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- 1
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Enrique Suárez Íñiguez,
``Por qué la tesis de licenciatura debe desaparacer,''
Ciencia 50 58-62 (Junio de 1999).
- 2
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Martín Aluja Schuneman, Rogelio Macías Ordíñez
y Pedro Bosch Giral,
``Por qué la tesis de licenciatura NO debe desaparacer,''
Ciencia 50 45-49 (Septiembre de 1999).
- 3
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Shahen Hacyan,
``Y usted, ¿cuántas citas tiene?''
Ciencia 50 54-57 (Junio de 1999).
Cross Ratio
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E. A. Maxwell,
The Methods of Plane Projective Geometry based on the use of General Homogeneous Coordinates,
Cambridge, at the University Press, 1963.
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E. A. Maxwell,
General Homogeneous Coordinates in Space of Three Dimensions,
Cambridge, at the University Press, 1961.
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Lancelot Hogben,
El Universo de los números,
Ediciones Destino, Barcelona, 1966, p. 145.
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Dirk J. Struik,
Lectures on Analytic and Projective Geometry,
Addison-Wesley Publishing Company, Inc., Cambridge, Massachusetts, 1953.
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Kenichi Kanatani,
Group-Theoretical Methods in Image Understanding,
Springer Verlag, Berlin, 1990 (ISBN 3-540-51253-5).
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Richard O. Duda and Peter E. Hart,
Pattern Classification and Scene Analysis,
John Wiley and Sons, New York, 1973 (ISBN 0-471-22361-1).
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Joseph L. Mundy and Andrew Zisserman (Eds.),
Geometric Invariance in Computer Vision,
The MIT Press, Cambridge, Massachussetts, 1992 (ISBN 0-262-13285-0).
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Joseph L. Mundy, Andrew Zisserman and David Forsyth (Eds.),
``Application of Invariance in Computer Vision,''
Lecture Notes in Computer Science 825,
Springer-Verlag, New York, 1994 (ISBN 0-387-58240-1).
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Thomas H. Reiss,
``Recognizing Planar Objects Using Invariant Image Feartures,''
Lecture Notes in Computer Science 676,
Springer-Verlag, New York, 1993 (ISBN 0-387-56713-5).
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T. Gevers and A. W. M. Smeulders,
``Efficient recognition of 3-D rigid solid objects from 2-D
projective images based on projective invariant descriptions,''
SPIE Volume 2357, pp. 296-302.
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Hazem F. Barakat and Edward M. Mikhail,
``Object model construction by invariance and photogrammetry,''
SPIE Volume 3072, pp. 295-306.
- 15
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Eamon B. Barrett, Paul M. Payton, Peter J. Marra, and Michael H. Brill,
``Geometric Interpretations of Algebraic Invariants in Images of 3D Scenes,''
SPIE Volume 3168 pp 286-299.
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Adolf Hurwitz and Richard Courant,
Vorlesungen über Allgemeine Funktionentheorie und Elliptische Funktionen,
Verlag von Julius Springer, Berlin, 1925.
Putzer's Method
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F. Silva Leite and P. Crouch,
``Closed forms for the exponential mapping on matrix Lie groups
based on Putzer's method,''
Journal of Mathematical Physics 40 3561-3568 (1999).
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E. J. Putzer,
``Avoiding the Jordan canonical form in the discussion of linear
systems with constant coefficients,''
American Mathematical Monthly 73 2-7 (1966).
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Cleve Moler and Charles van Loan,
``Nineteen dubious ways to compute the exponential of a matrix,''
SIAM Review 20 801-836 (1978).
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R. B. Kirchner,
``An explicit formula for eAt,''
American Mathematical Monthly 74 1200-1204 (1967).
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M. Kwapisz,
``The power of a matrix,''
SIAM Review 40 703-705 (1998).
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Shui-Hung Hou,
``A simple proof of the Leverrier-Faddeev
characteristic polynomial algorithm,''
SIAM Review 40 706-709 (1998).
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I. E. Leonard,
``The matrix exponential,''
SIAM Review 38 507-512 (1996).
- 24
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Eduardo Liz,
``A note on the matrix exponential,''
SIAM Review 40 700-702 (1998).
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Jack Macki,
``Three Notes on the Exponential of a Matrix and Applications,''
SIAM Review 40 699-699 (1998).
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I. Gohberg, P. Lancaster, and L. Rodman,
Invariant Subspaces of Matrices with Applications,
John Wiley and Sons, Inc., New York, 1986 (ISBN 0-471-84260-5).
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A. I. Mal'cev,
Foundations of Linear Algebra,
W. H. Freeman and Company, San Francisco and London, 1963.
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Saber N. Elaydi and William A. Harris, Jr.,
``On the computation of AN,''
SIAM Review 40 965-971 (1998).
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Edward P. Fulmer
''Computation of the matrix exponential,''
American Mathematical Monthly 82 156-159 (1975).
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Tom M. Apostol,
``Explicit formulas for solutions of the second-order matrix differential equation Y''=AY,''
American Mathematical Monthly 82 159-162 (1975).
- 31
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F. R. Gantmacher,
The Theory of Matrices, volume 1, volume 2,
Chelsea Publishing Company, New York, 1959.
Reversible Automata
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Jarkko Kari,
``Representation of Reversible Cellular Automata with Block Permutations,''
Mathematical Systems Theory 29 47-61 (1996).
- 43
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G. A. Hedlund,
``Endomorphisms and automorphisms of the shift dynamical system,''
Mathematical Systems Theory 3 320-375 (1969).
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Harold V. McIntosh,
``Cellular Automata via de Bruijn diagrams,''
1990.
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S. Amoroso and G. Cooper,
``The Garden of Eden theorem for finite configurations,''
Proceedings of the American Mathematical Society 26 158-164 (1970)
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S. Amoroso and Y. N. Patt,
``Decision Procedures for Surjectivity and Injectivity of Parallel Maps for
Tesselation Structures,''
Journal of Computer and System Sciences 6 448-464 (1972).
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Mike Boyle,
``Symbolic Dynamics and Matrices,''
in ``Combinatorial and Graph-Theoretical Problems in Linear Algebra,''
IMA Volumes in Mathematics and its Applications, Vol. 50,
Academic Press, New York, 1993, pp 1-38.
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Fan R. K. Chung,
``Spectral Graph Theory,''
CBMS Regional Conference Series in Mathematics Number 92,
American Mathematical Society, Providence, 1997.
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Dragos M. Cvetkovic, Michael Doob, and Horst Sachs,
Spectra of Graphs,
Academic Press, New York, 1979.
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P. Fatou,
``Sur les équations fonctionelles (premiere mémoire),''
Bulletin de la Societe Mathematique de France 47 161-271 (1919).
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P. Fatou,
``Sur les équations fonctionelles (deuxieme mémoire),''
Bulletin de la Societe Mathematique de France 48 33-94 (1920).
- 76
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P. Fatou,
``Sur les équations fonctionelles (troisieme mémoire),''
Bulletin de la Societe Mathematique de France 48 208-314 (1920).
- 43
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G. A. Hedlund,
``Endomorphisms and automorphisms of the shift dynamical system,''
Mathematical Systems Theory 3 320-375 (1969).
- 44
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David Hillman
``The structure of reversible one-dimensional automata,''
Physica D 52 277-292 (1991).
- 45
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Jarkko Kari,
``Reversibility and Surjectivity Problems of Cellullar Automata,''
Journal of Computer and System Sciences 48 149-182 (1994).
- 46
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Jarkko Kari,
``Representation of Reversible Cellular Automata with Block Permutations,''
Mathematical Systems Theory 29 47-61 (1996).
- 47
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D. Koenig,
Theorie der endlichen und unendlichen Graphen,
Akademische Verlagsgesellschaft, Leipzig, 1936.
Reprint: Chelsea Publishing Company, New York.
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Douglas Lind and Brian Marcus,
An Introduction to Symbolic Dynamics and Coding,
Cambridge University Press, Cambridge, 1995.
(ISBN 0-521-55124-2 hardback).
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Masakazu Nasu,
``Local Maps Inducing Surjective Global Maps of One
Dimensional Tessellation Automata,''
Mathematical Systems Theory 11 327-351 (1978).
- 50
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Stephen Wolfram,
``Statistical mechanics of cellular automata,''
Reviews of Modern Physics 55 601-644 (1983).
- 51
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Stephen Wolfram, ``Universality and complexity in cellular automata,''
Physica 10D 1-35 (1984).
- 52
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Stephen Wolfram,
``Computation theory of cellular automata,''
Communications in Mathematical Physics 96 15-57 (1984).
- 53
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Stephen Wolfram (Ed.),
Theory and Applications of Cellular Automata,
World Scientific Press, Singapore, 1986 (ISBN 9971-50-124-4 pbk).
Chaté-Manneville
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Bernard Barral, Hugues Chaté and Paul Manneville,
``Collective behaviors in a family of high-dimensional automata,''
Physics Letters A 163 279-285 (1992).
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R. Bidaux, N. Boccara, and H. Chaté,
``Order of the transition versus space dimension in a family of cellular
automata,''
Physical Review A 39 3094-3105 (1989).
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Jan Hemmingsson,
``A totalistic three-dimensional cellular automaton with quasiperiodic
behaviour,''
Physica A 183 255-261 (1992).
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J. Hemmingsson, A. Sørenson, H. Flyvbjerg and H. J. Herrmann,
``What Synchronization?''
Europhysics Letters 23 629-634 (1993).
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H. Chaté and P. Manneville,
``Evidence of Collective Behaviour in Cellular Automata,''
Europhysics Letters 14 409-413 (1991).
- 59
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Hugues Chaté and Paul Manneville,
``Collective Behaviors in Spatially Extended Systems with
Local Interactions and Synchronous Updating,''
Progress in Theoretical Physics 87 1-60 (1991).
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H. Chaté, A. Lemaître, Ph. Marcq, P. Manneville,
``Non-trivial collective behavior in extensively-chaotic
dynamical systems: an update,''
Physica A 224 447-457 (1996).
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Hugues Chaté, Jérôme Losson,
``Non-trivial collective behavior in coupled map lattices:
A transfer operator perspective,''
Physica D 103 51-72 (1997).
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Charles H. Bennett, G. Grinstein, Yu He, C. Jayaprakash and David Mukamel,
``Stability of temporally periodic states of classical many body systems,''
Physical Review A 41 1932-1935 (1990).
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Roger Bideaux, Nini Boccara and Hugues Chaté,
``Order of transition versus space dimension in a family
of cellular automata,''
Physical Review A 39 3094-3105 (1989).
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P. -M. Binder and V. Privman,
``Second-Order Dynamics in the Collective Temporal Evolution
of Complex Systems,''
Physical Review Letters 68 3830-3833 (1992).
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P. -M. Binder,
``Domains and synchronization in high-dimensional cellular automata,''
Physical Review E 51 R839-R840 (1995).
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Tomas Bohr, G. Grinstein, Yu He, and C. Jayaprakash,
``Coherence, Chaos, and Broken Symmetry in Classical, Many-Body
Dynamical Systems,''
Physical Review Letters 58 2155-2158 (1987).
- 67
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Hugues Chaté,
``On the analysis of spatiotemporally chaotic data,''
Physica D 86 238-247 (1995).
- 68
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Hugues Chaté, G. Grinstein and Lei-Han Tang,
``Long-Range Correlations in Systems with Coherent (Quasi)periodic
Oscillations,''
Physical Review Letters 74 912-915 (1995).
- 69
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H. Chaté, A. Lemaître, Ph. Marcq, P. Manneville,
``Non-trivial collective behavior in extensively-chaotic
dynamical systems: an update,''
Physica A 224 447-457 (1996).
- 70
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Hugues Chaté, Jérôme Losson,
``Non-trivial collective behavior in coupled map lattices:
A transfer operator perspective,''
Physica D 103 51-72 (1997).
- 71
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H. Chaté and P. Manneville,
``Evidence of Collective Behaviour in Cellular Automata,''
Europhysics Letters 14 409-413 (1991).
- 72
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Hugues Chaté and Paul Manneville,
``Collective Behaviors in Spatially Extended Systems with
Local Interactions and Synchronous Updating,''
Progress of Theoretical Physics 87 1-60 (1991).
- 73
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Hugues Chaté and Paul Manneville,
``Emergence of Effective Low-Dimensional Dynamics in the Macroscopic Behaviour of Coupled Map Lattices,''
Europhysics Letters 17 291-296 (1992).
- 74
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P. Fatou,
``Sur les équations fonctionelles (premiere mémoire),''
Bulletin de la Societe Mathematique de France 47 161-271 (1919).
- 75
-
P. Fatou,
``Sur les équations fonctionelles (deuxieme mémoire),''
Bulletin de la Societe Mathematique de France 48 33-94 (1920).
- 76
-
P. Fatou,
``Sur les équations fonctionelles (troisieme mémoire),''
Bulletin de la Societe Mathematique de France 48 208-314 (1920).
- 77
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J. A. C. Gallas, P. Grassberger, H.J. Herrmann and P. Ueberholz,
``Noisy collective behaviour in deterministic cellular automata,''
Physica A 180 19-41 (1992).
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J. Gorodkin, A. Sørensen, and O. Winther,
``Neural Networks and Cellular Automaton Complexity,''
Complex Systems 7 1-24 (1994).
- 79
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G. Grinstein,
``Stability of Nonstationary States of Many-Body Dynamical Systems,''
Journal of Statistical Physics 5 803-815 (1988).
- 80
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Jens M. Houlrick, Itzhak Webman and Mogens H. Jensen,
``Mean field theory and critical behavior of coupled map lattices,''
Physical Review A 41 4210-4222 (1990).
- 81
-
Jan Hemmingsson,
``A totalistic three-dimensional cellular automaton with quasiperiodic
behaviour,''
Physica A 183 255-261 (1992).
- 82
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J. Hemmingsson and J. Herrmann,
``On Oscillations in Cellular Automata,''
Europhysics Letters 23 15-19 (1993).
- 83
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F. Jiménez-Morales and J. J. Luque,
``Collective behavior of a probabilistic cellular automaton with
two absorbing phases,''
Physics Letters A 181 33-38 (1993).
- 84
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Anaël Lemaître, Hugues Chaté, and Paul Manneville,
``Cluster Expansion for Collective Behavior in Discrete-Space
Dynamical Systems,''
Physical Review Letters 77 486-489 (1996).
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Jérôme Losson and Michael C. Mackey,
``Coupled map lattices as models of deterministic and stochastic
differential delay equations,''
Physical Review E 52 115-128 (1995).
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Arkady S. Pikovsky and Jürgen Kurths,
``Do Globally Coupled Maps Really Violate the Law of Large Numbers?''
Physical Review Letters 72 1644-1646 (1994).
- 87
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Y. Pomeau,
``Periodic Behavior of Cellular Automata,''
Journal of Statistical Physics 70 1379-1382 (1993).
Rule 110
- 88
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Matthew Cook,
``Introduction to the activity of rule 110''
(copyright 1994-1998 Matthew Cook) http://w3.datanet.hu/ cook/Workshop/CellAut/
Elementary/Rule110/110pics.html
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Solomon W. Golomb,
Polyominoes
Charles Scribner's Sons, New York, 1965.
- 90
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Branko Grünbaum and G. C. Shepard,
Tilings and Patterns,
W. H. Freeman and Company, New York, 1987 (ISBN 0-7167-1193-1).
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Wentian Li and Mats G. Nordahl,
``Transient behavior of cellular automaton rule 110,''
Physics Letters A 166 335-339 (1992).
- 92
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Kristian. Lindgren and Mats. G. Nordahl,
``Universal Computation in Simple One-Dimensional Cellular Automata,''
Complex Systems 4 299-318 (1990).
- 93
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Harold V. McIntosh,
``Wolfram's Class IV automata and a good Life,''
Physica D 45 105-121 (1990).
- 94
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Grzegorz Rozenberg and Arto Salomaa,
Cornerstones of Undecidability,
Prentice Hall, New York, 1994 (ISBN 0-13-297425-8 pbk).
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W. T. Tutte,
Graph Theory As I Have Known It,
Clarendon Press, Oxford, 1998 (ISBN 0 19-850251-6).
Lorentz Contraction
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Serge Lang,
,
Addison Wesley Publishing Company, Reading, Massachussetts,
1975 (ISBN 0-201-04248-7)
- 97
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V. Bargmann,
``Irreducible unitary representations of the Lorentz group,''
Annals of Mathematics 48 568-640 (1947).
- 98
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E. Wigner,
``On unitary representations of the inhomogeneous Lorentz group,''
Annals of Mathematics 40 149-204 (1939).
Episode I
- 99
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Terry Brooks,
Star Wars: Episode I, the Phantom Menace,
Ballentine Publishing Company, 1999 (ISBN 0-345-42765-3).
- 100
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David West Reynolds,
Star Wars: Episode I, the Visual Dictionary,
D. K. Publishing Inc., New York, 1999 (ISBN 0-7894-4701-0).
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2000-03-17