Publications

• Public

  The Robin Inequality for 7-Free Integers Jan-2012

  DOI: 10.1515/integ.2011.103
  Solé, P & Planat, M, 2012, 'The Robin Inequality for 7-Free Integers', Integers, vol. 3, no. 9, p. 64.
• Public

  On the fine structure of the projective line over GF(2)⊗GF(2)⊗GF(2) July-2008

  DOI: 10.1016/j.chaos.2006.09.056
  Saniga, M & Planat, M, 2008, 'On the fine structure of the projective line over GF(2)⊗GF(2)⊗GF(2)', Chaos, Solitons & Fractals, vol. 37, no. 2, pp. 337-345.
• Public

  Projective planes over “Galois” double numbers and a geometrical principle of complementarity Apr-2008

  DOI: 10.1016/j.chaos.2006.06.068
  Saniga, M & Planat, M, 2008, 'Projective planes over “Galois” double numbers and a geometrical principle of complementarity', Chaos, Solitons & Fractals, vol. 2, no. 2, pp. 85-381.
• Public

  A classification of the projective lines over small rings Aug-2007

  DOI: 10.1016/j.chaos.2007.01.008
  Saniga, M, Planat, M, Kibler, M & Pracna, P, 2007, 'A classification of the projective lines over small rings', Chaos, Solitons & Fractals, vol. 13, no. 4, pp. 1537-1102.
• Public

  Quantum Entanglement and Projective Ring Geometry Aug-2006

  DOI: 10.3842/SIGMA.2006.066
  Planat, M, 2006, 'Quantum Entanglement and Projective Ring Geometry', Symmetry, Integrability and Geometry: Methods and Applications.
• Public

  Hjelmslev geometry of mutually unbiased bases Dec-2005

  DOI: 10.1088/0305-4470/39/2/013
  Saniga, M & Planat, M, 2005, 'Hjelmslev geometry of mutually unbiased bases', Journal of Physics A: Mathematical and General, vol. 48, no. 2, pp. 69-440.
• Public

  Viewing sets of mutually unbiased bases as arcs in finite projective planes Dec-2005

  DOI: 10.1016/j.chaos.2005.03.008
  Saniga, M & Planat, M, 2005, 'Viewing sets of mutually unbiased bases as arcs in finite projective planes', Chaos, Solitons & Fractals, vol. 6, no. 2, pp. 95-1270.
• Public

  Galois algebras of squeezed quantum phase states Nov-2005

  DOI: 10.1088/1464-4266/7/12/008
  Planat, M & Saniga, M, 2005, 'Galois algebras of squeezed quantum phase states', Journal of Optics B: Quantum and Semiclassical Optics, vol. 9, no. 12, pp. 582-S489.
• Public

  The hyperbolic, the arithmetic and the quantum phase May-2004

  DOI: 10.1088/1464-4266/6/6/018
  Planat, M & Rosu, H, 2004, 'The hyperbolic, the arithmetic and the quantum phase', Journal of Optics B: Quantum and Semiclassical Optics, vol. 6, no. 6, pp. S583-S590.
• Public

  Cyclotomy and Ramanujan sums in quantum phase locking Aug-2003

  DOI: 10.1016/S0375-9601(03)00942-3
  Planat, M & Rosu, H, 2003, 'Cyclotomy and Ramanujan sums in quantum phase locking', Physics Letters A, vol. 80, no. 1-2, pp. 1571-5.
• Public

  Thermal 1/f noise from the theory of partitions: application to a quartz resonator Feb-2003

  DOI: 10.1016/S0378-4371(02)01659-X
  Planat, M, 2003, 'Thermal 1/f noise from the theory of partitions: application to a quartz resonator', Physica A: Statistical Mechanics and its Applications, vol. 22, no. 3-4, pp. 875-386.
• Public

  Ramanujan sums for signal processing of low-frequency noise Nov-2002

  DOI: 10.1103/PhysRevE.66.056128
  Planat, M, Rosu, H & Perrine, S, 2002, 'Ramanujan sums for signal processing of low-frequency noise', Physical Review E, vol. 13, no. 5, p. 1407.
• Public

  1/f Frequency Noise in a Communication Receiver and the Riemann Hypothesis Dec-2000

  DOI: 10.1007/3-540-45463-2_13
  Planat, M & Planat, M, 2000, , Springer Berlin Heidelberg, Berlin, Heidelberg.
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  Algebraic Dynamics and Transcendental Numbers Dec-2000

  DOI: 10.1007/3-540-45463-2_19
  Waldschmidt, M & Planat, M, 2000, , Springer Berlin Heidelberg, Berlin, Heidelberg.
• Public

  Detection of Chaos in the Noise of Electronic Oscillators by Time Series Analysis Methods Dec-2000

  DOI: 10.1007/3-540-45463-2_14
  Eckert, C, Planat, M & Planat, M, 2000, , Springer Berlin Heidelberg, Berlin, Heidelberg.
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  Introduction Dec-2000

  DOI: 10.1007/3-540-45463-2_1
  Planat, M & Planat, M, 2000, , Springer Berlin Heidelberg, Berlin, Heidelberg.
• Public

  Noise, Oscillators and Algebraic Randomness Dec-2000

  DOI: 10.1007/3-540-45463-2
  Planat, M, 2000, , Springer Berlin Heidelberg, Berlin, Heidelberg.
• Public

  Frequency stability enhancement from carrier-envelope resonance in a surface acoustic wave delay line oscillator 1996

  DOI: 10.1063/1.363117
  Planat, M, Lardet-Vieudrin, F, Martin, G, Dos Santos, S & Marianneau, G, 1996, 'Frequency stability enhancement from carrier-envelope resonance in a surface acoustic wave delay line oscillator', Journal of Applied Physics, vol. 1, no. 4, p. 727.
• Public

  Multiple scale analysis of the nonlinear surface acoustic wave propagation in anisotropic crystals 1985

  DOI: 10.1063/1.335315
  Planat, M, 1985, 'Multiple scale analysis of the nonlinear surface acoustic wave propagation in anisotropic crystals', Journal of Applied Physics, vol. 39, no. 11, p. 5400.
• Public

  A physical basis to Riemann hypothesis 1/f frequency noise

  DOI: 10.1063/1.1291289
  Planat, M, 2000, 'A physical basis to Riemann hypothesis 1/f frequency noise', AIP Conference Proceedings, AIP, Liege (Belgium), pp. 538-551.

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Patents