Stretched exponential function (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Stretched exponential function" in English language version.

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21doi.org

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10harvard.edu

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9nih.gov

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5semanticscholar.org

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3arxiv.org

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1iop.org

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1loc.gov

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1fz-juelich.de

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arxiv.org

Trachenko, K.; Zaccone, A. (2021-06-14). "Slow stretched-exponential and fast compressed-exponential relaxation from local event dynamics". Journal of Physics: Condensed Matter. 33: 315101. arXiv:2010.10440. doi:10.1088/1361-648X/ac04cd. ISSN 0953-8984.
Wuttke, J. (2012). "Laplace–Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation "libkww"". Algorithms. 5 (4): 604–628. arXiv:0911.4796. doi:10.3390/a5040604. S2CID 15030084.
Ammar, H. A., Nasser, Y. and Artail, H. (2018). "Closed Form Expressions for the Probability Density Function of the Interference Power in PPP Networks". 2018 IEEE International Conference on Communications (ICC). pp. 1–6. arXiv:1803.10440. doi:10.1109/ICC.2018.8422214. ISBN 978-1-5386-3180-5. S2CID 4374550.{{cite book}}: CS1 maint: multiple names: authors list (link)

bnf.fr

gallica.bnf.fr

Kohlrausch, R. (1854). "Theorie des elektrischen Rückstandes in der Leidner Flasche". Annalen der Physik und Chemie. 91 (1): 56–82, 179–213. Bibcode:1854AnP...167...56K. doi:10.1002/andp.18541670103..

doi.org

Trachenko, K.; Zaccone, A. (2021-06-14). "Slow stretched-exponential and fast compressed-exponential relaxation from local event dynamics". Journal of Physics: Condensed Matter. 33: 315101. arXiv:2010.10440. doi:10.1088/1361-648X/ac04cd. ISSN 0953-8984.
Kohlrausch, R. (1854). "Theorie des elektrischen Rückstandes in der Leidner Flasche". Annalen der Physik und Chemie. 91 (1): 56–82, 179–213. Bibcode:1854AnP...167...56K. doi:10.1002/andp.18541670103..
Williams, G. & Watts, D. C. (1970). "Non-Symmetrical Dielectric Relaxation Behavior Arising from a Simple Empirical Decay Function". Transactions of the Faraday Society. 66: 80–85. doi:10.1039/tf9706600080. S2CID 95007734..
Holm, Sverre (2020). "Time domain characterization of the Cole-Cole dielectric model". Journal of Electrical Bioimpedance. 11 (1): 101–105. doi:10.2478/joeb-2020-0015. PMC 7851980. PMID 33584910.
Donsker, M. D. & Varadhan, S. R. S. (1975). "Asymptotic evaluation of certain Markov process expectations for large time". Comm. Pure Appl. Math. 28: 1–47. doi:10.1002/cpa.3160280102.
Takano, H. and Nakanishi, H. and Miyashita, S. (1988). "Stretched exponential decay of the spin-correlation function in the kinetic Ising model below the critical temperature". Phys. Rev. B. 37 (7): 3716–3719. Bibcode:1988PhRvB..37.3716T. doi:10.1103/PhysRevB.37.3716. PMID 9944981.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Shore, John E. and Zwanzig, Robert (1975). "Dielectric relaxation and dynamic susceptibility of a one-dimensional model for perpendicular-dipole polymers". The Journal of Chemical Physics. 63 (12): 5445–5458. Bibcode:1975JChPh..63.5445S. doi:10.1063/1.431279.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Brey, J. J. and Prados, A. (1993). "Stretched exponential decay at intermediate times in the one-dimensional Ising model at low temperatures". Physica A. 197 (4): 569–582. Bibcode:1993PhyA..197..569B. doi:10.1016/0378-4371(93)90015-V.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Lindsey, C. P. & Patterson, G. D. (1980). "Detailed comparison of the Williams-Watts and Cole-Davidson functions". Journal of Chemical Physics. 73 (7): 3348–3357. Bibcode:1980JChPh..73.3348L. doi:10.1063/1.440530.. For a more recent and general discussion, see Berberan-Santos, M.N., Bodunov, E.N. and Valeur, B. (2005). "Mathematical functions for the analysis of luminescence decays with underlying distributions 1. Kohlrausch decay function (stretched exponential)". Chemical Physics. 315 (1–2): 171–182. Bibcode:2005CP....315..171B. doi:10.1016/j.chemphys.2005.04.006.{{cite journal}}: CS1 maint: multiple names: authors list (link).
Zorn, R. (2002). "Logarithmic moments of relaxation time distributions" (PDF). Journal of Chemical Physics. 116 (8): 3204–3209. Bibcode:2002JChPh.116.3204Z. doi:10.1063/1.1446035.
Hilfer, J. (2002). "H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems". Physical Review E. 65 (6): 061510. Bibcode:2002PhRvE..65f1510H. doi:10.1103/physreve.65.061510. PMID 12188735. S2CID 16276298.
Alvarez, F., Alegría, A. and Colmenero, J. (1991). "Relationship between the time-domain Kohlrausch-Williams-Watts and frequency-domain Havriliak-Negami relaxation functions". Physical Review B. 44 (14): 7306–7312. Bibcode:1991PhRvB..44.7306A. doi:10.1103/PhysRevB.44.7306. PMID 9998642.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Wuttke, J. (2012). "Laplace–Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation "libkww"". Algorithms. 5 (4): 604–628. arXiv:0911.4796. doi:10.3390/a5040604. S2CID 15030084.
Dobrovolskis, A., Alvarellos, J. and Lissauer, J. (2007). "Lifetimes of small bodies in planetocentric (or heliocentric) orbits". Icarus. 188 (2): 481–505. Bibcode:2007Icar..188..481D. doi:10.1016/j.icarus.2006.11.024.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Bennett, K.; et al. (2003). "Characterization of Continuously Distributed Water Diffusion Rates in Cerebral Cortex with a Stretched Exponential Model". Magn. Reson. Med. 50 (4): 727–734. doi:10.1002/mrm.10581. PMID 14523958.
Valko, Peter P.; Lee, W. John (2010-01-01). "A Better Way To Forecast Production From Unconventional Gas Wells". SPE Annual Technical Conference and Exhibition. Society of Petroleum Engineers. doi:10.2118/134231-ms. ISBN 9781555633004.
B. M. Weon & J. H. Je (2009). "Theoretical estimation of maximum human lifespan". Biogerontology. 10 (1): 65–71. doi:10.1007/s10522-008-9156-4. PMID 18560989. S2CID 8554128.
B. M. Weon (2016). "Tyrannosaurs as long-lived species". Scientific Reports. 6: 19554. Bibcode:2016NatSR...619554W. doi:10.1038/srep19554. PMC 4726238. PMID 26790747.
Ammar, H. A., Nasser, Y. and Artail, H. (2018). "Closed Form Expressions for the Probability Density Function of the Interference Power in PPP Networks". 2018 IEEE International Conference on Communications (ICC). pp. 1–6. arXiv:1803.10440. doi:10.1109/ICC.2018.8422214. ISBN 978-1-5386-3180-5. S2CID 4374550.{{cite book}}: CS1 maint: multiple names: authors list (link)
Lei Guo, Enhua Tan, Songqing Chen, Zhen Xiao, and Xiaodong Zhang (2008). "The Stretched Exponential Distribution of Internet Media Access Patterns". PODC' 08. pp. 283–294. doi:10.1145/1400751.1400789.{{cite conference}}: CS1 maint: multiple names: authors list (link)
Adamic, Lada A.; Bernardo A., Huberman (2000). "Power-Law Distribution of the World Wide Web". Science. 287 (5461): 2115–2115. doi:10.1126/science.287.5461.2115a.

fz-juelich.de

juser.fz-juelich.de

Zorn, R. (2002). "Logarithmic moments of relaxation time distributions" (PDF). Journal of Chemical Physics. 116 (8): 3204–3209. Bibcode:2002JChPh.116.3204Z. doi:10.1063/1.1446035.

harvard.edu

ui.adsabs.harvard.edu

Kohlrausch, R. (1854). "Theorie des elektrischen Rückstandes in der Leidner Flasche". Annalen der Physik und Chemie. 91 (1): 56–82, 179–213. Bibcode:1854AnP...167...56K. doi:10.1002/andp.18541670103..
Takano, H. and Nakanishi, H. and Miyashita, S. (1988). "Stretched exponential decay of the spin-correlation function in the kinetic Ising model below the critical temperature". Phys. Rev. B. 37 (7): 3716–3719. Bibcode:1988PhRvB..37.3716T. doi:10.1103/PhysRevB.37.3716. PMID 9944981.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Shore, John E. and Zwanzig, Robert (1975). "Dielectric relaxation and dynamic susceptibility of a one-dimensional model for perpendicular-dipole polymers". The Journal of Chemical Physics. 63 (12): 5445–5458. Bibcode:1975JChPh..63.5445S. doi:10.1063/1.431279.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Brey, J. J. and Prados, A. (1993). "Stretched exponential decay at intermediate times in the one-dimensional Ising model at low temperatures". Physica A. 197 (4): 569–582. Bibcode:1993PhyA..197..569B. doi:10.1016/0378-4371(93)90015-V.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Lindsey, C. P. & Patterson, G. D. (1980). "Detailed comparison of the Williams-Watts and Cole-Davidson functions". Journal of Chemical Physics. 73 (7): 3348–3357. Bibcode:1980JChPh..73.3348L. doi:10.1063/1.440530.. For a more recent and general discussion, see Berberan-Santos, M.N., Bodunov, E.N. and Valeur, B. (2005). "Mathematical functions for the analysis of luminescence decays with underlying distributions 1. Kohlrausch decay function (stretched exponential)". Chemical Physics. 315 (1–2): 171–182. Bibcode:2005CP....315..171B. doi:10.1016/j.chemphys.2005.04.006.{{cite journal}}: CS1 maint: multiple names: authors list (link).
Zorn, R. (2002). "Logarithmic moments of relaxation time distributions" (PDF). Journal of Chemical Physics. 116 (8): 3204–3209. Bibcode:2002JChPh.116.3204Z. doi:10.1063/1.1446035.
Hilfer, J. (2002). "H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems". Physical Review E. 65 (6): 061510. Bibcode:2002PhRvE..65f1510H. doi:10.1103/physreve.65.061510. PMID 12188735. S2CID 16276298.
Alvarez, F., Alegría, A. and Colmenero, J. (1991). "Relationship between the time-domain Kohlrausch-Williams-Watts and frequency-domain Havriliak-Negami relaxation functions". Physical Review B. 44 (14): 7306–7312. Bibcode:1991PhRvB..44.7306A. doi:10.1103/PhysRevB.44.7306. PMID 9998642.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Dobrovolskis, A., Alvarellos, J. and Lissauer, J. (2007). "Lifetimes of small bodies in planetocentric (or heliocentric) orbits". Icarus. 188 (2): 481–505. Bibcode:2007Icar..188..481D. doi:10.1016/j.icarus.2006.11.024.{{cite journal}}: CS1 maint: multiple names: authors list (link)
B. M. Weon (2016). "Tyrannosaurs as long-lived species". Scientific Reports. 6: 19554. Bibcode:2016NatSR...619554W. doi:10.1038/srep19554. PMC 4726238. PMID 26790747.

iop.org

iopscience.iop.org

Trachenko, K.; Zaccone, A. (2021-06-14). "Slow stretched-exponential and fast compressed-exponential relaxation from local event dynamics". Journal of Physics: Condensed Matter. 33: 315101. arXiv:2010.10440. doi:10.1088/1361-648X/ac04cd. ISSN 0953-8984.

loc.gov

lccn.loc.gov

Gradshteyn, Izrail Solomonovich; Ryzhik, Iosif Moiseevich; Geronimus, Yuri Veniaminovich; Tseytlin, Michail Yulyevich; Jeffrey, Alan (2015) [October 2014]. "3.478.". In Zwillinger, Daniel; Moll, Victor Hugo (eds.). Table of Integrals, Series, and Products. Translated by Scripta Technica, Inc. (8 ed.). Academic Press, Inc. p. 372. ISBN 978-0-12-384933-5. LCCN 2014010276.

nih.gov

pubmed.ncbi.nlm.nih.gov

Holm, Sverre (2020). "Time domain characterization of the Cole-Cole dielectric model". Journal of Electrical Bioimpedance. 11 (1): 101–105. doi:10.2478/joeb-2020-0015. PMC 7851980. PMID 33584910.
Takano, H. and Nakanishi, H. and Miyashita, S. (1988). "Stretched exponential decay of the spin-correlation function in the kinetic Ising model below the critical temperature". Phys. Rev. B. 37 (7): 3716–3719. Bibcode:1988PhRvB..37.3716T. doi:10.1103/PhysRevB.37.3716. PMID 9944981.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Hilfer, J. (2002). "H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems". Physical Review E. 65 (6): 061510. Bibcode:2002PhRvE..65f1510H. doi:10.1103/physreve.65.061510. PMID 12188735. S2CID 16276298.
Alvarez, F., Alegría, A. and Colmenero, J. (1991). "Relationship between the time-domain Kohlrausch-Williams-Watts and frequency-domain Havriliak-Negami relaxation functions". Physical Review B. 44 (14): 7306–7312. Bibcode:1991PhRvB..44.7306A. doi:10.1103/PhysRevB.44.7306. PMID 9998642.{{cite journal}}: CS1 maint: multiple names: authors list (link)
Bennett, K.; et al. (2003). "Characterization of Continuously Distributed Water Diffusion Rates in Cerebral Cortex with a Stretched Exponential Model". Magn. Reson. Med. 50 (4): 727–734. doi:10.1002/mrm.10581. PMID 14523958.
B. M. Weon & J. H. Je (2009). "Theoretical estimation of maximum human lifespan". Biogerontology. 10 (1): 65–71. doi:10.1007/s10522-008-9156-4. PMID 18560989. S2CID 8554128.
B. M. Weon (2016). "Tyrannosaurs as long-lived species". Scientific Reports. 6: 19554. Bibcode:2016NatSR...619554W. doi:10.1038/srep19554. PMC 4726238. PMID 26790747.

ncbi.nlm.nih.gov

Holm, Sverre (2020). "Time domain characterization of the Cole-Cole dielectric model". Journal of Electrical Bioimpedance. 11 (1): 101–105. doi:10.2478/joeb-2020-0015. PMC 7851980. PMID 33584910.
B. M. Weon (2016). "Tyrannosaurs as long-lived species". Scientific Reports. 6: 19554. Bibcode:2016NatSR...619554W. doi:10.1038/srep19554. PMC 4726238. PMID 26790747.

semanticscholar.org

api.semanticscholar.org

Williams, G. & Watts, D. C. (1970). "Non-Symmetrical Dielectric Relaxation Behavior Arising from a Simple Empirical Decay Function". Transactions of the Faraday Society. 66: 80–85. doi:10.1039/tf9706600080. S2CID 95007734..
Hilfer, J. (2002). "H-function representations for stretched exponential relaxation and non-Debye susceptibilities in glassy systems". Physical Review E. 65 (6): 061510. Bibcode:2002PhRvE..65f1510H. doi:10.1103/physreve.65.061510. PMID 12188735. S2CID 16276298.
Wuttke, J. (2012). "Laplace–Fourier Transform of the Stretched Exponential Function: Analytic Error Bounds, Double Exponential Transform, and Open-Source Implementation "libkww"". Algorithms. 5 (4): 604–628. arXiv:0911.4796. doi:10.3390/a5040604. S2CID 15030084.
B. M. Weon & J. H. Je (2009). "Theoretical estimation of maximum human lifespan". Biogerontology. 10 (1): 65–71. doi:10.1007/s10522-008-9156-4. PMID 18560989. S2CID 8554128.
Ammar, H. A., Nasser, Y. and Artail, H. (2018). "Closed Form Expressions for the Probability Density Function of the Interference Power in PPP Networks". 2018 IEEE International Conference on Communications (ICC). pp. 1–6. arXiv:1803.10440. doi:10.1109/ICC.2018.8422214. ISBN 978-1-5386-3180-5. S2CID 4374550.{{cite book}}: CS1 maint: multiple names: authors list (link)

worldcat.org

search.worldcat.org

Trachenko, K.; Zaccone, A. (2021-06-14). "Slow stretched-exponential and fast compressed-exponential relaxation from local event dynamics". Journal of Physics: Condensed Matter. 33: 315101. arXiv:2010.10440. doi:10.1088/1361-648X/ac04cd. ISSN 0953-8984.