value problems in mathematical physics”, J. Math. Phys., Vol. 40, (1999), pp. 5247–5263. http://dx.doi.org/10.1063/1.533028[Crossref]
  • [16] M. Makai and Y. Orechwa: “Solutions of boundary-Value Problems in Discretized Volumes”, Electronic Journal of Differential Equations, Vol. 1, (2002), pp. 1–20.
  • [17] M. Makai: Group Theory Applied to Boundary Value Problems, report ANL-FRA-1996-5, Argonne, IL, 1996.
  • [18] P.J. Olver: Application of Lie Groups to Differential Equations, Springer, New York, 1986.
  • [19] L.V. Ovsiannikov: Group Analysis of Differential Equations, Academic Press, New York, 1982.
  • [20] M.C. Payne, M.P. Teter, D.C. Altan and T.A. Arias: “Iterative minimization techniques for ab initio total energy calculations: molecular dynamics and conjugate gradients”, Rev. Mod. Phys., Vol. 64, (1992), pp. 1045–1097. http://dx.doi.org/10.1103/RevModPhys.64.1045[Crossref]
  • [21] M. Schönert et al.: GAP- Groups, Algorithms and Programming, Lehrstuhl für Mathematik, Rheinisch Westfälische Technische Hochschule, Aachen, Germany, 1995.
  • [22] G. Strang and G.J. Fix: Analysis of the Finite Element Method, Prentice-Hall, Englewood Cliffs, NJ (USA), 1973.
  • [23] T. Sunada: “Riemannian coverings and isospectral manifolds”, Ann. Math., Vol. 121, (1985), pp. 248–277. http://dx.doi.org/10.2307/1971195[Crossref]
  • [24] V.S. Vladimirov: Equations of Mathematical Physics, Marcel Dekker, New York, 1971.
  • [25] A.M. Weinberg and H.C. Schweinler: “Theory of Oscillating Absorber in a Chain Reactor”, Phys. Rev., Vol. 74, (1948), pp. 851–863. http://dx.doi.org/10.1103/PhysRev.74.851[Crossref]
  • [26] Z. Weiss: “Some Basic Properties of the Response Matrix Equations”, Nucl. Sci. Eng., Vol. 63, (1977), pp. 457–492.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.-psjd-doi-10_2478_BF02475568
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