Andrei Khrennikov

Articles in Scholarly Journals [Incomplete List]

  1. Analysis of explicit and implicit assumptions in the theorems of J. Von Neumann and J. Bell
    Journal of Russian Laser Research, vol. 28, no. 3, pp. 244–254, 2007
  2. Quantum mechanics as the quadratic Taylor approximation of classical mechanics: The finite-dimensional case
    Theoretical and Mathematical Physics, vol. 152, no. 2, pp. 1111–1121, 2007
  3. Some remarks on an experiment suggesting quantum-like behavior of cognitive entities and formulation of an abstract quantum mechanical formalism to describe cognitive entity and its dynamics
    Chaos, Solitons & Fractals, vol. 31, no. 5, pp. 1076–1088, 2007
  4. Replica symmetry breaking related to a general ultrametric space III: The case of general measure
    Physica A: Statistical Mechanics and its Applications, vol. 378, no. 2, pp. 283–298, 2007
  5. Genetic code on the diadic plane
    Physica A: Statistical Mechanics and its Applications, vol. 381, pp. 265–272, 2007
  6. To quantum averages through asymptotic expansion of classical averages on infinite-dimensional space
    Journal of Mathematical Physics, vol. 48, no. 1, p. 013512, 2007
  7. Quantumlike representation of extensive form games: Probabilistic aspects
    Journal of Mathematical Physics, vol. 48, no. 7, p. 072107, 2007
  8. Is the fair sampling assumption supported by EPR experiments?
    Journal of Physics B: Atomic, Molecular and Optical Physics, vol. 40, no. 1, pp. 131–141, 2007
  9. Quantum mechanics from statistical mechanics of classical fields
    Journal of Physics: Conference Series, vol. 70, p. 012009, 2007
  10. Generalized probabilities taking values in non-Archimedean fields and in topological groups
    Russian Journal of Mathematical Physics, vol. 14, no. 2, pp. 142–159, 2007
  11. Prequantum classical statistical field theory: Time scale of fluctuations
    Doklady Mathematics, vol. 75, no. 3, pp. 456–459, 2007
  12. p-Adic semilinear evolutionary pseudodifferential equations in Lizorkin spaces
    Doklady Mathematics, vol. 76, no. 1, pp. 539–543, 2007
  13. Quantum equilibria for macroscopic systems
    Journal of Physics A: Mathematical and General, vol. 39, no. 26, pp. 8461–8475, 2006
  14. Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 9, no. 2, p. 199, 2006
  15. Nonstationary Kolmogorov probability models describing quantum measurements
    Doklady Mathematics, vol. 73, no. 2, pp. 286–291, 2006
  16. Classical representation of quantum means and quantum dynamics
    Doklady Mathematics, vol. 73, no. 3, pp. 445–448, 2006
  17. Representation of quantum field theory as classical statistical mechanics for field functionals
    Doklady Mathematics, vol. 74, no. 2, pp. 758–761, 2006
  18. Localization in space for a free particle in ultrametric quantum mechanics
    Doklady Mathematics, vol. 74, no. 3, pp. 906–909, 2006
  19. Tauberian theorems for p-adic distributions
    Integral Transforms and Special Functions, vol. 17, no. 2, pp. 141–147, 2006
  20. Associated homogeneous -adic distributions
    Journal of Mathematical Analysis and Applications, vol. 313, no. 1, pp. 64–83, 2006
  21. Quantum-like brain: “Interference of minds”
    Biosystems, vol. 84, no. 3, pp. 225–241, 2006
  22. Replica symmetry breaking related to a general ultrametric space I: Replica matrices and functionals
    Physica A: Statistical Mechanics and its Applications, vol. 359, pp. 222–240, 2006
  23. Replica symmetry breaking related to a general ultrametric space—II: RSB solutions and the n→0n→0 limit
    Physica A: Statistical Mechanics and its Applications, vol. 359, pp. 241–266, 2006
  24. Nonlinear Schrödinger equations from prequantum classical statistical field theory
    Physics Letters A, vol. 357, no. 3, pp. 171–176, 2006
  25. Energy Levels of “Hydrogen Atom” in Discrete Time Dynamics
    Open Systems and Information Dynamics, vol. 13, no. 2, pp. 119–132, 2006
  26. Prequantum Classical Statistical Field Theory: Complex Representation, Hamilton-Schrödinger Equation, and Interpretation of Stationary States
    Foundations of Physics Letters, vol. 19, no. 4, pp. 299–319, 2006
  27. Representation Theorem of Observables on a Quantum System
    International Journal of Theoretical Physics, vol. 45, no. 3, pp. 469–482, 2006
  28. Von Neumann Uniqueness Theorem doesn't Hold in Hyperbolic Quantum Mechanics
    International Journal of Theoretical Physics, vol. 45, no. 10, pp. 1869–1890, 2006
  29. Harmonic Analysis in the p-Adic Lizorkin Spaces: Fractional Operators, Pseudo-Differential Equations, p-Adic Wavelets, Tauberian Theorems
    Journal of Fourier Analysis and Applications, vol. 12, no. 4, pp. 393–425, 2006
  30. Local realistic representation for correlations in the original EPR-model for position and momentum
    Soft Computing, vol. 10, no. 6, pp. 521–529, 2006
  31. The Principle of Supplementarity: A Contextual Probabilistic Viewpoint to Complementarity, the Interference of Probabilities and Incompatibility of Variables in Quantum Mechanics
    Foundations of Physics, vol. 35, no. 10, pp. 1655–1693, 2005
  32. Kolmogorov Probability Spaces Describing Accardi Models of Quantum Correlations
    Open Systems and Information Dynamics, vol. 12, no. 4, pp. 371–384, 2005
  33. p-Adic Pseudodifferential Operators and Analytic Continuation of Replica Matrices
    Theoretical and Mathematical Physics, vol. 144, no. 2, pp. 1166–1170, 2005
  34. Interference of probabilities in the classical probabilistic framework
    Fuzzy Sets and Systems, vol. 155, no. 1, pp. 4–17, 2005
  35. Measures and conditioning
    Fuzzy Sets and Systems, vol. 155, no. 1, pp. 1–3, 2005
  36. Generalizations of Quantum Mechanics Induced by Classical Statistical Field Theory
    Foundations of Physics Letters, vol. 18, no. 7, pp. 637–650, 2005
  37. Wavelets on ultrametric spaces
    Applied and Computational Harmonic Analysis, vol. 19, no. 1, pp. 61–76, 2005
  38. p-Adic Colombeau-Egorov type theory of generalized functions
    Mathematische Nachrichten, vol. 278, no. 1-2, pp. 3–16, 2005
  39. Financial heat machine
    Physica A: Statistical Mechanics and its Applications, vol. 350, no. 2-4, pp. 487–490, 2005
  40. Interference in the classical probabilistic model and its representation in complex Hilbert space
    Physica E: Low-dimensional Systems and Nanostructures, vol. 29, no. 1-2, pp. 226–236, 2005
  41. Representation of the contextual statistical model by hyperbolic amplitudes
    Journal of Mathematical Physics, vol. 46, no. 6, p. 062111, 2005
  42. Izvestiya: Mathematics, vol. 69, no. 2, p. 221, 2005
  43. Izvestiya: Mathematics, vol. 69, no. 5, p. 989, 2005
  44. Brownian entanglement
    Physical Review A, vol. 72, no. 3, 2005
  45. Agents with left and right dominant hemispheres and quantum statistics
    Physical Review E, vol. 71, no. 1, 2005
  46. Schrödinger dynamics as the Hilbert space projection of a realistic contextual probabilistic dynamics
    Europhysics Letters (EPL), vol. 69, no. 5, pp. 678–684, 2005
  47. On the Concept of Random Sequence with Respect to p-Adic Valued Probabilities
    Theory of Probability and its Applications, vol. 49, no. 1, p. 65, 2005
  48. A pre-quantum classical statistical model with infinite-dimensional phase space
    Journal of Physics A: Mathematical and General, vol. 38, no. 41, pp. 9051–9073, 2005
  49. On unification of classical and quantum probability
    Journal of Modern Optics, vol. 51, no. 6-7, pp. 1109–1109, 2004
  50. Discrete time dynamical models and their quantum-like context-dependent properties
    Journal of Modern Optics, vol. 51, no. 6-7, pp. 1113–1114, 2004
  51. Contextual approach to quantum mechanics and the theory of the fundamental prespace
    Journal of Mathematical Physics, vol. 45, no. 3, p. 902, 2004
  52. Probabilistic pathway representation of cognitive information
    Journal of Theoretical Biology, vol. 231, no. 4, pp. 597–613, 2004
  53. Nonclassical total probability formula and quantum interference of probabilities
    Statistics & Probability Letters, vol. 70, no. 1, pp. 49–58, 2004
  54. On Relations Between Probabilities Under Quantum and Classical Measurements
    Foundations of Physics, vol. 34, no. 4, pp. 689–704, 2004
  55. On Quantum-Like Probabilistic Structure of Mental Information
    Open Systems & Information Dynamics, vol. 11, no. 3, pp. 267–275, 2004
  56. EPR-Bohm Experiment and Interference of Probabilities
    Foundations of Physics Letters, vol. 17, no. 7, pp. 691–700, 2004
  57. Interference of probabilities and number field structure of quantum models
    Annalen der Physik, vol. 12, no. 10, pp. 575–585, 2003
  58. Analysis Mathematica, vol. 29, no. 2, pp. 107–133, 2003
  59. Quantum-like formalism for cognitive measurements
    Biosystems, vol. 70, no. 3, pp. 211–233, 2003
  60. Noncommutative probability in classical disordered systems
    Physica A: Statistical Mechanics and its Applications, vol. 326, no. 3-4, pp. 456–463, 2003
  61. p-Adic interpolation and approximation of a continuous function by linear combinations of shifts of p-adic valuations
    Journal of Approximation Theory, vol. 120, no. 1, pp. 124–135, 2003
  62. Representation of the Kolmogorov model having all distinguishing features of quantum probabilistic model
    Physics Letters A, vol. 316, no. 5, pp. 279–296, 2003
  63. Contextual viewpoint to quantum stochastics
    Journal of Mathematical Physics, vol. 44, no. 6, p. 2471, 2003
  64. Interpretations of Probability and Their p-Adic Extensions
    Theory of Probability and its Applications, vol. 46, no. 2, p. 256, 2002
  65. Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 5, no. 4, p. 483, 2002
  66. On infinite products of non-Archimedean measure spaces
    Indagationes Mathematicae, vol. 13, no. 2, pp. 177–183, 2002
  67. Ensemble fluctuations and the origin of quantum probabilistic rule
    Journal of Mathematical Physics, vol. 43, no. 2, p. 789, 2002
  68. Foundations of Physics, vol. 32, no. 7, pp. 1159–1174, 2002
  69. Contextualist viewpoint to Greenberger–Horne–Zeilinger paradox
    Physics Letters A, vol. 278, no. 6, pp. 307–314, 2001
  70. Limit behaviour of sums of independent random variables with respect to the uniform p-adic distribution
    Statistics & Probability Letters, vol. 51, no. 3, pp. 269–276, 2001
  71. Small denominators in complex -adic dynamics
    Indagationes Mathematicae, vol. 12, no. 2, pp. 177–189, 2001
  72. On the Number of Cycles of p-adic Dynamical Systems
    Journal of Number Theory, vol. 90, no. 2, pp. 255–264, 2001
  73. Infinite Dimensional Analysis, Quantum Probability and Related Topics, vol. 4, no. 4, p. 569, 2001
  74. Journal of Physics A: Mathematical and General, vol. 34, no. 47, pp. 9965–9981, 2001
  75. Non-Kolmogorov probability models and modified Bell’s inequality
    Journal of Mathematical Physics, vol. 41, no. 4, p. 1768, 2000
  76. Classical and quantum dynamics on p-adic trees of ideas
    Biosystems, vol. 56, no. 2-3, pp. 95–120, 2000
  77. Acta Applicandae Mathematicae, vol. 64, no. 1, pp. 33–73, 2000
  78. A perturbation of CHSH inequality induced by fluctuations of ensemble distributions
    Journal of Mathematical Physics, vol. 41, no. 9, p. 5934, 2000
  79. Potential Analysis, vol. 11, no. 2, pp. 157–181, 1999
  80. Acta Applicandae Mathematicae, vol. 57, no. 3, pp. 205–237, 1999
  81. Memory retrieval as a p-adic dynamical system
    Biosystems, vol. 49, no. 2, pp. 105–115, 1999
  82. Attractors of random dynamical systems over p-adic numbers and a model of 'noisy' cognitive processes
    Physica D: Nonlinear Phenomena, vol. 130, no. 1-2, pp. 1–12, 1999
  83. Ap-Adic Model for the Process of Thinking Disturbed by Physiological and Information Noise
    Journal of Theoretical Biology, vol. 197, no. 4, pp. 451–467, 1999
  84. P-Adic Dynamical Systems and Neural Networks
    Mathematical Models and Methods in Applied Sciences, vol. 09, no. 09, pp. 1417–1437, 1999
  85. p-adic Behavior of Bernoulli Probabilities
    Theory of Probability and its Applications, vol. 42, no. 4, p. 689, 1998
  86. p-adic stochastic hidden variable model
    Journal of Mathematical Physics, vol. 39, no. 3, p. 1388, 1998
  87. Human Subconscious as ap-adic Dynamical System
    Journal of Theoretical Biology, vol. 193, no. 2, pp. 179–196, 1998
  88. Human memory as ap-adic dynamic system
    Theoretical and Mathematical Physics, vol. 117, no. 3, pp. 1414–1422, 1998
  89. p-adic dynamic systems
    Theoretical and Mathematical Physics, vol. 114, no. 3, pp. 276–287, 1998
  90. p-Adic behaviour of Bernoulli probabilities
    Statistics & Probability Letters, vol. 37, no. 4, pp. 375–379, 1998
  91. Acta Applicandae Mathematicae, vol. 50, no. 3, pp. 225–251, 1998
  92. -adic analogues of the law of large numbers and the central limit theorem
    Indagationes Mathematicae, vol. 8, no. 1, pp. 61–77, 1997
  93. Representation of a quantum field Hamiltonian inp-adic Hilbert space
    Theoretical and Mathematical Physics, vol. 112, no. 3, pp. 1081–1096, 1997
  94. Journal of Physics A: Mathematical and General, vol. 30, no. 16, pp. 5767–5784, 1997
  95. Journal of Physics A: Mathematical and General, vol. 30, no. 3, pp. 881–889, 1997
  96. On the physical interpretation of negative probabilities in Prugovecki's empirical theory of measurement
    Canadian Journal of Physics, vol. 75, no. 5, pp. 291–298, 1997
  97. International Journal of Modern Physics B [Condensed Matter Physics; Statistical Physics; Applied Physics], vol. 10, no. 13 & 14, p. 1665, 1996
  98. Journal of Physics A: Mathematical and General, vol. 29, no. 17, pp. 5515–5527, 1996
  99. The ultrametric Hilbert-space description of quantum measurements with a finite exactness
    Foundations of Physics, vol. 26, no. 8, pp. 1033–1054, 1996
  100. p-adic valued probability measures
    Indagationes Mathematicae, vol. 7, no. 3, pp. 311–330, 1996
  101. p-Adic stochastics and Dirac quantization with negative probabilities
    International Journal of Theoretical Physics, vol. 34, no. 12, pp. 2423–2433, 1995
  102. Canp-adic numbers be useful to regularize divergent expectation values of quantum observables?
    International Journal of Theoretical Physics, vol. 33, no. 6, pp. 1217–1228, 1994
  103. p-adic numbers and renormalization of eigenfunctions in quantum mechanics
    Physics Letters B, vol. 328, no. 1-2, pp. 109–112, 1994
  104. Non-Archimedean superfields
    Russian Physics Journal, vol. 36, no. 11, pp. 1043–1045, 1993
  105. Nonlinear evolution equations with (1,1)-supersymmetric time
    Theoretical and Mathematical Physics, vol. 97, no. 2, pp. 1267–1272, 1993
  106. Pseudo-topological commutative superalgebras with nilpotent ghosts
    Mathematical Notes of the Academy of Sciences of the USSR, vol. 48, no. 2, pp. 790–795, 1990
  107. Gaussian quantization of the Klein-Gordon equation in variational derivatives and secondary quantization of a Boson string
    Soviet Physics Journal, vol. 33, no. 1, pp. 26–29, 1990
  108. Schr�dinger representation in the bosonic string theory: Quantization without anomalous terms
    Soviet Physics Journal, vol. 33, no. 10, pp. 827–830, 1990
  109. Feynman integral in the phase space and symbols of infinite-dimensional pseudodifferential operators
    Mathematical Notes of the Academy of Sciences of the USSR, vol. 37, no. 5, pp. 404–409, 1985
  110. Dirichlet's problem in banach space
    Mathematical Notes of the Academy of Sciences of the USSR, vol. 34, no. 4, pp. 804–808, 1983