Applications of Math Microscope in the Event Horizon Telescope

Evgeni Nikolaevich Terentiev; Nikolay Evgenyevich Shilin-Terentyev

doi:doi:10.11648/j.ijass.20210902.11

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Applications of Math Microscope in the Event Horizon Telescope

Evgeni Nikolaevich Terentiev, Nikolay Evgenyevich Shilin-Terentyev

Published in International Journal of Astrophysics and Space Science (Volume 9, Issue 2)

Received: 18 October 2020 Accepted: 7 November 2020 Published: 30 June 2021

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Abstract

The paper describes the insides - the basic concepts of the Math Microscope, demonstrates the results of Super-Resolution images obtained from the Event Horizon Telescope and analyzes the results of the movement of clusters of stars that go around the Black Hole. The presence of point objects - single stars in the SR image allowed us to implement a new breakthrough approach in the problem of SR images of Powehi Black Hole in the concept of MM. In the paper, we reviewed and illustrated new concepts: Invertability Indicators and Adequacy Characteristics of discrete Models of Apparatus Functions. With these new concepts, in the inverse problem, for the first time, we were able to answer simple questions: What are we dealing with? Moreover, have we solved the inverse problem? The paper demonstrates the “manual solution” of the problem of Reconstruction of AFs and Super-Resolution on MM. In the Discussion at the end of the paper, we pose the problem of creating two Artificial Intelligences for the automated solution of the R&SR problem with the interpretation of the SR results of BH images from EHT.

Published in	International Journal of Astrophysics and Space Science (Volume 9, Issue 2)
DOI	10.11648/j.ijass.20210902.11
Page(s)	21-31
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Super-Resolution, Conditionality, Apodization in Inevitability, Modulation Transfer Function, Convolution, Fourier Transform

References

[1]	A. N. Tikhonov, M. V. Ufimtsev “Statistical processing of experimental results”, ed. Moscow University Press, 1988 (in Russian).
[2]	https://www.eso.org/public/images/eso1907a/.
[3]	E. N. Terentiev, N. E. Terentyev//Izvestia RAN, PHYSICAL SERIES, 2015, volume 79, № 12, с. 1633-1637 (in Russian).
[4]	Terentiev, E. N. and Terentiev, N. E.//ISSN 1062-8738, Bulletin of the Russian Academy of Science. Physics, 2015, Vol. 79, No 12, pp. 1427-1431, DOI 10.3103/S1062873815120229.
[5]	E. N. Terentiev, N. E. Terentyev, Yu. A. Pirogov, I. I. Farshakova//SCIENTIFIC NOTES OF THE PHYSICAL FACULTY, 9 p., №6, 1761005,(2017) (in Russian).
[6]	Terentiev, E. N., Terentiev, N. E., Farshakova, I. I.//DOI: 10.1007/978-3-319-77788-7_19.
[7]	E. N. Terentiev, N. E. Shilin-Terentyev//doi.org/10.1007/978-3-030-11533-3_44.
[8]	E. N. Terentiev, I. I. Farshakova, I. N. Prikhodko, N. E. Shilin-Terentyev//doi: 10.11648/j.sjams.20190705.12, ISSN: 2376-9491 (Print); ISSN: 2376-9513 (Online).
[9]	E. N. Terentiev, I. I. Farshakova, N. E. Shilin-Terentyev//http://www.sciencepublishinggroup.com/journal/paperinfo?journalid=301&doi=10.11648/j.ajaa.20190703.11.
[10]	E. N. Terentiev, I. N. Prikhodko and I. I. Farshakova//Concept of mathematical microscope, AIP Conference Proceedings 2171, 110010 (2019); https://doi.org/10.1063/1.5133244.
[11]	The Event Horizon Telescope Collaboration, First M87 Event Horizon Telescope Results. I. The Shadow of the Supermassive Black Hole, The Astrophysical Journal Letters, 875: L1 (17pp), 2019 April 10, https://doi.org/10.3847/2041-8213/ab0ec7.
[12]	Bouman, Katherine L.; Johnson, Michael D.; Zoran, Daniel; Fish, Vincent L.; Doeleman, Sheperd S.; Freeman, William T. (2016). "Computational Imaging for VLBI Image Reconstruction": 913–922. arXiv: 1512.01413, doi: 10.1109/CVPR.2016.105, hdl: 1721.1/103077. Cite journal requires \|journal=(help).
[13]	E. N. Terentiev, I. N. Prikhodko and I. I. Farshakova//Problems of accurate localization objects in imagers, AIP Conference Proceedings 2171, 110009 (2019); https://doi.org/10.1063/1.5133243.
[14]	E. N. Terentiev, I. N. Prikhodko, and I. I. Farshakova//Applications of finite dimensional sampling theories, AIP Conference Proceedings 2195, 020019 (2019); https://doi.org/10.1063/1.5140119.

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APA Style

Evgeni Nikolaevich Terentiev, Nikolay Evgenyevich Shilin-Terentyev. (2021). Applications of Math Microscope in the Event Horizon Telescope. International Journal of Astrophysics and Space Science, 9(2), 21-31. https://doi.org/10.11648/j.ijass.20210902.11

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ACS Style

Evgeni Nikolaevich Terentiev; Nikolay Evgenyevich Shilin-Terentyev. Applications of Math Microscope in the Event Horizon Telescope. Int. J. Astrophys. Space Sci. 2021, 9(2), 21-31. doi: 10.11648/j.ijass.20210902.11

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AMA Style

Evgeni Nikolaevich Terentiev, Nikolay Evgenyevich Shilin-Terentyev. Applications of Math Microscope in the Event Horizon Telescope. Int J Astrophys Space Sci. 2021;9(2):21-31. doi: 10.11648/j.ijass.20210902.11

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@article{10.11648/j.ijass.20210902.11,
  author = {Evgeni Nikolaevich Terentiev and Nikolay Evgenyevich Shilin-Terentyev},
  title = {Applications of Math Microscope in the Event Horizon Telescope},
  journal = {International Journal of Astrophysics and Space Science},
  volume = {9},
  number = {2},
  pages = {21-31},
  doi = {10.11648/j.ijass.20210902.11},
  url = {https://doi.org/10.11648/j.ijass.20210902.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijass.20210902.11},
  abstract = {The paper describes the insides - the basic concepts of the Math Microscope, demonstrates the results of Super-Resolution images obtained from the Event Horizon Telescope and analyzes the results of the movement of clusters of stars that go around the Black Hole. The presence of point objects - single stars in the SR image allowed us to implement a new breakthrough approach in the problem of SR images of Powehi Black Hole in the concept of MM. In the paper, we reviewed and illustrated new concepts: Invertability Indicators and Adequacy Characteristics of discrete Models of Apparatus Functions. With these new concepts, in the inverse problem, for the first time, we were able to answer simple questions: What are we dealing with? Moreover, have we solved the inverse problem? The paper demonstrates the “manual solution” of the problem of Reconstruction of AFs and Super-Resolution on MM. In the Discussion at the end of the paper, we pose the problem of creating two Artificial Intelligences for the automated solution of the R&SR problem with the interpretation of the SR results of BH images from EHT.},
 year = {2021}
}

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TY  - JOUR
T1  - Applications of Math Microscope in the Event Horizon Telescope
AU  - Evgeni Nikolaevich Terentiev
AU  - Nikolay Evgenyevich Shilin-Terentyev
Y1  - 2021/06/30
PY  - 2021
N1  - https://doi.org/10.11648/j.ijass.20210902.11
DO  - 10.11648/j.ijass.20210902.11
T2  - International Journal of Astrophysics and Space Science
JF  - International Journal of Astrophysics and Space Science
JO  - International Journal of Astrophysics and Space Science
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EP  - 31
PB  - Science Publishing Group
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AB  - The paper describes the insides - the basic concepts of the Math Microscope, demonstrates the results of Super-Resolution images obtained from the Event Horizon Telescope and analyzes the results of the movement of clusters of stars that go around the Black Hole. The presence of point objects - single stars in the SR image allowed us to implement a new breakthrough approach in the problem of SR images of Powehi Black Hole in the concept of MM. In the paper, we reviewed and illustrated new concepts: Invertability Indicators and Adequacy Characteristics of discrete Models of Apparatus Functions. With these new concepts, in the inverse problem, for the first time, we were able to answer simple questions: What are we dealing with? Moreover, have we solved the inverse problem? The paper demonstrates the “manual solution” of the problem of Reconstruction of AFs and Super-Resolution on MM. In the Discussion at the end of the paper, we pose the problem of creating two Artificial Intelligences for the automated solution of the R&SR problem with the interpretation of the SR results of BH images from EHT.
VL  - 9
IS  - 2
ER  -

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Author Information

Evgeni Nikolaevich Terentiev

Department Mathematical Modelling and Informatics, Faculty of Physics, M. V. Lomonosov Moscow State University, Moscow, Russia
Nikolay Evgenyevich Shilin-Terentyev

EPAM Systems, Moscow, Russia

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Plain Text BibTeX RIS

APA Style

Evgeni Nikolaevich Terentiev, Nikolay Evgenyevich Shilin-Terentyev. (2021). Applications of Math Microscope in the Event Horizon Telescope. International Journal of Astrophysics and Space Science, 9(2), 21-31. https://doi.org/10.11648/j.ijass.20210902.11

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ACS Style

Evgeni Nikolaevich Terentiev; Nikolay Evgenyevich Shilin-Terentyev. Applications of Math Microscope in the Event Horizon Telescope. Int. J. Astrophys. Space Sci. 2021, 9(2), 21-31. doi: 10.11648/j.ijass.20210902.11

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AMA Style

Evgeni Nikolaevich Terentiev, Nikolay Evgenyevich Shilin-Terentyev. Applications of Math Microscope in the Event Horizon Telescope. Int J Astrophys Space Sci. 2021;9(2):21-31. doi: 10.11648/j.ijass.20210902.11

Copy | Download

@article{10.11648/j.ijass.20210902.11,
  author = {Evgeni Nikolaevich Terentiev and Nikolay Evgenyevich Shilin-Terentyev},
  title = {Applications of Math Microscope in the Event Horizon Telescope},
  journal = {International Journal of Astrophysics and Space Science},
  volume = {9},
  number = {2},
  pages = {21-31},
  doi = {10.11648/j.ijass.20210902.11},
  url = {https://doi.org/10.11648/j.ijass.20210902.11},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijass.20210902.11},
  abstract = {The paper describes the insides - the basic concepts of the Math Microscope, demonstrates the results of Super-Resolution images obtained from the Event Horizon Telescope and analyzes the results of the movement of clusters of stars that go around the Black Hole. The presence of point objects - single stars in the SR image allowed us to implement a new breakthrough approach in the problem of SR images of Powehi Black Hole in the concept of MM. In the paper, we reviewed and illustrated new concepts: Invertability Indicators and Adequacy Characteristics of discrete Models of Apparatus Functions. With these new concepts, in the inverse problem, for the first time, we were able to answer simple questions: What are we dealing with? Moreover, have we solved the inverse problem? The paper demonstrates the “manual solution” of the problem of Reconstruction of AFs and Super-Resolution on MM. In the Discussion at the end of the paper, we pose the problem of creating two Artificial Intelligences for the automated solution of the R&SR problem with the interpretation of the SR results of BH images from EHT.},
 year = {2021}
}

Copy | Download

TY  - JOUR
T1  - Applications of Math Microscope in the Event Horizon Telescope
AU  - Evgeni Nikolaevich Terentiev
AU  - Nikolay Evgenyevich Shilin-Terentyev
Y1  - 2021/06/30
PY  - 2021
N1  - https://doi.org/10.11648/j.ijass.20210902.11
DO  - 10.11648/j.ijass.20210902.11
T2  - International Journal of Astrophysics and Space Science
JF  - International Journal of Astrophysics and Space Science
JO  - International Journal of Astrophysics and Space Science
SP  - 21
EP  - 31
PB  - Science Publishing Group
SN  - 2376-7022
UR  - https://doi.org/10.11648/j.ijass.20210902.11
AB  - The paper describes the insides - the basic concepts of the Math Microscope, demonstrates the results of Super-Resolution images obtained from the Event Horizon Telescope and analyzes the results of the movement of clusters of stars that go around the Black Hole. The presence of point objects - single stars in the SR image allowed us to implement a new breakthrough approach in the problem of SR images of Powehi Black Hole in the concept of MM. In the paper, we reviewed and illustrated new concepts: Invertability Indicators and Adequacy Characteristics of discrete Models of Apparatus Functions. With these new concepts, in the inverse problem, for the first time, we were able to answer simple questions: What are we dealing with? Moreover, have we solved the inverse problem? The paper demonstrates the “manual solution” of the problem of Reconstruction of AFs and Super-Resolution on MM. In the Discussion at the end of the paper, we pose the problem of creating two Artificial Intelligences for the automated solution of the R&SR problem with the interpretation of the SR results of BH images from EHT.
VL  - 9
IS  - 2
ER  -

Copy | Download