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Mathematical methods for restoration of images in magnetism of nanoparticles

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Abstract

It is shown that the formalism of “restoration and improvement of image qualities” can be considered as an effective tool for mathematical correction of initial experimental conditions in various cases of magnetometry. As a concrete example, the case of identification of magnetic phase transitions, both field and temperature ones, in nanoparticle systems with log-normal distribution of their sizes has been considered.

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References

  1. Yu. S. Avraamov, V. M. Belova, V. I. Nikolaev, V. M. Stuchebnikov, “Temperature dependence of superparamagnetic magnetization,” Fiz. Tverd. Tela, 16, No. 10, 3180–3181 (1981).

    Google Scholar 

  2. I. P. Bazarov, Thermodynamics, Vysshaya Shkola, Moscow (1991).

    Google Scholar 

  3. I. P. Bazarov and V. V. Bondarenko, “On the impossibility of phase transitions of the third and higher kinds,” Zh. Fiz. Khim., 70, No. 7, 1198–1200 (1996).

    Google Scholar 

  4. C. Bréchignac, P. Houdy, and M. Lahmani, Nanomaterials and Nanochemistry, Springer, Berlin (2008).

    Google Scholar 

  5. G. Cao, Nanostructures and Nanomaterials: Synthesis, Properties and Applications, Imperial College Press (2004).

  6. G. Gerritzen, Li-Chin Huang, K. Killpack, M. Mircheva, and J. Conti, A Review of Current Practices in the Nanotechnology Industry, Univ. of California (2006).

  7. A. N. Kolmogorov, “On the log-normal law of distribution of particle sizes upon their fragmentation,” Dokl. Akad. Nauk SSSR, 31, No. 2, 99–101 (1941).

    Google Scholar 

  8. V. I. Nikolaev and T. A. Bushina, “On a paraprocess of superparamagnetic type,” Vestn. Mosk. Univ. Ser. 3 Fiz. Astronom., No. 2, 48–51 (1998).

  9. V. I. Nikolaev, Yu. P. Pyt’ev, V. S. Rusakov, A. G. Sveshnikov, and E. N. Terent’ev, “A new principle of organization of the spectrometer–computer complex in Mössbauer spectroscopy,” Dokl. Akad. Nauk SSSR, 260, 848–852 (1981).

    Google Scholar 

  10. V. I. Nikolaev and V. S. Rusakov, Mössbauer Study of Ferrites, Izd. Mosk. Univ., Moscow (1985).

    Google Scholar 

  11. V. I. Nikolaev and O. P. Tretyakova, “Method of measurement reduction in the problem of discovering the paramagnetism–induced superparamagnetism phase transition,” Vestn. Mosk. Univ. Ser. 3 Fiz. Astronom., No. 1, 73–75 (2006).

  12. V. I. Nikolaev and O. P. Tretyakova, “On restoration of the magnetic phase diagram of a superparamagnetic material,” Vestn. Mosk. Univ. Ser. 3 Fiz. Astronom., No. 1, 75–78 (2008).

  13. Yu. P. Pyt’ev, “Problem of improvement of image quality,” Dokl. Akad. Nauk SSSR, 245, 315–319 (1979).

    MathSciNet  Google Scholar 

  14. Yu. P. Pyt’ev, “Problem of restoration of images,” Dokl. Akad. Nauk SSSR, 245, 42–46 (1979).

    MathSciNet  Google Scholar 

  15. Yu. P. Pyt’ev, “Suppression of false signals in the problem of resolution improvement,” Dokl. Akad. Nauk SSSR, 255, 540–544 (1980).

    MathSciNet  Google Scholar 

  16. Yu. P. Pyt’ev, Methods of Analysis and Interpretation for Experiment [in Russian], Izd. Mosk. Univ., Moscow (1990).

    MATH  Google Scholar 

  17. Yu. P. Pyt’ev, Methods of Mathematical Modeling of Measuring Systems [in Russian], Fizmatlit, Moscow (2004).

    Google Scholar 

  18. A. N. Tikhonov, “On solution of ill-posed problems and regularization methods,” Dokl. Akad. Nauk SSSR, 151, No. 3, 501–504 (1963).

    MathSciNet  Google Scholar 

  19. A. N. Tikhonov and V. Yu. Arsenin, Methods of Solution of Ill-Posed Problems [in Russian], Nauka, Moscow (1979).

    MATH  Google Scholar 

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Authors and Affiliations

  1. Moscow State University, Moscow, Russia

    V. I. Nikolaev & O. P. Tretyakova

Authors
  1. V. I. Nikolaev
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  2. O. P. Tretyakova
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Correspondence to V. I. Nikolaev.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 15, No. 6, pp. 99–117, 2009.

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Nikolaev, V.I., Tretyakova, O.P. Mathematical methods for restoration of images in magnetism of nanoparticles. J Math Sci 172, 824–836 (2011). https://doi.org/10.1007/s10958-011-0226-9

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  • DOI: https://doi.org/10.1007/s10958-011-0226-9

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