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A class of negatively fractal dimensional Gaussian random functions. (English) Zbl 1209.28015

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References:
[1] S. R. Massel, Ocean Surface Waves: Their Physics and Prediction, World Scientific, River Edge, NJ, USA, 1997.
[2] ITTC, “The Specialist Committee on Waves-final report and recommendations to the 23rd ITTC,” in Proceedings of the 23rd ITTC, vol. 2, pp. 497-543, 2002.
[3] M. Li, “A method for requiring block size for spectrum measurement of ocean surface waves,” IEEE Transactions on Instrumentation and Measurement, vol. 55, no. 6, pp. 2207-2215, 2006. · doi:10.1109/TIM.2006.884134
[4] J. Alvarez-Ramirez, J. Alvarez, L. Dagdug, E. Rodriguez, and J. Carlos Echeverria, “Long-term memory dynamics of continental and oceanic monthly temperatures in the recent 125 years,” Physica A, vol. 387, no. 14, pp. 3629-3640, 2008. · doi:10.1016/j.physa.2008.02.051
[5] J. Beran, Statistics for Long-Memory Processes, vol. 61 of Monographs on Statistics and Applied Probability, Chapman & Hall, New York, NY, USA, 1994. · Zbl 0869.60045
[6] B. B. Mandelbrot, The Fractal Geometry of Nature, W. H. Freeman, San Francisco, Calif, USA, 1982. · Zbl 0504.28001
[7] G. Korvin, “Fractal Models in the Earth Sciences,” Elsevier, New York, NY, USA, 1992.
[8] B. J. West and W. Deering, “Fractal physiology for physicists: Lévy statistics,” Physics Report, vol. 246, no. 1-2, pp. 1-100, 1994.
[9] T. Schreiber, “Interdisciplinary application of nonlinear time series methods,” Physics Reports, vol. 308, no. 1, pp. 1-64, 1999. · doi:10.1016/S0370-1573(98)00035-0
[10] P. Abry, P. Borgnat, F. Ricciato, A. Scherrer, and D. Veitch, “Revisiting an old friend: on the observability of the relation between long range dependence and heavy tail,” Telecommunication Systems, vol. 43, no. 3-4, pp. 147-165, 2010. · doi:10.1007/s11235-009-9205-6
[11] G. Werner, “Fractals in the nervous system: conceptual implications for theoretical neuroscience,” Frontiers in Fractal Physiology, vol. 1, p. 12, 2010. · doi:10.3389/fphys.2010.00015
[12] J. Levy-Vehel, E. Lutton, and C. Tricot, Eds., Fractals in Engineering, Springer, New York, NY, USA, 1997.
[13] C. Cattani, “Harmonic wavelet approximation of random, fractal and high frequency signals,” Telecommunication Systems, vol. 43, no. 3-4, pp. 207-217, 2010. · doi:10.1007/s11235-009-9208-3
[14] C. Cattani, “Fractals and hidden symmetries in DNA,” Mathematical Problems in Engineering, vol. 2010, Article ID 507056, 31 pages, 2010. · Zbl 1189.92015 · doi:10.1155/2010/507056 · eudml:232469
[15] B. B. Mandelbrot, Gaussian Self-Affinity and Fractals, Springer, New York, NY, USA, 2002. · Zbl 1007.01020
[16] M. Li, “Fractal time series-a tutorial review,” Mathematical Problems in Engineering, vol. 2010, Article ID 2570932, 26 pages, 2010. · Zbl 1191.37002 · doi:10.1155/2010/157264
[17] B. B. Mandelbrot and J. W. van Ness, “Fractional Brownian motions, fractional noises and applications,” SIAM Review, vol. 10, pp. 422-437, 1968. · Zbl 0179.47801 · doi:10.1137/1010093
[18] V. M. Sithi and S. C. Lim, “On the spectra of Riemann-Liouville fractional Brownian motion,” Journal of Physics A, vol. 28, no. 11, pp. 2995-3003, 1995. · Zbl 0828.60099 · doi:10.1088/0305-4470/28/11/005
[19] S. V. Muniandy and S. C. Lim, “Modeling of locally self-similar processes using multifractional Brownian motion of Riemann-Liouville type,” Physical Review E, vol. 63, no. 4, Article ID 046104, 7 pages, 2001. · Zbl 1029.60026
[20] A. Razdan, “Multifractal nature of extensive air showers,” Chaos, Solitons & Fractals, vol. 42, no. 5, pp. 2735-2740, 2009. · doi:10.1016/j.chaos.2009.04.023
[21] B. J. West, “Fractal physiology and the fractional calculus: a perspective,” Frontiers in Fractal Physiology, vol. 1, p. 5, 2010. · doi:10.3389/fphys.2010.00012
[22] A. Neuenkirch, S. Tindel, and J. Unterberger, “Discretizing the fractional Lévy area,” Stochastic Processes and Their Applications, vol. 120, no. 2, pp. 223-254, 2010. · Zbl 1185.60076 · doi:10.1016/j.spa.2009.10.007
[23] G. W. Wornell, “Wavelet-based representations for the 1/f family of fractal processes,” Proceedings of the IEEE, vol. 81, no. 10, pp. 1428-1450, 1993. · doi:10.1109/5.241506
[24] H. E. Schepers, J. H. G. M. van Beek, and J. B. Bassingthwaighte, “Four methods to estimate the fractal dimension from self-affine signals [medical application],” IEEE Engineering in Medicine and Biology Magazine, vol. 11, no. 2, pp. 57-64, 1992. · doi:10.1109/51.139038
[25] C. Fortin, R. Kumaresan, W. Ohley, and S. Hoefer, “Fractal dimension in the analysis of medical images,” IEEE Engineering in Medicine and Biology Magazine, vol. 11, no. 2, pp. 65-71, 1992. · doi:10.1109/51.139039
[26] T. Bedford, “Hölder exponents and box dimension for self-affine fractal functions,” Constructive Approximation, vol. 5, no. 1, pp. 33-48, 1989. · Zbl 0665.28004 · doi:10.1007/BF01889597
[27] H. E. Stanley, L. A. N. Amaral, A. L. Goldberger, S. Havlin, P. Ch. Ivanov, and C. K. Peng, “Statistical physics and physiology: monofractal and multifractal approaches,” Physica A, vol. 270, no. 1, pp. 309-324, 1999. · doi:10.1016/S0378-4371(99)00230-7
[28] P. Flandrin, “Wavelet analysis and synthesis of fractional Brownian motion,” IEEE Transactions on Information Theory, vol. 38, no. 2, part 2, pp. 910-917, 1992. · Zbl 0743.60078 · doi:10.1109/18.119751
[29] P. Christie, “Fractal analysis of interconnection complexity,” Proceedings of the IEEE, vol. 81, no. 10, pp. 1492-1499, 1993. · doi:10.1109/5.241509
[30] K. Chandra and C. Thompson, “Ultrasonic characterization of fractal media,” Proceedings of the IEEE, vol. 81, no. 10, pp. 1523-1533, 1993. · doi:10.1109/5.241512
[31] A. A. Suleymanov, A. A. Abbasov, and A. J. Ismaylov, “Fractal analysis of time series in oil and gas production,” Chaos, Solitons & Fractals, vol. 41, no. 5, pp. 2474-2483, 2009. · doi:10.1016/j.chaos.2008.09.039
[32] E. Conte, A. Federici, and J. P. Zbilut, “A new method based on fractal variance function for analysis and quantification of sympathetic and vagal activity in variability of R-R time series in ECG signals,” Chaos, Solitons & Fractals, vol. 41, no. 3, pp. 1416-1426, 2009. · doi:10.1016/j.chaos.2008.05.025
[33] W. Deering and B. J. West, “Fractal physiology,” IEEE Engineering in Medicine and Biology Magazine, vol. 11, no. 2, pp. 40-46, 1992. · doi:10.1109/51.139035
[34] A. K. Mishra and S. Raghav, “Local fractal dimension based ECG arrhythmia classification,” Biomedical Signal Processing and Control, vol. 5, no. 2, pp. 114-123, 2010. · doi:10.1016/j.bspc.2010.01.002
[35] D. Khoshnevisan and Y. Xiao, “Packing-dimension profiles and fractional Brownian motion,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 145, no. 1, pp. 205-213, 2008. · Zbl 1152.28009 · doi:10.1017/S0305004108001394
[36] A. Das and P. Das, “Fractal analysis of songs: performer’s preference,” Nonlinear Analysis: Real World Applications, vol. 11, no. 3, pp. 1790-1794, 2010. · Zbl 1192.37109 · doi:10.1016/j.nonrwa.2009.04.004
[37] J. Dávila and A. C. Ponce, “Hausdorff dimension of ruptures sets and removable singularities,” Comptes Rendus Mathématique, vol. 346, no. 1-2, pp. 27-32, 2008. · Zbl 1135.35033 · doi:10.1016/j.crma.2007.11.007
[38] G. Kekovic, M. Culic, L. Martac et al., “Fractal dimension values of cerebral and cerebellar activity in rats loaded with aluminium,” Medical & Biological Engineering & Computing, vol. 48, no. 7, pp. 671-679, 2010. · doi:10.1007/s11517-010-0620-3
[39] S. Rehman and A. H. Siddiqi, “Wavelet based Hurst exponent and fractal dimensional analysis of Saudi climatic dynamics,” Chaos, Solitons & Fractals, vol. 40, no. 3, pp. 1081-1090, 2009. · doi:10.1016/j.chaos.2007.08.063
[40] K. Falconer, Fractal Geometry: Mathematical Foundations and Applications, John Wiley & Sons, Hoboken, NJ, USA, 2nd edition, 2003. · Zbl 1060.28005 · doi:10.1002/0470013850
[41] P. Ch. Ivanov, L. A. Nunes Amaral, A. L. Goldberger et al., “Multifractality in human heartbeat dynamics,” Nature, vol. 399, no. 6735, pp. 461-465, 1999. · doi:10.1038/20924
[42] K. Daoudi and J. L. Véhel, “Signal representation and segmentation based on multifractal stationarity,” Signal Processing, vol. 82, no. 12, pp. 2015-2024, 2002. · Zbl 1012.94510 · doi:10.1016/S0165-1684(02)00198-6
[43] M. Tanaka, R. Kato, Y. Kimura, and A. Kayama, “Automated image processing and analysis of fracture surface patterns formed during creep crack growth in austenitic heat-resisting steels with different microstructures,” ISIJ International, vol. 42, no. 12, pp. 1412-1418, 2002.
[44] R. Zuo, Q. Cheng, Q. Xia, and F. P. Agterberg, “Application of fractal models to distinguish between different mineral phases,” Mathematical Geosciences, vol. 41, no. 1, pp. 71-80, 2009. · doi:10.1007/s11004-008-9191-3
[45] B. Kaulakys and M. Alaburda, “Modeling scaled processes and 1/f\beta noise using nonlinear stochastic differential equations,” Journal of Statistical Mechanics: Theory and Experiment, vol. 2009, no. 2, Article ID P02051, 2009. · doi:10.1088/1742-5468/2009/02/P02051
[46] C. Song, L. K. Gallos, S. Havlin, and H. A. Makse, “How to calculate the fractal dimension of a complex network: the box covering algorithm,” Journal of Statistical Mechanics: Theory and Experiment, no. 3, Article ID P03006, 2007. · doi:10.1088/1742-5468/2007/03/P03006
[47] R. C. García, A. S. Galán, J. R. Castrejón Pita, and A. A. Castrejón Pita, “The fractal dimension of an oil spray,” Fractals, vol. 11, no. 2, pp. 155-161, 2003. · Zbl 1062.92006 · doi:10.1142/S0218348X03001641
[48] M. Radziejewski and Z. W. Kundzewicz, “Fractal analysis of flow of the river Warta,” Journal of Hydrology, vol. 200, no. 1-4, pp. 280-294, 1997. · doi:10.1016/S0022-1694(97)00024-3
[49] J. Shinmoto and F. Takeo, “The Hausdorff dimension of sub-self-similar sets,” Fractals, vol. 11, no. 1, pp. 9-18, 2003. · Zbl 1044.28007 · doi:10.1142/S0218348X03001549
[50] M. Li and W. Zhao, “Detection of variations of local irregularity of traffic under DDOS flood attack,” Mathematical Problems in Engineering, vol. 2008, Article ID 475878, 11 pages, 2008. · Zbl 1189.68114 · doi:10.1155/2008/475878 · eudml:45486
[51] B. R. Hunt, “The Hausdorff dimension of graphs of Weierstrass functions,” Proceedings of the American Mathematical Society, vol. 126, no. 3, pp. 791-800, 1998. · Zbl 0897.28004 · doi:10.1090/S0002-9939-98-04387-1
[52] M. Li, “Self-similarity and long-range dependence in teletraffic,” in Proceedings of the 9th WSEAS International Conference on Multimedia Systems and Signal Processing, Hangzhou, China, May 2009.
[53] G. A. Hirchoren and C. E. D’Attellis, “Estimation of fractal signals using wavelets and filter banks,” IEEE Transactions on Signal Processing, vol. 46, no. 6, pp. 1624-1630, 1998.
[54] H. E. Stanley and P. Meakin, “Multifractal phenomena in physics and chemistry,” Nature, vol. 335, no. 6189, pp. 405-409, 1988.
[55] R. D. Mauldin and S. C. Williams, “On the Hausdorff dimension of some graphs,” Transactions of the American Mathematical Society, vol. 298, no. 2, pp. 793-803, 1986. · Zbl 0603.28003 · doi:10.2307/2000650
[56] R. R. Prasad, C. Meneveau, and K. R. Sreenivasan, “Multifractal nature of the dissipation field of passive scalars in fully turbulent flows,” Physical Review Letters, vol. 61, no. 1, pp. 74-77, 1988. · doi:10.1103/PhysRevLett.61.74
[57] T. Higuchi, “Approach to an irregular time series on the basis of the fractal theory,” Physica D, vol. 31, no. 2, pp. 277-283, 1988. · Zbl 0649.58046 · doi:10.1016/0167-2789(88)90081-4
[58] B. Dubuc, J. F. Quiniou, C. Roques-Carmes, C. Tricot, and S. W. Zucker, “Evaluating the fractal dimension of profiles,” Physical Review A, vol. 39, no. 3, pp. 1500-1512, 1989. · Zbl 0703.28006 · doi:10.1103/PhysRevA.39.1500
[59] N. Patzschke and M. Zähle, “Self-similar random measures are locally scale invariant,” Probability Theory and Related Fields, vol. 97, no. 4, pp. 559-574, 1993. · Zbl 0794.60045 · doi:10.1007/BF01192964
[60] B. Ninness, “Estimation of 1/f noise,” IEEE Transactions on Information Theory, vol. 44, no. 1, pp. 32-46, 1998. · Zbl 0905.94009 · doi:10.1109/18.650986
[61] J. M. Girault, D. Kouamé, and A. Ouahabi, “Analytical formulation of the fractal dimension of filtered stochastic signals,” Signal Processing, vol. 90, no. 9, pp. 2690-2697, 2010. · Zbl 1194.94090 · doi:10.1016/j.sigpro.2010.03.019
[62] P. Paramanathan and R. Uthayakumar, “An algorithm for computing the fractal dimension of waveforms,” Applied Mathematics and Computation, vol. 195, no. 2, pp. 598-603, 2008. · Zbl 1129.92049 · doi:10.1016/j.amc.2007.05.011
[63] B. B. Mandelbrot, “Self-affine fractals and fractal dimension,” Physica Scripta, vol. 32, no. 4, pp. 257-260, 1985. · Zbl 1063.28500 · doi:10.1088/0031-8949/32/4/001
[64] A. Das and P. Das, “Fractal analysis of different eastern and western musical instruments,” Fractals, vol. 14, no. 3, pp. 165-170, 2006. · doi:10.1142/S0218348X06003192
[65] S. C. Lim, L. Ming, and L. P. Teo, “Locally self-similar fractional oscillator processes,” Fluctuation and Noise Letters, vol. 7, no. 2, pp. L169-L179, 2007. · doi:10.1142/S0219477507003817
[66] C. R. Tolle, T. R. McJunkin, and D. J. Gorsich, “Suboptimal minimum cluster volume cover-based method for measuring fractal dimension,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 25, no. 1, pp. 32-41, 2003. · doi:10.1109/TPAMI.2003.1159944
[67] P. Maragos and A. Potamianos, “Fractal dimensions of speech sounds: computation and application to automatic speech recognition,” Journal of the Acoustical Society of America, vol. 105, no. 3, pp. 1925-1932, 1999. · doi:10.1121/1.426738
[68] J. M. Halley, S. Hartley, A. S. Kallimanis, W. E. Kunin, J. J. Lennon, and S. P. Sgardelis, “Uses and abuses of fractal methodology in ecology,” Ecology Letters, vol. 7, no. 3, pp. 254-271, 2004. · doi:10.1111/j.1461-0248.2004.00568.x
[69] B. B. Mandelbrot, “Negative fractal dimensions and multifractals,” Physica A, vol. 163, no. 1, pp. 306-315, 1990. · Zbl 0713.58034 · doi:10.1016/0378-4371(90)90339-T
[70] B. B. Mandelbrot, “Multifractal power law distributions: negative and critical dimensions and other “anomalies,” explained by a simple example,” Journal of Statistical Physics, vol. 110, no. 3-6, pp. 739-774, 2003. · Zbl 1026.28007 · doi:10.1023/A:1022159802564
[71] B. B. Mandelbrot, “Random multifractals: negative dimensions and the resulting limitations of the thermodynamic formalism,” Proceedings of the Royal Society. Series A, vol. 434, no. 1890, pp. 79-88, 1991. · Zbl 0850.76277 · doi:10.1098/rspa.1991.0081
[72] B. B. Mandelbrot, “Negative dimensions and Hölders, multifractals and their Hölder spectra, and the role of lateral preasymptotics in science,” The Journal of Fourier Analysis and Applications, vol. 2, pp. 409-432, 1995. · Zbl 0887.28004
[73] B. B. Mandelbrot and R. H. Riedi, “Inverse measures, the inversion formula, and discontinuous multifractals,” Advances in Applied Mathematics, vol. 18, no. 1, pp. 50-58, 1997. · Zbl 0870.28004 · doi:10.1006/aama.1996.0500
[74] B. B. Mandelbrot and M. Frame, “A primer of negative test dimensions and degrees of emptiness for latent sets,” Fractals, vol. 17, no. 1, pp. 1-14, 2009. · Zbl 1168.28005 · doi:10.1142/S0218348X09004211
[75] B. B. Mandelbrot, “Heavy tails in finance for independent or multifractal price increments,” in Handbook on Heavy Tailed Distributions in Finance, S. T. Rachev, Ed., vol. 1 of Handbooks in Finance 30, pp. 1-34, Elsevier, New York, NY, USA, 2003.
[76] J. Molenaar, J. Herweijer, and W. van de Water, “Negative dimensions of the turbulent dissipation field,” Physical Review E, vol. 52, no. 1, pp. 496-509, 1995. · doi:10.1103/PhysRevE.52.496
[77] A. B. Chhabra and K. R. Sreenivasan, “Negative dimensions: theory, computation, and experiment,” Physical Review A, vol. 43, no. 2, pp. 1114-1117, 1991. · doi:10.1103/PhysRevA.43.1114
[78] A. B. Chhabra and K. R. Sreenivasan, “Scale-invariant multiplier distributions in turbulence,” Physical Review Letters, vol. 68, no. 18, pp. 2762-2765, 1992. · doi:10.1103/PhysRevLett.68.2762
[79] T. Gneiting and M. Schlather, “Stochastic models that separate fractal dimension and the Hurst effect,” SIAM Review, vol. 46, no. 2, pp. 269-282, 2004. · Zbl 1062.60053 · doi:10.1137/S0036144501394387
[80] S. C. Lim and M. Li, “A generalized Cauchy process and its application to relaxation phenomena,” Journal of Physics A, vol. 39, no. 12, pp. 2935-2951, 2006. · Zbl 1090.82013 · doi:10.1088/0305-4470/39/12/005
[81] M. Li and S. C. Lim, “Modeling network traffic using generalized Cauchy process,” Physica A, vol. 387, no. 11, pp. 2584-2594, 2008. · doi:10.1016/j.physa.2008.01.026
[82] M. Li, W. Jia, and W. Zhao, “A whole correlation structure of asymptotically self-similar traffic in communication networks,” in Proceedings of the 1st International Conference on Web Information Systems Engineering (WISE ’00), pp. 461-466, Hong Kong, June 2000.
[83] M. Li and S. C. Lim, “Modeling network traffic using cauchy correlation model with long-range dependence,” Modern Physics Letters B, vol. 19, no. 17, pp. 829-840, 2005. · Zbl 1076.90010 · doi:10.1142/S0217984905008864
[84] M. Li and S. C. Lim, “Power spectrum of generalized Cauchy process,” Telecommunication Systems, vol. 43, no. 3-4, pp. 219-222, 2010. · doi:10.1007/s11235-009-9209-2
[85] A. Papoulis, Probability, Random Variables and Stochastic Processes, McGraw-Hill, New York, NY, USA, 1997. · Zbl 0191.46704
[86] H. Cramer, Random Variable and Probability Distributions, Cambridge Tracts in Mathematics, no. 36, Cambridge University, Cambridge, UK, 1937. · Zbl 0016.36304
[87] H. Cramer, “On the theory of stationary random processes,” The Annals of Mathematics, vol. 43, no. 2, pp. 351-369, 1942.
[88] C. K. Liu, Applied Functional Analysis, Defense Press, Beijing, China, 1986.
[89] I. M. Gelfand and K. Vilenkin, Generalized Functions, vol. 4, Academic Press, New York, NY, USA, 1964.
[90] R. J. Adler, R. E. Feldman, and M. S. Taqqu, Eds., A Practical Guide to Heavy Tails: Statistical Techniques and Applications, Birkhäuser, Boston, Mass, USA, 1998. · Zbl 0901.00010
[91] D. H. Griffel, Applied Functional Analysis, Ellis Horwood Series in Mathematics and Its Application, Ellis Horwood, Chichester, UK, 1981. · Zbl 0461.46001
[92] R. P. Kanwal, Generalized Functions: Theory and Applications, Birkhäuser, Boston, Mass, USA, 3rd edition, 2004.
[93] J. T. Kent and A. T. A. Wood, “Estimating the fractal dimension of a locally self-similar Gaussian process by using increments,” Journal of the Royal Statistical Society. Series B, vol. 59, no. 3, pp. 679-699, 1997. · Zbl 0889.62072
[94] P. Hall and R. Roy, “On the relationship between fractal dimension and fractal index for stationary stochastic processes,” The Annals of Applied Probability, vol. 4, no. 1, pp. 241-253, 1994. · Zbl 0798.60035 · doi:10.1214/aoap/1177005210
[95] G. Chan, P. Hall, and D. S. Poskitt, “Periodogram-based estimators of fractal properties,” The Annals of Statistics, vol. 23, no. 5, pp. 1684-1711, 1995. · Zbl 0843.62090 · doi:10.1214/aos/1176324319
[96] R. J. Adler, The Geometry of Random Fields, Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, Chichester, UK, 1981. · Zbl 0478.60059
[97] P. Todorovic, An Introduction to Stochastic Processes and Their Applications, Springer Series in Statistics: Probability and Its Applications, Springer, New York, NY, USA, 1992. · Zbl 0759.60033
[98] S. C. Lim and S. V. Muniandy, “Generalized Ornstein-Uhlenbeck processes and associated self-similar processes,” Journal of Physics A, vol. 36, no. 14, pp. 3961-3982, 2003. · Zbl 1083.60029 · doi:10.1088/0305-4470/36/14/303
[99] R. L. Wolpert and M. S. Taqqu, “Fractional Ornstein-Uhlenbeck Lévy processes and the Telecom process: upstairs and downstairs,” Signal Processing, vol. 85, no. 8, pp. 1523-1545, 2005. · Zbl 1160.94370 · doi:10.1016/j.sigpro.2004.09.016
[100] M. Li and W. Zhao, “Representation of a Stochastic Traffic Bound,” IEEE Transactions on Parallel and Distributed Systems, vol. 21, no. 9, pp. 1368-1372, 2010. · doi:10.1109/TPDS.2009.162
[101] S. V. Muniandy and J. Stanslas, “Modelling of chromatin morphologies in breast cancer cells undergoing apoptosis using generalized Cauchy field,” Computerized Medical Imaging and Graphics, vol. 32, no. 7, pp. 631-637, 2008. · doi:10.1016/j.compmedimag.2008.07.003
[102] A. Spector and F. S. Grant, “Statistical methods for interpreting aeromagnetic data,” Geophysics, vol. 35, no. 2, pp. 293-302, 1970.
[103] J.-P. Chilès and P. Delfiner, Geostatistics, Modeling Spatial Uncertainty, Wiley Series in Probability and Statistics: Applied Probability and Statistics, John Wiley & Sons, New York, NY, USA, 1999. · Zbl 0922.62098 · doi:10.1002/9780470316993
[104] M. Li, “Generation of teletraffic of generalized Cauchy type,” Physica Scripta, vol. 81, no. 2, Article ID 025007, 2010. · Zbl 1191.90013 · doi:10.1088/0031-8949/81/02/025007
[105] S. C. Lim and L. P. Teo, “Gaussian fields and Gaussian sheets with generalized Cauchy covariance structure,” Stochastic Processes and Their Applications, vol. 119, no. 4, pp. 1325-1356, 2009. · Zbl 1161.60314 · doi:10.1016/j.spa.2008.06.011
[106] M. Scalia, G. Mattioli, and C. Cattani, “Analysis of large-amplitude pulses in short time intervals: application to neuron interactions,” Mathematical Problems in Engineering, vol. 2010, Article ID 895785, 15 pages, 2010. · Zbl 1189.37099 · doi:10.1155/2010/895785 · eudml:233617
[107] E. G. Bakhoum and C. Toma, “Dynamical aspects of macroscopic and quantum transitions due to coherence function and time series events,” Mathematical Problems in Engineering, vol. 2010, Article ID 428903, 13 pages, 2010. · Zbl 1191.35219 · doi:10.1155/2010/428903 · eudml:225118
[108] E. G. Bakhoum and C. Toma, “Mathematical transform of traveling-wave equations and phase aspects of quantum interaction,” Mathematical Problems in Engineering, vol. 2010, Article ID 695208, 15 pages, 2010. · Zbl 1191.35220 · doi:10.1155/2010/695208 · eudml:229128
[109] X. Yang and D. She, “A new adaptive local linear prediction method and its application in hydrological time series,” Mathematical Problems in Engineering, vol. 2010, Article ID 205438, 15 pages, 2010. · Zbl 1189.37089 · doi:10.1155/2010/205438 · eudml:225058
[110] T. Y. Sung, Y. S. Shieh, and H. C. Hsin, “An efficient VLSI linear array for DCT/IDCT using subband decomposition algorithm,” Mathematical Problems in Engineering, vol. 2010, Article ID 185398, 21 pages, 2010. · Zbl 1189.94025 · doi:10.1155/2010/185398 · eudml:226300
[111] M. Humi, “Assessing local turbulence strength from a time series,” Mathematical Problems in Engineering, vol. 2010, Article ID 316841, 13 pages, 2010. · Zbl 1189.37088 · doi:10.1155/2010/316841 · eudml:231736
[112] A. R. Messina, P. Esquivel, and F. Lezama, “Time-dependent statistical analysis of wide-area time-synchronized data,” Mathematical Problems in Engineering, vol. 2010, Article ID 751659, 17 pages, 2010. · Zbl 1189.62188 · doi:10.1155/2010/751659 · eudml:229984
[113] K. Friston, K. Stephan, B. Li, and J. Daunizeau, “Generalised filtering,” Mathematical Problems in Engineering, vol. 2010, Article ID 621670, 34 pages, 2010. · Zbl 1189.94032 · doi:10.1155/2010/621670 · eudml:224317
[114] M. Dong, “A tutorial on nonlinear time-series data mining in engineering asset health and reliability prediction: concepts, models, and algorithms,” Mathematical Problems in Engineering, vol. 2010, Article ID 175936, 22 pages, 2010. · Zbl 1189.90047 · doi:10.1155/2010/175936 · eudml:231199
[115] M. Li and J.-Y. Li, “On the predictability of long-range dependent series,” Mathematical Problems in Engineering, vol. 2010, Article ID 397454, 9 pages, 2010. · Zbl 1191.62160 · doi:10.1155/2010/397454
[116] W. Qiu, Y. Zheng, and K. Chen, “Building representative-based data aggregation tree in wireless sensor networks,” Mathematical Problems in Engineering, vol. 2010, Article ID 732892, 11 pages, 2010. · Zbl 1191.68067 · doi:10.1155/2010/732892 · eudml:229508
[117] Z. Liu, “Chaotic time series analysis,” Mathematical Problems in Engineering, vol. 2010, Article ID 720190, 31 pages, 2010. · Zbl 1191.37046 · doi:10.1155/2010/720190
[118] G. Toma, “Specific differential equations for generating pulse sequences,” Mathematical Problems in Engineering, vol. 2010, Article ID 324818, 11 pages, 2010. · Zbl 1191.37052 · doi:10.1155/2010/324818 · eudml:224453
[119] A. N. Al-Rabadi, O. M. Abuzeid, and H. S. Alkhaldi, “Fractal geometry-based hypergeometric time series solution to the hereditary thermal creep model for the contact of rough surfaces using the Kelvin-Voigt medium,” Mathematical Problems in Engineering, vol. 2010, Article ID 652306, 22 pages, 2010. · Zbl 05793780 · doi:10.1155/2010/652306
[120] X. Zhao, J. Yue, and P. Shang, “Effect of trends on detrended fluctuation analysis of precipitation series,” Mathematical Problems in Engineering, vol. 2010, Article ID 749894, 15 pages, 2010. · doi:10.1155/2010/749894
[121] L. Li, H. Peng, Y. Shao, and Y. Yang, “Cryptanalysis of a chaotic communication scheme using parameter observer,” Mathematical Problems in Engineering, vol. 2010, Article ID 361860, 18 pages, 2010. · Zbl 1191.94099 · doi:10.1155/2010/361860 · eudml:226225
[122] M. Li and M. Li, “An adaptive approach for defending against DDoS attacks,” Mathematical Problems in Engineering, vol. 2010, Article ID 570940, 15 pages, 2010. · Zbl 1189.68020 · doi:10.1155/2010/570940 · eudml:229214
[123] M. Li, “Change trend of averaged Hurst parameter of traffic under DDOS flood attacks,” Computers and Security, vol. 25, no. 3, pp. 213-220, 2006. · doi:10.1016/j.cose.2005.11.007
[124] M. Li, S. C. Lim, and S.-Y. Chen, “Exact solution of impulse response to a class of fractional oscillators and its stability,” Mathematical Problems in Engineering, vol. 2011, 9 pages, 2011. · Zbl 1202.34018 · doi:10.1155/2011/657839 · eudml:231368
[125] M. Li, C. Cattani, and S.-Y. Chen, “Viewing sea level by a one-dimensional random function with long memory,” Mathematical Problems in Engineering, vol. 2011, Article ID 654284, 13 pages, 2011. · doi:10.1155/2011/654284
[126] W. B. Mikhael and T. Yang, “A gradient-based optimum block adaptation ICA technique for interference suppression in highly dynamic communication channels,” EURASIP Journal on Applied Signal Processing, vol. 2006, 10 pages, 2006. · doi:10.1155/ASP/2006/84057
[127] X. Fu, W. Yu, S. Jiang, S. Graham, and Y. Guan, “TCP performance in flow-based mix networks: modeling and analysis,” IEEE Transactions on Parallel and Distributed Systems, vol. 20, no. 5, pp. 695-709, 2009. · doi:10.1109/TPDS.2008.135