Jiri Patera

 

Affiliation

Membre régulier du CRM

Bureau / Office

4441, Pavillon André Aisenstadt

Téléphone

CRM: 514-343-6419

Courrier électronique / E-Mail

patera@CRM.UMontreal.CA

 

 

Refereed articles 1998-2009 (accepted or published)

  • J. Hrivnak, J. Patera, On discretization of tori of compact simple Lie groups, J. Phys.A: Math. Theor. 42 (2009) 385208 (26pp); arXiv:0905.2395
  • M.Grundland, J. Patera, Z. Masakova, N. Dodgson, Image sampling on quasicrystals,  SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 5 (2009), paper 075, 23 pages
  • L.Hakova, M.Larouche, J.Patera, The rings of n-dimensional polytopes, J.Phys.A: Math. Theor., 41 (2008) 495202; arXiv:0901.4686
  • M. Nesterenko, J, Patera, Three dimensional C-, S- and E-transforms, J.Phys.A: Math. Theor., 41 (2008) 475205; arXiv:0805.3731v1
  • R.V. Moody, M. Nesterenko, J. Patera, Acta Crystallographica A64 (2008) 654-669; arXiv:0808.1814
  • A.U. Klimyk, J. Patera J, Alternating group and multivariate exponential functions, in Groups and Symmetries: from the Neolithic Scots to John McKay, AMS-CRM Proceedings and Lectures Notes Series, eds. J. Harnad and P. Winternitz (to appear 2008)
  • A. Klimyk, J. Patera, Alternating multivariate trigonometric functions and corresponding Fourier transfdorms, J.Phys.A: Math. Theor. 41 (2008) 145205 (16pp)
  • D.G. Asatryan, J, Patera, Edge detection algorithm based on DCT continuous extension technique, Physics of Atomic Nuclei 71 (2008) 795-799
  • A. Klimyk, J. Patera, E-orbit functions, SIGMA (Symmetry,Integrability and Geometry: Methods and Applications) 4 (2008), 002, 57 pages; arXiv:0801.0822
  • V.Boyko, J.Patera and R.Popovych, Invariants of solvable Lie algebras with triangular nilradicals and diagonal nilindependent elements, Linear Algebra Appl., 428 (2008) 834-854, arXiv:0706.2465
  • A. Klimyk, J. Patera, (Anti)symmetric multidimensional trigonometric functions and the corresponding Fourier transforms, J. Math. Phys. 48 093504 (2007) 24 pages; arXiv:0705.4186v1
  • A. Klimyk, J. Patera, (Anti)symmetric multidimensional exponential functions and the corresponding Fourier transforms, J. Phys. A: Math. Theor., 40 (2007), 10473 - 10489; arXiv:0705.3572v1
  • V. Boyko, J. Patera, R. Popovych, Invariants of solvable Lie algebras with one nilindependent diagonal element, J. Phys. A: Math. Theor., 40 (2007), 9783 - 9792; arXiv:0705.2394v1
  • V. Boyko, J. Patera, R. Popovych, Invariants of triangular Lie algebras, J. Phys. A: Math. Theor. 40 (2007), 7557-7572, arXiv:0704.0937
  • I. Kashuba, J. Patera, Discrete and continuous exponential transforms of simple Lie groups of rank two, J. Phys. A: Math. Theor. 40 (2007) 4751-4774; math-ph/0702016
  • J.Patera, E.Pelantova, M.Svobodova, Fine gradings of the real forms of sl(4,C), sp(4,C), and o(4,C), J. Math. Phys 48 093503 (2007), 28 pages; math-ph/0608032.
  • A. Klimyk, J. Patera, Antisymmetric orbit functions, SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 3 (2007), paper 023, 83 pages; math-ph/0702040
  • A. Atoyan, J. Patera, The discrete SU(3) transform and its continuous extension for triangular lattices, J. Geom. Physics, 57 (2007) 745-764.
  • V. Boyko, J. Patera, R. Popovych, Invariants of Lie algebras with fixed structure of nilradicals, J. Phys. A: Math. Theor. 40 (2007) 113-130;
  • R.V.Moody, J.Patera, Orthogonality within the families of C-, S-, and E- functions of any compact semisimple Lie group, SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 2 (2006) 076, 14 pages, math-ph/0611020
  • J. Hrivnak, P. Novotny, J. Patera and J. Tolar, Graded contractions of the Pauli graded sl(3,C), Linear Algebra Appl. 418 (2006) 498-550; math-ph/0509033
  • J. Patera, A. Zaratsyan, Discrete and continuous sine transform generalized to the semisimple Lie groups of rank two, J. Math. Phys. 47 (2006) 043512 (22 pages)
  • V. Boyko, J. Patera, R. Popovych, Computation of invariants of Lie algebras by means of moving frames, J. Phys. A: Math. Gen. 39 (2006) 5749-5762, math-ph/0602046
  • Klimyk, J. Patera, Orbit functions, SIGMA (Symmetry, Integrability and Geometry: Methods and Applications), 2 (2006), 006, (60 pages); math-ph/0601037.
  • J. Patera, Compact simple Lie groups and theirs C-, S-, and E-transforms, SIGMA (Symmetry, Integrability and Geometry: Methods and Applications) 1 (2005) 025, (6 pages); math-ph/0512029
  • J. Patera, A. Zaratsyan, Discrete and Continuous Cosine Transform Generalized to Lie Groups SU(3) and G(2), J. Math. Phys., 46, (2005) 113506-113523.
  • J. Patera, A. Zaratsyan, Discrete and Continuous Cosine Transform Generalized to Lie Groups SU(2)xSU(2) and O(5), J. Math. Phys., 46, (2005) 053514-053539.
  • Z. Masáková, J. Patera, J. Zich, Classification of Voronoi and Delone tiles in quasicrystals: III. Decagonal window of any size, J. Phys. A: Math. Gen., 38, (2005) 1947-1960.
  • Atoyan, J. Patera, V. Sahakian, A. Akhperjanian, Fourier transform method for imaging atmospheric Cherenkov telescopes, Astroparticle Phys., 23, (2005) 79-95
  • Atoyan, J. Patera, Properties of continuous Fourier extension of the discrete cosine transform and its multidimensional generalization, J. Math. Phys. 45 (2004) 2468-2491
  • J. Patera, E. Pelantová, M. Svobodová, Fine gradings of o(4,C), J. Math. Phys. 45 (2004) 2188-2198
  • Kashuba, J. Patera, Graded contractions of Jordan algebras and their representations, J. Phys. A: Math. Gen. 36 (2003) 12453-12473
  • L. S. Guimond, Jan Patera, Jiri Patera, Statistics and implementation of aperiodic pseudorandom number generators, Applied Numerical Mathematics, 46 (2003) 295-318; special issue Applied Numerical Computing: Grid Generation and Solution Methods for Advanced Simulations.
  • Z. Masáková, J. Patera, J. Zich, Classification of distinct Voronoi and Delone tiles in two-dimensional quasicrystals: II. Circular acceptance window of arbitrary size, J. Phys. A: Math. Gen. 36 (2003) 1895-1912
  • Z. Masáková, J. Patera, J. Zich, Classification of distinct Voronoi and Delone tiles in two-dimensional quasicrystals: I. General Method, J. Phys. A: Math. Gen. 36 (2003) 1869-1894
  • J. Patera, E. Pelantová, M. Svobodová, The eight fine gradings of sl(4,C) and o(6,C), J. Math. Phys. 43 (2002) 6353-6378
  • M. Bodner, C. Derr, X. Leng, J. Patera, M. Petterson, F. Ticheli, S. Vuong, G. Shaw, The Music-Math Connection, Early Childhood Connections, 8, No.3 (2002) 9-16
  • M. Havlicek, J. Patera, E. Pelantová, J. Tolar, Automorphisms of a finest grading of sl(n,C), J. Math. Phys. 43 (2002) 1083-1094
  • L.S. Guimond, J. Patera, Proving the deterministic period breaking of linear congruential generators using two tile quasicrystals, Mathematics of Computation 71 (2002) 319-332
  • J. Patera, R. Twarock, Affine extension of noncrystallographic Coxeter groups and quasicrystals, J. Phys. A: Math. Gen. 35 (2002) 1551-1574
  • J. Patera, E. Pelantová, M. Svobodová, Fine gradings of o(5,C), sp(4,C) and of their real forms, J. Math. Phys. 42 (2001) 3839-3853
  • Z. Masáková, J. Patera, and E. Pelantová, Exceptional algebraic properties of the three quadratic irrationalities observed in quasicrystals, Can. J. Phys. (Gerhard Herzberg memorial issue) 79 (2001) 687-696
  • L.S. Guimond, Jan Patera, Jiri Patera, Combining random number generators using cut and project sequences, Czech. J. Phys. 51 (2001) 305-311
  • M. Havlicek, J. Patera, E. Pelantová, and J. Tolar, On fine gradings and their symmetries, Czech. J. Phys. 51 (2001) 383-391
  • Z. Masáková, J. Patera, and E. Pelantová, Substitution rules for aperiodic sequence of the cut and project type, J. Phys. A: Math. Gen. 33 (2000) 8867-8887
  • M. Havlicek, J. Patera, and E. Pelantová, On Lie gradings III. Gradings of the real forms of classical Lie algebras (dedicated to the memory of H. Zassenhaus), Linear Alg. and its Applic. 314 (2000) 1-47
  • H. de Guise, J. Patera, R.T. Sharp, SL(3,C) generator matrix elements in a Pauli subgroup basis, J. Math. Phys. 41 (2000) 4860-4880
  • Z. Masáková, J. Patera, and E. Pelantová, Acceptance windows compatible with a quasicrystal fragment, From Quasicrystals to More Complex Systems, eds. F. Axel, F. Denoyer, J.P. Gazeau, Springer, Centre de Physique des Houches, 13 (2000) 167-193,
  • J. Patera, R. Twarock, Quasicrystal Lie algebras and their generalizations, (dedicated to the memory of Richard Slansky), Phys. Rep. 315 (1999) 241-256
  • J. Patera, G. Pogosyan, P. Winternitz, Graded Contractions of the Lie Algebra e(2,1), J. Phys. A: Math. Gen.,32 (1999) 805-826
  • J. Patera, E. Pelantová, R. Twarock, Quasicrystal Lie algebras, Phys. Lett. A, 246 (1998) 209-213
  • J. P. Gazeau, J. Patera, E. Pelantová, Tau wavelets in the plane, J. Math. Phys. 39 (1998) 4201-4212
  • R. V. Moody, J. Patera, Densities, minimal distances, and coverings of quasicrystals, Comm. Math. Phys. 195 (1998) 613-626
  • M. Havlicek, J. Patera, and E. Pelantová, On Lie gradings II, (dedicated to the memory of Hans Zassenhaus), Linear Algebra and its Applic. 277 (1998) 97-125
  • Z. Masáková, J. Patera, E. Pelantová, Selfsimilar Delone sets and cut and project quasicrystals, J. Phys. A: Math. Gen. 31 (1998) 4927-4946
  • Z. Masáková, J. Patera, E. Pelantová, Minimal distances in quasicrystals, J. Phys. A: Math. Gen. 31 (1998) 1539-1552
  • Z. Masáková, J. Patera, E. Pelantová, Inflation centers in cut and project quasicrystals, J. Phys. A: Math. Gen. 31 (1998) 1443-1453
  • L. Chen, R. V. Moody, J. Patera, Non-crystallographic root systems, in Quasicrystals and Discrete Geometry, Fields Institute Monograph Series, 10 (1998) 135-178, ed. J. Patera, Amer. Math. Soc.

 

 

Articles in refereed proceedings 1998-2009 (accepted or published)

  •  V.Boyko, J.Patera, R.Popovych, Invariants of Lie algebras via moving frame approach, Proc. Workshop  on Group Analysis of Differential Equations and Integrable Systems, Cyprus (2009) 36-44
  • M.Nesterenko, J.Patera, On orbit functions, their properties and applications, Proc. Worshop on Group Analysis of Differential Equations and Integrable Systems, Cyprus (2009) 155-163
  • J. Hrivnak, J. Patera, Discretization of compact semisimple Lie groups, in Geometric Methods in Physics, AIP Conf. Proc 1079, 196-202, Bialowieza (2008)
  • J. Patera, M. Nesterenko, Quasicrystals in cryptography, in Aspects of Networks and Information Security, eds. E. Kranakis, E. Haroutunian, E.Shahbazian, IOS Press, Amsterdam, 2008; pp. 274-282
  • J. Patera, A. Zaratsyan, H. Zhu, Interpolation using cosine transforms generalized to Lie groups, Proc. SPIE 6064, Image Processing: Algorithms and Systems, Neural Networks, and Machine Learning, Edward R. Dougherty, Jaako T. Astola, Karen O. Egiazarian, Nasser M. Nasrabadi, Syed A. Rizvi; Eds. (Feb. 16, 2006)
  • M. Germain, J. Patera, Y. Allard, Cosine transform generalized to lie groups SU(2)xSU(2), O(5), and SU(2)xSU(2)xSU(2): application to digital image processing, Proc. SPIE 6065, pp. 387-395, Computational Imaging IV; Charles A. Bouman, Eric L. Miller, Ilya Pollak; Eds.
  • M. Germain, J. Patera, Multiresolution analysis of digital images using the continuous extension of discrete group transforms, Proc. SPIE 6065, pp. 6-15, Computational Imaging IV; Charles A. Bouman, Eric L. Miller, Ilya Pollak; Eds.
  • M. Germain, J. Patera, Cosine transform generalized to Lie groups SU(2)xSU(2) and O(5): application to textural image processing, Canadian Conference on Electrical and Computer Engineering, IEEE Canada, May 7 to 10, 2006
  • Akhperjanian, A. Atoyan, J. Patera, V. Sahakian, Application of Multi-Dimensional Discrete Transforms on Lie Groups for Image Processing, in Data Fusion for Situation Monitoring, Incident Detection, Alert and Response Management, E. Shahbazian et al. (Eds.), IOS Press (2005), pp. 404-416
  • Atoyan, J. Patera, Application of Continuous Extension of DCT to FLIR Images, in Data Fusion for Situation Monitoring, Incident Detection, Alert and Response Management, E. Shahbazian et al. (Eds.), IOS Press (2005), pp. 417-425
  • Atoyan, J. Patera, Continuous Extension of Discrete Cosine Transform, and Its Applications to Data Processing, in CRM Proceedings and Lecture Notes, 39 (2005), 15 pages
  • S. Grimm, F. W. Lemire, J. Patera, Discrete group transforms on SU(2)xSU(2) and SU(3), Resenhas do Instituto de Matematica e Estatistica da Universidade de Sao Paolo, 6, No 2/3 (2004) 199-214.
  • M. Havlicek, J. Patera, E. Pelantová, J. Tolar, On Pauli graded contractions of sl(3,C), J. Nonlinear Math. Phys., Suppl., 11 (2004) 37-42
  • J. Patera, Orbit functions of compact semisimple Lie groups as special functions, in Symmetry in Nonlinear Mathematical Physics, Proceedings of the Nat. Acad. Sci., 30 (2004) 1152-1160, Kiev, Ukraine
  • J. Patera, Algebraic solutions of the Neumann boundary value problems on fundamental region of a compact semisimple Lie group, Proceedings of the Workshop on group theory and numerical methods, Montreal 26-31 May, 2003
  • Atoyan, J. Patera, Continuous extension of the discrete cosine transform, and its applications to data processing, Proceedings of the Workshop on group theory and numerical methods, Montreal 26-31 May, 2003
  • Atoyan, J. Patera, Application of the continuous extension of DCT to images taken by FLIR detectors, Proc. NATO ASI 2003: Data Fusion for Situation Monitoring, Incident Detection, Alert and Response Management, August, 2003, Tsakhkadzor, Armenia
  • Akhperjanian, A. Atoyan, J. Patera, V. Sahakian, Application of multidimensional discrete transforms on Lie groups for image processing, Proc. NATO ASI 2003, Data Fusion for Situation Monitoring, Incident Detection, Alert and Response Management, August, 2003, Tsakhkadzor, Armenia
  • G. Shaw, M. Bodner, J. Patera, Innate brain language and grammar: Implications for human language and music, in Stochastic point processes, eds. S.K. Srinivasan and A. Vihayakumar, Narosa Publishing, New Delhi 2003. pp. 287-305
  • J. Patera, R.T. Sharp and generating functions in group representation theory, in Symmetry in Physics, (in memory of R.T. Sharp), eds. P. Winternitz, J. Harnad, C.S. Lam, J. Patera, CRM Proceedings and Lecture Notes, 34 (2003) 159-164
  • M. Havlicek, J. Patera, E. Pelantová, and J.Tolar, The fine gradings of sl(3,C) and their symmetries, Proc. of XXIII Int. Coll. Group Theor. Methods in Physics, Eds. A.N.Sissakian, G.S.Pogosyan and L.G.Mardoyan, Vol 1, Dubna, JINR, (2002), 57-61.
  • Z. Masáková, J. Patera, E. Pelantová, Lattice-like properties of quasicrystal models with quadratic irrationalities, in Quantum Theory and Symmetries, eds. H.-D. Doebner, V. K. Dobrev, J. D. Hennig, W. Lucke, World Scientific, 2000, p. 499-509
  • J. Patera and J. Tolar, On gradings of Lie algebras and representations, in Lie Theory and its Applications II, eds. H.-D. Doebner, V.K. Dobrev, and J. Hilgert, World Scientific, Singapore, 1998, pp. 109-118
  • M. Havlicek, J. Patera, E. Pelantová, On fine gradings of real forms of sl(n,C), in Lie Theory and its Applications II, eds. H.-D. Doebner, V.K. Dobrev, and J. Hilgert, World Scientific, Singapore, 1998, pp. 119-129
  • H. De Guise, J. Patera, Graded contractions of the C2 algebras with respect to their reductive subalgebras of maximal rank, Proc. of 5th Wigner Symp., Vienna, eds. P. Kasperkowitz and D. Grau, World Scientific, 1998, pp. 91-93
  • Z. Masáková, J. Patera, E. Pelantová, Scaling invariances of quasicrystalline sets, Proc. of 5th Wigner Symp., Vienna, eds. P. Kasperkowitz and D. Grau, World Scientific, 1998, pp. 94-96
  • Z. Masáková, J. Patera, E. Pelantová, Internal and external quasicrystal inflation centers and their scaling factors, Physics of Atomic Nuclei, 61 (1998) 1978-1982

 

Patents

  • Atoyan, J. Patera, Continuous extension of discrete transform for data processing, US patent pending
  • Z. Masáková, J. Patera, E. Pelantová, Aperiodic Encryption Method, US patent, September, 2004, US 6,792,108 B1

 

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