Analytical images of Kepler’s equation solutions and their applications

Simple item page
dc.citation.epage358
dc.citation.issue2
dc.citation.journalTitleМатематичне моделювання та комп'ютинг
dc.citation.spage351
dc.contributor.affiliationЛьвівський національний університет імені Івана Франка
dc.contributor.affiliationIvan Franko National University of Lviv
dc.contributor.authorВаврух, М.
dc.contributor.authorДзіковський, Д.
dc.contributor.authorСтельмах, О.
dc.contributor.authorVavrukh, M.
dc.contributor.authorDzikovskyi, D.
dc.contributor.authorStelmakh, O.
dc.coverage.placenameЛьвів
dc.coverage.placenameLviv
dc.date.accessioned2025-03-04T10:28:18Z
dc.date.created2023-02-28
dc.date.issued2023-02-28
dc.description.abstractЗапропоновано прості швидкозбіжні алгоритми аналітичного розрахунку ексцентричної аномалії для довільного ексцентриситету 0 < e 6 ⩽ 1. Для ілюстрацій розраховано кінематичні характеристики комети Галлея як функції часу та виконано оцінку маси системи Галактика + NGC 224 на основі моделі з еліптичним відносним рухом.
dc.description.abstractThe simple fast-converging analytical calculations algorithms for eccentric anomaly are proposed for an arbitrary eccentricity 0 < e 6 ⩽ 1. The kinematic characteristics of Halley’s comet are calculated as the function of time. Mass of Galaxy + NGC 224 system using the model of elliptical relative motion is also estimated.
dc.format.extent351-358
dc.format.pages8
dc.identifier.citationVavrukh M. Analytical images of Kepler’s equation solutions and their applications / M. Vavrukh, D. Dzikovskyi, O. Stelmakh // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 2. — P. 351–358.
dc.identifier.citationenVavrukh M. Analytical images of Kepler’s equation solutions and their applications / M. Vavrukh, D. Dzikovskyi, O. Stelmakh // Mathematical Modeling and Computing. — Lviv : Lviv Politechnic Publishing House, 2023. — Vol 10. — No 2. — P. 351–358.
dc.identifier.doi10.23939/mmc2023.02.351
dc.identifier.urihttps://ena.lpnu.ua/handle/ntb/63428
dc.language.isoen
dc.publisherВидавництво Львівської політехніки
dc.publisherLviv Politechnic Publishing House
dc.relation.ispartofМатематичне моделювання та комп'ютинг, 2 (10), 2023
dc.relation.ispartofMathematical Modeling and Computing, 2 (10), 2023
dc.relation.references[1] Zadeh L. A. Fuzzy sets. Information and Control. 8 (3), 338–353 (1965).
dc.relation.references[2] Atanassov K. T. Intuitionistic fuzzy sets. Fuzzy Sets And Systems. 20 (1), 87–96 (1986).
dc.relation.references[3] Atanassov K. T. New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems. 61 (2), 137–142 (1994).
dc.relation.references[4] Atanassov K. T. Intuitionistic fuzzy sets. In: Intuitionistic Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol. 35. Physica, Heidelberg (1999).
dc.relation.references[5] Hadi–Vencheh A., Mirjaberi M. Fuzzy inferior ratio method for multiple attribute decision making problems. Information Sciences. 277, 263–272 (2014)
dc.relation.references[6] Joshi R., Kumar S. (R, S)-norm information measure and a relation between coding and questionnaire theory. Open Systems & Information Dynamics. 23 (03), 1650015 (2016).
dc.relation.references[7] Joshi R., Kumar S. A dissimilarity Jensen–Shannon divergence measure for intuitionistic fuzzy sets. International Journal of Intelligent Systems. 33 (11), 2216–2235 (2018).
dc.relation.references[8] Joshi R. A novel decision-making method using R-Norm concept and VIKOR approach under picture fuzzy environment. Expert Systems with Applications. 147, 113228 (2020).
dc.relation.references[9] Joshi R. A new picture fuzzy information measure based on Tsallis–Havrda–Charvat concept with applications in presaging poll outcome. Computational and Applied Mathematics. 39 (2), 71 (2020).
dc.relation.references[10] Arya V., Kumar S. A picture fuzzy multiple criteria decision-making approach based on the combined TODIM–VIKOR and entropy weighted method. Cognitive Computation. 13 (5), 1172–1184 (2021).
dc.relation.references[11] Arya V., Kumar S. Extended TODIM method based on VIKOR for q-rung orthopair fuzzy information measures and their application in MAGDM problem of medical consumption products. International Journal of Intelligent Systems. 36 (11), 6837–6870 (2021).
dc.relation.references[12] Garg H., Rani D. Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision-making. Expert Systems. 35 (6), e12325 (2018).
dc.relation.references[13] Garg H., Kumar K. Multiattribute decision making based on power operators for linguistic intuitionistic fuzzy set using set pair analysis. Expert Systems. 36 (4), e12428 (2019).
dc.relation.references[14] Garg H., Ali Z., Mahmood T. Algorithms for complex interval-valued q-rung orthopair fuzzy sets in decision making based on aggregation operators, AHP, and TOPSIS. Expert Systems. 38 (1), e12609 (2021).
dc.relation.references[15] Garg H., Rani D. An efficient intuitionistic fuzzy MULTIMOORA approach based on novel aggregation operators for the assessment of solid waste management techniques. Applied Intelligence. 52 (4), 4330–4363 (2022).
dc.relation.references[16] Garg H., Rani D. Novel distance measures for intuitionistic fuzzy sets based on various triangle centers of isosceles triangular fuzzy numbers and their applications. Expert Systems with Applications. 191, 116228 (2022).
dc.relation.references[17] Vlachos I., Sergiadis G. Intuitionistic fuzzy information – Applications to pattern recognition. Pattern Recognition Letters. 28 (2), 197–206 (2007).
dc.relation.references[18] Papakostas G. A., Hatzimichailidis A. G., Kaburlasos V. G. Distance and similarity measures between intuitionistic fuzzy sets: A comparative analysis from a pattern recognition point of view. Pattern Recognition Letters. 34 (14), 1609–1622 (2013).
dc.relation.references[19] Nguyen H. A novel similarity/dissimilarity measure for intuitionistic fuzzy sets and its application in pattern recognition. Expert Systems with Applications. 45, 97–107 (2016).
dc.relation.references[20] Jiang Q., Jin X., Lee S.-J., Yao S. A new similarity/distance measure between intuitionistic fuzzy sets based on the transformed isosceles triangles and its applications to pattern recognition. Expert Systems with Applications. 116, 439–453 (2019).
dc.relation.references[21] De S. K., Biswas R., Roy A. R. An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems. 117 (2), 209–213 (2001).
dc.relation.references[22] Hung K. Medical pattern recognition: applying an improved intuitionistic fuzzy cross-entropy approach. Advances In Fuzzy Systems. 2012, 863549 (2012).
dc.relation.references[23] Luo M., Zhao R. A distance measure between intuitionistic fuzzy sets and its application in medical diagnosis. Artificial Intelligence in Medicine. 89, 34–39 (2018).
dc.relation.references[24] Gau W.-L., Buehrer D. J. Vague sets. IEEE Transactions On Systems, Man, and Cybernetics. 23 (2), 610–614 (1993).
dc.relation.references[25] Bustince H., Burillo P. Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems. 79 (3), 403–405 (1996).
dc.relation.references[26] Szmidt E., Kacprzyk J. Intuitionistic fuzzy sets in some medical applications. International Conference on Computational Intelligence. 148–151 (2001).
dc.relation.references[27] Szmidt E., Kacprzyk J. A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. International Conference on Artificial Intelligence and Soft Computing. 388–393 (2004).
dc.relation.referencesen[1] Zadeh L. A. Fuzzy sets. Information and Control. 8 (3), 338–353 (1965).
dc.relation.referencesen[2] Atanassov K. T. Intuitionistic fuzzy sets. Fuzzy Sets And Systems. 20 (1), 87–96 (1986).
dc.relation.referencesen[3] Atanassov K. T. New operations defined over the intuitionistic fuzzy sets. Fuzzy Sets and Systems. 61 (2), 137–142 (1994).
dc.relation.referencesen[4] Atanassov K. T. Intuitionistic fuzzy sets. In: Intuitionistic Fuzzy Sets. Studies in Fuzziness and Soft Computing, vol. 35. Physica, Heidelberg (1999).
dc.relation.referencesen[5] Hadi–Vencheh A., Mirjaberi M. Fuzzy inferior ratio method for multiple attribute decision making problems. Information Sciences. 277, 263–272 (2014)
dc.relation.referencesen[6] Joshi R., Kumar S. (R, S)-norm information measure and a relation between coding and questionnaire theory. Open Systems & Information Dynamics. 23 (03), 1650015 (2016).
dc.relation.referencesen[7] Joshi R., Kumar S. A dissimilarity Jensen–Shannon divergence measure for intuitionistic fuzzy sets. International Journal of Intelligent Systems. 33 (11), 2216–2235 (2018).
dc.relation.referencesen[8] Joshi R. A novel decision-making method using R-Norm concept and VIKOR approach under picture fuzzy environment. Expert Systems with Applications. 147, 113228 (2020).
dc.relation.referencesen[9] Joshi R. A new picture fuzzy information measure based on Tsallis–Havrda–Charvat concept with applications in presaging poll outcome. Computational and Applied Mathematics. 39 (2), 71 (2020).
dc.relation.referencesen[10] Arya V., Kumar S. A picture fuzzy multiple criteria decision-making approach based on the combined TODIM–VIKOR and entropy weighted method. Cognitive Computation. 13 (5), 1172–1184 (2021).
dc.relation.referencesen[11] Arya V., Kumar S. Extended TODIM method based on VIKOR for q-rung orthopair fuzzy information measures and their application in MAGDM problem of medical consumption products. International Journal of Intelligent Systems. 36 (11), 6837–6870 (2021).
dc.relation.referencesen[12] Garg H., Rani D. Complex intuitionistic fuzzy power aggregation operators and their applications in multicriteria decision-making. Expert Systems. 35 (6), e12325 (2018).
dc.relation.referencesen[13] Garg H., Kumar K. Multiattribute decision making based on power operators for linguistic intuitionistic fuzzy set using set pair analysis. Expert Systems. 36 (4), e12428 (2019).
dc.relation.referencesen[14] Garg H., Ali Z., Mahmood T. Algorithms for complex interval-valued q-rung orthopair fuzzy sets in decision making based on aggregation operators, AHP, and TOPSIS. Expert Systems. 38 (1), e12609 (2021).
dc.relation.referencesen[15] Garg H., Rani D. An efficient intuitionistic fuzzy MULTIMOORA approach based on novel aggregation operators for the assessment of solid waste management techniques. Applied Intelligence. 52 (4), 4330–4363 (2022).
dc.relation.referencesen[16] Garg H., Rani D. Novel distance measures for intuitionistic fuzzy sets based on various triangle centers of isosceles triangular fuzzy numbers and their applications. Expert Systems with Applications. 191, 116228 (2022).
dc.relation.referencesen[17] Vlachos I., Sergiadis G. Intuitionistic fuzzy information – Applications to pattern recognition. Pattern Recognition Letters. 28 (2), 197–206 (2007).
dc.relation.referencesen[18] Papakostas G. A., Hatzimichailidis A. G., Kaburlasos V. G. Distance and similarity measures between intuitionistic fuzzy sets: A comparative analysis from a pattern recognition point of view. Pattern Recognition Letters. 34 (14), 1609–1622 (2013).
dc.relation.referencesen[19] Nguyen H. A novel similarity/dissimilarity measure for intuitionistic fuzzy sets and its application in pattern recognition. Expert Systems with Applications. 45, 97–107 (2016).
dc.relation.referencesen[20] Jiang Q., Jin X., Lee S.-J., Yao S. A new similarity/distance measure between intuitionistic fuzzy sets based on the transformed isosceles triangles and its applications to pattern recognition. Expert Systems with Applications. 116, 439–453 (2019).
dc.relation.referencesen[21] De S. K., Biswas R., Roy A. R. An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems. 117 (2), 209–213 (2001).
dc.relation.referencesen[22] Hung K. Medical pattern recognition: applying an improved intuitionistic fuzzy cross-entropy approach. Advances In Fuzzy Systems. 2012, 863549 (2012).
dc.relation.referencesen[23] Luo M., Zhao R. A distance measure between intuitionistic fuzzy sets and its application in medical diagnosis. Artificial Intelligence in Medicine. 89, 34–39 (2018).
dc.relation.referencesen[24] Gau W.-L., Buehrer D. J. Vague sets. IEEE Transactions On Systems, Man, and Cybernetics. 23 (2), 610–614 (1993).
dc.relation.referencesen[25] Bustince H., Burillo P. Vague sets are intuitionistic fuzzy sets. Fuzzy Sets and Systems. 79 (3), 403–405 (1996).
dc.relation.referencesen[26] Szmidt E., Kacprzyk J. Intuitionistic fuzzy sets in some medical applications. International Conference on Computational Intelligence. 148–151 (2001).
dc.relation.referencesen[27] Szmidt E., Kacprzyk J. A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. International Conference on Artificial Intelligence and Soft Computing. 388–393 (2004).
dc.rights.holder© Національний університет “Львівська політехніка”, 2023
dc.subjectрівняння Кеплера
dc.subjectексцентрична аномалія
dc.subjectістинна аномалія
dc.subjectкомета Галлея
dc.subjectмаса Місцевої системи Галактик
dc.subjectKepler’s equation
dc.subjecteccentric anomaly
dc.subjectHalley’s comet
dc.subjectmass of Local System of Galaxies
dc.titleAnalytical images of Kepler’s equation solutions and their applications
dc.title.alternativeАналітичні зображення розв’язків рівняння Кеплера та їх застосування
dc.typeArticle

Files

Original bundle

Now showing 1 - 2 of 2
Thumbnail Image
Name:
2023v10n2_Vavrukh_M-Analytical_images_of_Keplers_351-358.pdf
Size:
1.23 MB
Format:
Adobe Portable Document Format
Download
Thumbnail Image
Name:
2023v10n2_Vavrukh_M-Analytical_images_of_Keplers_351-358__COVER.png
Size:
314.69 KB
Format:
Portable Network Graphics
Download

License bundle

Now showing 1 - 1 of 1
Thumbnail Image
Name:
license.txt
Size:
1.83 KB
Format:
Plain Text
Description:
Download

Collections

Mathematical Modeling And Computing. – 2023. – Vol. 10, No. 2