Publications

Geometric Calculus in Fukui

Aire, and ye Elements the eldest birth,
Of Natures Womb, that in
quaternion run
Perpetual Circle, multiform, and mix
And nourish all things, let your ceasless change
Varie to our great Maker still new praise.


Paradise Lost, Book V, 180-184, John Milton


These are preprints of papers written by Geometric Calculus Researchers in Japan. Click on the title of a paper to read its abstract, if one is available. Postscript or PDF files of most of the papers are also available.

The postscript versions of the papers have been compressed using the gzip utility, which can be freely downloaded from any of the GNU ftp sites (UK mirror). If your browser does not automatically decompress the file then save it, decompress it manually and view it with a postscript viewer such as Ghostview/GSview. For PDF papers the free ADOBE Reader is recommended.

2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999  Math. Revs.  Oth. Publs.  Video Lects.


2012

R. Bujack, G. Scheuermann, E. Hitzer
A General Geometric Fourier Transform Convolution Theorem
submitted to Adv. Appl. Clifford Alg., (2012).

E. Hitzer
Introduction to Clifford's Geometric Algebra
accepted for SICE Journal of Control, Measurement, and System Integration, April 2012, (2012).

Y. Kuroe, T. Nitta, E. Hitzer
Applications of Clifford's Geometric Algebra
accepted for SICE Journal of Control, Measurement, and System Integration, April 2012, (2012) [English draft, final version = Japanese].

E. Hitzer
Algebraic foundations of split hypercomplex nonlinear adaptive filtering
submitted to Math. Methods in the Applied Sciences, (2012).

2011

E. Hitzer
Non-constant bounded holomorphic functions of hyperbolic numbers - Candidates for hyperbolic activation functions
in Y. Kuroe, T. Nitta (eds.), Proceedings of The First SICE Symposium on Computational Intelligence [Concentrating on Clifford Neural Computing], 30 Sep. 2011, KIT, Kyoto, Japan, catalogue no. 11PG0009, pp. 23 - 28, 2011.

E. Hitzer
OPS-QFTs: A new type of quaternion Fourier transforms based on the orthogonal planes split with one or two general pure quaternions
Numerical Analysis and Applied Mathematics ICNAAM 2011, AIP Conf. Proc. 1389, pp. 280--283 (2011), doi: 10.1063/1.3636721

R. Bujack, G. Scheuermann, E. Hitzer
A General Geometric Fourier Transform
In K. Guerlebeck (ed.), Electronic Proceedings of The 9th International Conference on Clifford Algebras and their Applications in Mathematical Physics (ICCA9), 15-10 July 2011, Weimar, Germany, (2011).

E. Hitzer, S. J. Sangwine
The orthogonal planes split of quaternions
In K. Guerlebeck (ed.), Electronic Proceedings of The 9th International Conference on Clifford Algebras and their Applications in Mathematical Physics (ICCA9), 15-10 July 2011, Weimar, Germany, (2011).

E. Hitzer, J. Helmstetter, R. Ablamowicz
Square roots of -1 in real Clifford algebras
In K. Guerlebeck (ed.), Electronic Proceedings of The 9th International Conference on Clifford Algebras and their Applications in Mathematical Physics (ICCA9), 15-10 July 2011, Weimar, Germany, (2011).

E. Hitzer
Crystal planes and reciprocal space in Clifford geometric algebra
Math. Methods in the Applied Sciences, Vol. 34, Iss. 12, pp. 1421-1429, August 2011, Article first published online: 15 Feb. 2011, (2011), DOI: 10.1002/mma.1442.

E.S.M. Hitzer, R. Ablamowicz
Geometric Roots of -1 in Clifford Algebras Cl(p,q) with p+q <= 4
Adv. In Appl. Cliff. Algebras, Vol. 21(1) pp. 121-144, (2011), DOI 10.1007/s00006-010-0240-x. Preprint version: Technical Report 2009-3, Department of Mathematics, Tennessee Technological University, Tennessee, USA, May 2009. Also available as: arXiv:0905.3019v1 [math.RA]

2010

E. Hitzer
Interactive Visualization of Plane Space Groups with the Space Group Visualizer
preprint, 36 pp. (2010), with 32 color figures.

E. Hitzer
Angles Between Subspaces Computed in Clifford Algebra
in T. E. Simos et al. (eds.), ICNAAM 2010: Int. Conf. of Num. Analysis and App. Math. 2010, AIP Conf. Proc., Vol. 1281, pp. 1476-1479, (2010).

E. Hitzer
Interactive visualization of plane groups
in G. Lugosi, D. Nagy (eds.), Symmetry: Art and Science, Spec. Iss. of The Journal of the Int. Soc. For the Interdisc. Study of Symmetry (ISIS): Proc. of Symmetry: Art and Science, 8th Congress of ISIS, Days of Harmonics, Gmund, Austria, 23-28 Aug. 2010, Vol. 2010 (1-4), pp. 80-83, (2010).

E. Hitzer
Angles between subspaces
in V. Skala, E.Hitzer (eds.), Workshop Proceedings: Computer Graphics, Computer Vision and Mathematics 2010, Sep. 07-10, 2010, Brno University of Technology, Brno, Czech Republic, published by UNION Agency, Plzen (2010), ISBN 978-80-86943-85-5.

E. Hitzer
Reciprocal space and crystal planes in geometric algebra
in Electronic Proceedings of AGACSE 2010, Amsterdam, The Netherlands, 14-16 June 2010.

K. Tachibana, E. Hitzer, M. T. Pham, T. Yoshikawa, T. Furuhashi
A Note on Geometric Algebra and Neural Networks
Proc. of 20th Intelligent Systems Symposium (FAN 2010), 25-26 Sep. 2010, Tokyo, Japan, pp. 116 – 117 (2010).

E.S.M. Hitzer, C. Perwass, D. Ichikawa
Interactive 3D Space Group Visualization with CLUCalc and Crystallographic Subperiodic Groups in Geometric Algebra
in G. Scheuermann, E. Bayro-Corrochano (eds.), Geometric Algebra Computing, Springer, New York, 2010, pp. 385-400.

B. Mawardi, E.S.M. Hitzer, S. Adji
Two-Dimensional Clifford Windowed Fourier Transform
in G. Scheuermann, E. Bayro-Corrochano (eds.), Geometric Algebra Computing, Springer, New York, 2010, pp. 93-106.

M. T. Pham, K. Tachibana, E.S.M. Hitzer, T. Yoshikawa, T. Furuhashi
Classification and Clustering of Spatial Patterns with Geometric Algebra
in G. Scheuermann, E. Bayro-Corrochano (eds.), Geometric Algebra Computing, Springer, New York, 2010, pp. 231-248.

B. Mawardi, E.S.M. Hitzer, R. Ashino, R. Vaillancourt
Windowed Fourier transform of two-dimensional quaternionic signals
Appl. Math. and Computation, 216, Iss. 8, pp. 2366-2379, 15 June 2010.

E.S.M. Hitzer
New views of crystal symmetry guided by profound admiration of the extraordinary works of Grassmann and Clifford
in Petsche, H.-J.; Lewis, A.C.; Liesen, J.; Russ, S. (eds.), From Past to Future: Grasmann's Work in Context, Grasmann Bicentennial Conference, September 2009, Springer, Basel, pp. 413 - 422 (2010).

E.S.M. Hitzer, C. Perwass
Interactive 3D Space Group Visualization with CLUCalc and the Clifford Geometric Algebra Description of Space Groups
Adv. Appl. Clifford Alg., Vol. 20(3-4), pp. 631-658, (2010), DOI 10.1007/s00006-010-0214-z.

2009

E. Hitzer, C. Perwass
Algorithm for conversion between geometric algebra versor notation and conventional crystallographic symmetry-operation symbols
preprint, 14 pp. (2009).

E.S.M. Hitzer, D. Ichikawa
Representation of Crystallographic Subperiodic Groups in Clifford's Geometric Algebra
submitted to: Acta Crystallographica Section A: Foundations of Crystallography, (2009).

E.S.M. Hitzer
Clifford (Geometric) Algebra Wavelet Transform
in V. Skala and D. Hildenbrand (eds.), Proceedings of GraVisMa 2009, 02-04 Sep. 2009, Plzen, Czech Republic, pp. 94-101 (2009). Revised: 22 January 2010.

E.S.M. Hitzer
New views of crystal symmetry
Proceedings of Symmetries of Forms and Structures, Wroclaw and Cracow, Poland, 14-19 Sep. 2009.

E.S.M. Hitzer
Real Clifford Algebra Cl(n,0), n = 2,3(mod 4) Wavelet Transform
edited by T.E. Simos et al., AIP Proceedings of ICNAAM 2009, No. 1168, pp. 781-784 (2009).

E.S.M. Hitzer, C. Perwass
Visualization of fundamental symmetries in nature
Proceedings of Fuzzy System Symposium (FSS 2009), Tsukuba, Japan, 14-16 Jul. 2009.

E.S.M. Hitzer, K. Tachibana, S. Buchholz, I. Yu
Carrier method for the general evaluation and control of pose, molecular conformation, tracking, and the like
Advances in Applied Clifford Algebras, Vol. 19(2), pp. 339-364 (2009).

E.S.M. Hitzer
Directional Uncertainty Principle for Quaternion Fourier Transforms
Advances in Applied Clifford Algebras, 20(2), pp. 271-284 (2010), online since 08 July 2009.

2008

K. Tachibana, E. Hitzer
Tutorial Note on Geometric Algebra Neural Networks
Tutorial Notes, AGACSE 3, Leipzig, Germany, 17-19 Aug. 2008, 20 pages.

B. Mawardi, E. Hitzer, A. Hayashi, R. Ashino
An Uncertainty Principle for Quaternion Fourier Transform
Computer & Mathematics with Applications, Vol. 56, pp. 2398-2410 (2008).

E.M.S. Hitzer, B. Mawardi
Clifford Fourier Transform on Multivector Fields and Uncertainty Principles for Dimensions n = 2 (mod 4) and n = 3 (mod 4)
P. Angles (ed.), Adv. App. Cliff. Alg., Vol. 18, S3,4, pp. 715-736 (2008).

D. Hildenbrand, E.S.M.Hitzer
Analysis of point clouds - using conformal geometric algebra
in Braz, J. (ed.), GRAPP 2008, 3rd Int. Conf. on Computer Graphics Theory and Applications. Proc.: Funchal, Madeira, Portugal, January 22-25, 2008, Porto: INSTICC Press, pp. 99-106 (2008).

M.T. Pham, K. Tachibana, E.S.M. Hitzer, S. Buchholz, T. Yoshikawa, T. Furuhashi
Feature Extraction with Geometric Algebra from Geometric Data
Proceedings of The Institute of Statistical Mathematics (Tokyo), December, Vol. 56, No. 2 (2008). [Japanese]

M.T. Pham, K. Tachibana, E.S.M. Hitzer, S. Buchholz, T. Yoshikawa, T. Furuhashi
Feature Extractions with Geometric Algebra for Classification of Objects
Proceedings of IEEE World Congress on Computational Intelligence - International Joint Conference on Neural Networks (IJCNN 2008), Hong Kong, 1-6 June 2008, pp. 4069 - 4073, 2008.

M. T. Pham, K. Tachibana, E.S.M. Hitzer, S. Buchholz, T. Yoshikawa, T. Furuhashi
Robust geometric feature extraction and classification
Proceedings of ISAMPE 2008, Busan, South Korea, 9-11 Oct. 2008, 8 pages.

E.S.M. Hitzer
Basic Multivector Calculus
Proceedings of 18th Intelligent Systems Symposium (FAN 2008), 23-24 Oct. 2008, Hiroshima, Japan, pp. 185 - 190 (2008).

E.S.M. Hitzer, D. Ichikawa
Representation of crystallographic subperiodic groups by geometric algebra
Electronic (USB flash memory for participants) Proceedings of AGACSE 3, Leipzig, Germany, 17-19 Aug. 2008, 11 pages (2008).

M. T. Pham, K. Tachibana, E.S.M. Hitzer, T. Yoshikawa, T. Furuhashi
Clustering of Questionnaire Based on Features Extracted by Geometric Algebra
Proceedings of Joint 4th Int. Conf. on Soft Comp. and Intel. Sys., and 9th Int. Symp. on Adv. Intel. Sys., 17-21 Sep. 2008, Nagoya, Japan, pp. 798-803 (2008).

S. Buchholz, E.S.M. Hitzer, K. Tachibana
Coordinate independent update formulas for versor Clifford neurons
Proceedings of Joint 4th Int. Conf. on Soft Comp. and Intel. Sys., and 9th Int. Symp. on Adv. Intel. Sys., 17-21 Sep. 2008, Nagoya, Japan, pp. 814 - 819 (2008).

E.S.M. Hitzer
Geometric operations implemented by conformal geometric algebra neural nodes
Proceedings of SICE Symposium on Systems and Information 2008, 26-28 Nov. 2008, Himeji, Japan, pp. 357 ? 362 (2008).

2007

S. Buchholz, K. Tachibana, E. Hitzer
Introduction to Theory, Construction and Application of Clifford Neural Networks
Tutorial Notes for 14th International Conf. on Neural Information Processing (ICONIP 2007), Japan, 13 Nov. 2007, 14 pages.

E. Hitzer
Tutorial on Reflections in Geometric Algebra
in K. Tachibana (ed.) Lecture notes of the International Workshop for "Computational Science with Geometric Algebra" (FCSGA2007), Nagoya University, Japan, 14-21 Feb. 2007, pp. 34-44 (2007).

E. Hitzer
Tutorial on Fourier Transformations and Wavelet Transformations in Clifford Geometric Algebra
in K. Tachibana (ed.) Lecture notes of the International Workshop for "Computational Science with Geometric Algebra" (FCSGA2007), Nagoya University, Japan, 14-21 Feb. 2007, pp. 65-87 (2007).

E.M.S. Hitzer
Quaternion Fourier Transform on Quaternion Fields and Generalizations
in S.L. Eriksson, R.S. Krausshar (eds.), Proc. of Function Theories in Higher Dimensions, Tampere 2006, Advances in Applied Clifford Algebras, 17(3), pp. 497-517 (2007).

E.M.S. Hitzer, C. Perwass
The hidden beauty of gold
Proceedings of the International Symposium on Advanced Mechanical Engineering, between University of Fukui (Japan), Pukyong National University (Korea) and University of Shanghai for Science and Technology (China), 22-25 Nov. 2007, pp. 157-167.

D. Ichikawa, E.M.S. Hitzer
Symmetry of orthorhombic materials and interactive 3D visualization in geometric algebra
Proceedings of the International Symposium on Advanced Mechanical Engineering, between University of Fukui (Japan), Pukyong National University (Korea) and University of Shanghai for Science and Technology (China), 22-25 Nov. 2007, pp. 302-312.

B. Mawardi, E.M.S. Hitzer
Clifford Algebra Cl(3,0)-valued Wavelet Transformation, Clifford Wavelet Uncertainty Inequality and Clifford Gabor Wavelets
International Journal of Wavelets, Multiresolution and Information Processing, 5(6), pp. 997-1019 (2007).

S. Buchholz, K. Tachibana, E.S.M.Hitzer
Optimal Learning Rates for Clifford Neurons
Proceedings of International Conference on Artificial Neural Networks 2007, Springer, New York, LNCS 4668, pp. 864-873 (2007).

2006

E. Hitzer, C. Perwass
Crystallogaphic space groups: Representation and interactive visualization by geometric algebra
submitted to: Proceedings of the 26th Int. Conference on Group Theoretical Methods in Physics, New York, USA, 2006.

B. Mawardi, E.M.S. Hitzer
Clifford Fourier Transformation and Uncertainty Principle for the Clifford Geometric Algebra Cl(3,0)
Advances in Applied Clifford Algebras, 16(1), pp. 41-61 (2006).

E.M.S. Hitzer, C. Perwass
Three Vector Generation of Crystal Space Groups in Geometric Algebra
Bulletin of the Society for Science on Form, 21(1), pp. 55,56 (2006).

C. Perwass, E.M.S. Hitzer
Space Group Visualizer for Monoclinic Space Groups
Bulletin of the Society for Science on Form, 21(1), pp. 38,39 (2006).

E.M.S. Hitzer, B. Mawardi
Uncertainty Principle for Clifford Geometric Algebras Cl_{n,0} , n = 3 (mod 4) based on Clifford Fourier Transform
in T. Qian, M.I. Vai, X.Yusheng (eds.), Wavelet Analysis and Applications, Springer (SCI) Book Series Applied and Numerical Harmonic Analysis, Springer (2006), pp. 45-54.

B. Mawardi, E.M.S. Hitzer
Clifford Algebra Cl(3,0)-valued Wavelets and Uncertainty Inequality for Clifford Gabor Wavelet Transformation
in Preprints of Meeting of the Japan Society for Industrial and Applied Mathematics, ISSN: 1345-3378, Tsukuba University, 16-18 Sep. 2006, Tsukuba, Japan, pp. 64,65. Updated version, 130K PDF.

E.M.S. Hitzer
Foundations of Multidimensional Wavelet Theory: The Quaternion Fourier Transform and its Generalizations
in Preprints of Meeting of the Japan Society for Industrial and Applied Mathematics, ISSN: 1345-3378, Tsukuba University, 16-18 Sep. 2006, Tsukuba, Japan, pp. 66,67. Updated version, 263K PDF.

E.M.S. Hitzer, C. Perwass
The Space Group Visualizer
Proceedings of the International Symposium on Advanced Mechanical Engineering, between University of Fukui (Japan), Pukyong National University (Korea) and University of Shanghai for Science and Technology (China), 26-29 Nov. 2006, pp. 172-181.

2005

E.M.S. Hitzer
Conic Sections and Meet Intersections in Geometric Algebra
in H. Li, P. Olver, G. Sommer (eds.), Computer Algebra and Geometric Algebra with Applications, 6th International Workshop, IWMM 2004, Shanghai, China, May 19-21, 2004, and International Workshop, GIAE 2004, Xian, China, May 24-28, 2004, Revised Selected Papers, Springer, Lecture Notes in Computer Science, 3519, pp. 350-362 (2005).

E.M.S. Hitzer, G. Utama
The GeometricAlgebra Java Package - Novel Structure Implementation of 5D Geometric Algebra R_(4,1) for Object Oriented Euclidean Geometry, Space-Time Physics and Object Oriented Computer Algebra
Mem. Fac. Eng. Univ. Fukui 53(1), pp. 47-59 (2005).

E.M.S. Hitzer, C. Perwass
Crystal Cell and Space Lattice Symmetries in Clifford Geometric Algebra
in TE. Simos, G. Sihoyios, C. Tsitouras (eds.), International Conference on Numerical Analysis and Applied Mathematics 2005, Wiley-VCH, Weinheim, 2005, pp. 937-941.

E.M.S. Hitzer, B. Mawardi
Uncertainty Principle for the Clifford Geometric Algebra Cl(3,0) based on Clifford Fourier Transform
in TE. Simos, G. Sihoyios, C. Tsitouras (eds.), International Conference on Numerical Analysis and Applied Mathematics 2005, Wiley-VCH, Weinheim, 2005, pp. 922-925.

E.M.S. Hitzer, C. Perwass
Full Geometric Description of All Symmetry Elements of Crystal Space Groups by the Suitable Choice of Only Three Vectors for Each Bravais Cell or Crystal Family
Proceedings of the International Symposium on Advanced Mechanical Engineering, between University of Fukui (Japan), Pukyong National University (Korea) and University of Shanghai for Science and Technology (China), 23-26 Nov. 2005, pp. 19-25.

C. Perwass, E.M.S. Hitzer
Interactive Visualization of Full Geometric Description of Cyrstal Space Groups
Proceedings of the International Symposium on Advanced Mechanical Engineering, between University of Fukui (Japan), Pukyong National University (Korea) and University of Shanghai for Science and Technology (China), 23-26 Nov. 2005, pp. 276-282.

E.M.S. Hitzer
Relativistic Physics as Application of Geometric Algebra
K. Adhav (ed.), Proceedings of the International Conference on Relativity 2005 (ICR2005), University of Amravati, India, January 2005, pp. 71-90.

2004

E.M.S. Hitzer
Euclidean Geometric Objects in the Clifford Geometric Algebra of {Origin, 3-Space, Infinity}
Bulletin of the Belgian Mathematical Society - Simon Stevin, 11(5) pp. 653-662 (2004).

E.M.S. Hitzer, C. Perwass
Crystal Cells in Geometric Algebra
Proceedings of the International Symposium on Advanced Mechanical Engineering, between University of Fukui (Japan) - Pukyong National University (Korea), 27 Nov. 2004, pp. 290-295 (2004).

L. Redaelli
Historical Introduction to Geometric Algebra
Proceedings of the International Symposium on Advanced Mechanical Engineering, between University of Fukui (Japan) - Pukyong National University (Korea), 27 Nov. 2004, pp. 216-217 (2004).

C. Yamamoto, T. Matsumoto, M. Watanabe, E. M. S. Hitzer, S. Mataka and T. Thiemann
6-[3-Hydroxy-17-oxoestra-1,3,5(10)-trien-7[beta]-yl]hexanenitrile
Acta Crystallographica Section C, C(60), o130-o132 (2004).

2003

E.M.S. Hitzer
KamiWaAi - Interactive 3D Sketching with Java based on Cl(4,1) Conformal Model of Euclidean Space
Advances in Applied Clifford Algebras, 13(1) pp. 11-45 (2003).

E.M.S. Hitzer, L. Redaelli
Geometric Algebra illustrated by Cinderella
Advances in Applied Clifford Algebras, 13(2) pp. 157-181 (2003)

E.M.S. Hitzer
Learning about Conic Sections with Geometric Algebra and Cinderella
Proceedings of the Symposium Innovative Teaching of Mathematics with Geometric Algebra 2003, Nov. 20-22, 2003, RIMS, University of Kyoto, Japan.

E.M.S. Hitzer
Conic sections through five points - classical, projective, conformal
Proceedings of the International Symposium 2003 of Advanced Mechanical Engineering, Pukyong National University, Busan, Korea, 22-25 Nov. 2003, pp. 109-114 (2003)

E.M.S. Hitzer
Geometric algebra topics

2002

E.M.S. Hitzer
Geometric Calculus - Engineering Mathematics for the 21st Century
Mem. Fac. Eng. Fukui Univ. 50(1) (2002). With GC software review!

E.M.S. Hitzer
Vector Differential Calculus
Mem. Fac. Eng. Fukui Univ. 50(1) (2002).

E.M.S. Hitzer, L. Redaelli
Play with Geometry - Animated and Interactive, Free, Instant Access, Online Geometric Algebra Java Applets
Proceedings of Fukui University International Congress, International Symposium on Advanced Mechanical Engineering, 11-13 Sep. 2002, pp. 7-12 (2002).

E.M.S. Hitzer
Multivector Differential Calculus
Advances in Applied Clifford Algebras 12(2) pp. 135-182 (2002).

2001

E.M.S. Hitzer
A real explanation for imaginary eigenvalues and complex eigenvectors
(Nat. Symp. on Math. Sc., 2001.3, Nagpur, India.) Proc. Einst. Foundation Int. 1, 1-26 (2001.4), Nagpur, India.

E.M.S. Hitzer
Imaginary eigenvalues and complex eigenvectors explained by real geometry
To appear in C. Doran, L. Dorst and J. Lasenby eds. Applied Geometrical Algebras in Computer Science and Engineering, AGACSE 2001, Birkhauser 2001.

E.M.S. Hitzer
Antisymmetric Matrices are Real Bivectors
Mem. Fac. Eng. Fukui Univ. 49(2), 283 (2001).

E.M.S. Hitzer
Geometric Calculus for Engineers
Proc. of the Pukyong National University - Fukui University International Symposium 2001 for Promotion of Research Cooperation, Pukyong National University, Busan, Korea, 59 (2001).

E.M.S. Hitzer
Geometric Calculus for Engineers - You can see it -
Poster presented at the Pukyong National University - Fukui University International Symposium 2001 for Promotion of Research Cooperation, 23 Nov. 2001, Pukyong National University, Busan, Korea.

2000

E.M.S. Hitzer
Closed Light Paths in Equiangular Spiral Disks
Advances in Applied Clifford Algebras 10(2), 225 (2000).

E.M.S. Hitzer
Classical and Semi-Classical Optics with MAPLE: Investigating a Two-dimensional Light Ray Geometry
in C.H. Patterson, J. Nadrchal (eds.), Proceedings of Teaching Computational Physics, 12th Summer School on Computational Techniques in Physics, Trest, Czech Republic, 28 Aug.-2 Sep. 2000, pp. 54-56 (2000).

1999

E.M.S. Hitzer
The Geometry of Light Paths for Equiangular Spirals
Advances in Applied Clifford Algebras 9(2), 261 (1999).

2012  2011  2010  2009  2008  2007  2006  2005  2004  2003  2002  2001  2000  1999



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