Curves,
Surfaces,
Linear Imagery,
Metrics by Cayley–Klein.
UDC:
514.754, 514.133, 514.17, 514.174.5
Subject:
Geometry of Spaces with Generalized Projective Metric.
Main publications:
L. N. Romakina, “An eye as the tool of a choice of the Euclidean metric for the description of real physical space”, Journal of Basic and Applied Research International (IKP), 9:3 (2015), 147–154http://www.ikpress.org/
Lyudmila Romakina, “The area of a generalized polygon without parabolic edges of a hyperbolic plane of positive curvature”, Asian Journal of Mathematics and Computer Research, 10:4 (2016), 293–310
L. N. Romakina, Geometrii koevklidovoi i kopsevdoevklidovoi ploskostei, Izd-vo “Nauchnaya kniga”, Saratov, 2008, 279 с.
L. N. Romakina, Geometriya giperbolicheskoi ploskosti polozhitelnoi krivizny. Ch. 1: Trigonometriya, Izd-vo Sarat. un-ta, Saratov, 2013, 244 с. http://window.edu.ru/resource/006/80006
L. N. Romakina, Geometriya giperbolicheskoi ploskosti polozhitelnoi krivizny. Ch. 2: Preobrazovaniya i prostye razbieniya, Izd-vo Sarat. un-ta, Saratov, 2013, 274 с. http://window.edu.ru/resource/007/80007
L. N. Romakina, I. V. Ushakov, “Generalized Chaos game in an extended hyperbolic plane”, Theoret. and Math. Phys., 220:2 (2024), 1361–1384
2023
3.
L. N. Romakina, I. V. Ushakov, “Chaos game in an extended hyperbolic plane”, Theoret. and Math. Phys., 215:3 (2023), 793–804
4.
Lyudmila. N. Romakina, “Coordinates of the midpoint of a segment in an extended hyperbolic space”, International Electronic Journal of Geometry, 16:1 (2023), 272–282
L. N. Romakina, I. V. Ushakov,, “The Chaos game on polygons in a hyperbolic plane of positive curvature”, Informatsionnye tekhnologii v obrazovanii i nauke (ITON-2023): materialy IX Mezhdunarodnoi nauchno-prakticheskoi konferentsii v ramkakh IV Mezhdunarodnogo foruma po matematicheskomu obrazovaniyu (27 marta – 1 aprelya 2023 g., Kazan), eds. A.A. Agafonov, Izd-vo Akademii nauk RT, Kazan, 2023, 156–159https://kpfu.ru/portal/docs/F_970833811/ITON_2023.pdf
L. N. Romakina, “Constant rations for inflection points of a cubic curve with a node or an acnode”, Chebyshevskii Sb., 24:3 (2023), 122–138
8.
Romakina, L. N., “Podery oritsiklov na rasshirennoi giperbolicheskoi ploskosti”, Algebra, teoriya chisel, diskretnaya geometriya i mnogomasshtabnoe modelirovanie: Sovremennye problemy, prilozheniya i problemy istorii: Materialy XXII Mezhdunarodnoi konferentsii, posvyaschennoi 120-letiyu so dnya rozhdeniya akademika A. N. Kolmogorova i 60-letiyu so dnya otkrytiya shkoly-internata # 18 pri Moskovskom universitete. — Tula: Tul. gos. ped. un-t im. L. N. Tolstogo, https://www.elibrary.ru/download/elibrary_55080603_37282845.pdf (Tula, 26–29 sentyabrya 2023 goda), Tul. gos. ped. un-t im. L. N. Tolstogo, Tula, 2023, 340–342http://poivs.tsput.ru/conf/international/XXII/files/Conference2023S.pdf?v=3
2022
9.
L. N. Romakina, I. V. Ushakov,, “The Chaos game in the hyperbolic plane of positive curvature”, NONLINEAR DYNAMICS & INTEGRABILITY (NDI-2022) : Abstracts. (Satellite International Conference on NONLINEAR DYNAMICS & INTEGRABILITY and Scientific School “Nonlinear days” (NDI–2022) (Yaroslavl, June 27 — July 1, 2022), Yaroslavl: YarSU, 2022, 86–88https://lomonosov-msu.ru/file/event/6251/eid6251_attach_6196e3b7acf3be664a5374d942dbfff78b412c06.pdf
10.
Romakina, L. N., “O parabolicheskikh R-orbitakh vtorogo poryadka na rasshirennoi giperbolicheskoi ploskosti”, Matematika. Mekhanika, 24, eds. Khromova G. V., Blinkov Yu. A., Prokhorov D. V., Khromov A. P., Korobchenko E. V., Izd-vo Saratovskogo universiteta, Saratov, 2022, 48–53
2021
11.
Romakina, Lyudmila, “Isoptic Curves of Cycles on a Hyperbolic Plane of Positive Curvature”, ICGG 2020 - Proceedings of the 19th International Conference on Geometry and Graphics, eds. Cheng, Liang-Yee, Springer Nature, 2021, 943–946https://www.springer.com/gp/book/9783030634025#
12.
Lyudmila Romakina, “Isoptic Curves of Cycles on a Hyperbolic Plane of Positive Curvature”, International Conference on Geometry and Graphics (19th : 2021 : São Paulo) ICGG 2020 book of abstracts: livro digital, ISBN 978-65-89190-00-4, eds. Liang-Yee Cheng, Rubens Augusto Amaro Junior, Epusp, São Paulo, 2021, 193
13.
Lyudmila N. Romakina, “Hyperbolic Raisa Orbits of the Second Order in an Extended Hyperbolic Plane”, International Electronic Journal of Geometry, 14:1 (2021), 194–206
14.
Romakina, L. N., “O klassifikatsii trekhvershinnikov rasshirennoi giperbolicheskoi ploskosti po tipu polyarnoi osi”, Algebra, teoriya chisel, diskretnaya geometriya i mnogomasshtabnoe modelirovanie: sovremennye problemy, prilozheniya i problemy istorii : Materialy XIX Mezhdunarodnoi konferentsii, posvyaschennoi 200-letiyu so dnya rozhdeniya akademika P.L. Chebysheva, Tula, 18–22 maya 2021 goda. – Tula: Tulskii gosudarstvennyi pedagogicheskii universitet im. L.N. Tolstogo, 2021., ISBN 978-5-6045159-8-3 (Tula, 18–22 maya 2021 g.), Tulskii gos. ped. un-t im. L.N. Tolstogo, 2021, 232–233
15.
Romakina, L. N., “Polyariki rasshirennoi giperbolicheskoi ploskosti”, Materialy IV Mezhdunarodnoi nauchnoi konferentsii «Osennie matematicheskie chteniya v Adygee», ISBN 978-5-85108-381-5, izd-vo AGU, Maikop, 2021, 44–46
16.
Romakina, L. N., “Sootnosheniya v trekhrebernike tipa eee(I) rasshirennoi giperbolicheskoi ploskosti, obuslovlennye tipom ego polyarnoi osi”, Matematika. Mekhanika, 23, Izd–vo Saratovskogo un–ta, 2021, 52–55https://elibrary.ru/download/elibrary_48539110_81939523.pdf
Romakina, L. N., “Otnosheniya dlya tochek peregiba kubicheskoi krivoi s uzlovoi ili izolirovannoi tochkoi”, Materialy XVII Mezhdunar. konf., posv. stoletiyu so dnya rozhdeniya professorov B.M.Bredikhina, V.I.Nechaeva i S.B.Stechkina: Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy, prilozheniya i problemy istorii, Tulskii gos. ped. un-t im. L.N. Tolstogo, 2020, 2020, 427–429
2019
19.
Lyudmila N. Romakina, “Construction of cubic curves with a node”, Beitr Algebra Geom, 60:4 (2019), 761–781https://rdcu.be/buOiI
L. N. Romakina, “Inversiya otnositelno ellipticheskogo tsikla giperbolicheskoi ploskosti polozhitelnoi krivizny”, Trudy Instituta matematiki. NAN Belarusi, 27:1-2 (2019), 60–78
Lyudmila N. Romakina, “Helixes on Clifford Surfaces in a Hyperbolic Space of Positive Curvature”, 6TH INTERNATIONAL EURASIAN CONFERENCE ON MATHEMATICAL SCIENCES AND APPLICATIONS (IECMSA-2017) (Budapest, 15–18 August 2017), AIP Conference Proceedings, 1926, 020037, eds. Murat Tosun, Soley Ersoy and Kazim Ilarslan, American Institute of Physics, USA, 2018, 020037-1–020037-7aip.scitation.org/doi/10.1063/1.5020486
L. N. Romakina, “Svoistvo ortoskhemy rasshirennogo giperbolicheskogo prostranstva”, Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy i prilozheniya: Materialy XV Mezhdunar. konf., posvyaschennoi stoletiyu so dnya rozhdeniya professora Nikolaya Mikhailovicha Korobova, TGPU im. L. N. Tolstogo, Tula, 2018, 287–289www.mathnet.ru/ConfLogos/1304/Conference2018_1.pdf
L. Romakina, “To a question on the existence of regular mosaics on a hyperbolic plane of positive curvature”, Miskolc Mathematical Notes, 19:2 (2018), 1117–1132http://mat76.mat.uni-miskolc.hu/mnotes/article/2104
Lyudmila N. Romakina, “Regular and Equiangular Polygons of a Hyperbolic Plane of Positive Curvature”, This paper is devoted to the 225-th anniversary of the birth of Nikolai Ivanovich Lobachevsky, International Electronic Journal of Geometry, 10:2 (2017), 20–31https://dergipark.org.tr/en/download/article-file/680417
L. N. Romakina, “Ob'em konechnogo ortogonalnogo h-konusa v giperbolicheskom prostranstve polozhitelnoi krivizny”, Proceedings of the International Geometry Center, 10:2 (2017), 56–71
L. N. Romakina, “Elementy ob'ema v giperbolicheskom prostranstve polozhitelnoi krivizny”, International scientific conference «Algebraic and geometric methods of analysis». Odessa. Book of abstracts (Odessa, 31 May – 5 June, 2017), Odesskaya Natsionalnaya Akademiya pischevykh tekhnologii, Odessa, 2017, 135–136imath.kiev.ua/~topology/conf/agma2017/
L. N. Romakina, “Ploschad ellipticheskogo sektora oritsikla giperbolicheskoi ploskosti polozhitelnoi krivizny”, Pevznerovskie chteniya, 1 (2017), 60–65elibrary.ru/item.asp?id=30708358
41.
L. N. Romakina, “Metod vizualizatsii figur “vblizi beskonechnosti””, Matem. metody i informatsionnye tekhnologii upravleniya v nauke, obrazovanii i pravookhranitelnoi sfere: sb. mater. Vseros. nauchno-tekhn. konf. (Moskva – Ryazan, 27–28 aprelya 2017 g.), Akademiya prava i upravleniya Federalnoi sluzhby ispolneniya nakazanii, Ryazan, 2017, 321–323elibrary.ru/item.asp?id=29728241
42.
Lyudmila Romakina, “Loxodromic spirals on elliptic Clifford surfaces in a hyperbolic space of positive curvature”, Abstracts of the VI Congress of the Turkic World Mathematical Society (Astana, 2–5 October), L.N. Gumilyov Eurasian National University, Astana, 2017, 274www.twms-astana-2017.kz/site_media/media/uploads/site-1/download/Abstracts_TWMS-2017.pdf
L. N. Romakina, “Inversiya otnositelno absolyuta rasshirennoi giperbolicheskoi ploskosti”, N.I. Lobachevskii i matematicheskoe obrazovanie v Rossii, Materialy Mezhdunarodnogo foruma po matematicheskomu obrazovaniyu, posvyaschennogo 225-letiyu N.I. Lobachevskogo (Kazan, 18–22 oktyabrya 2017 g.), 1, Izd-vo Kazanskogo un-ta, Kazan, 2017, 111–114
45.
Romakina L. N., Kharchenko A. A., Kharchenko N. A., “Geometricheskie postroeniya na idealnoi oblasti ploskosti Lobachevskogo”, Materialy Mezhdunarodnogo foruma po matematicheskomu obrazovaniyu, posvyaschennogo 225-letiyu N.I. Lobachevskogo (Kazan, 18–22 oktyabrya 2017 g.), Izd-vo Kazanskogo un-ta, Kazan, 2017, 114–118
46.
Lyudmila N. Romakina, Review of the book Il’in, V.A.; Poznyak, È. G. Analytic geometry. Textbook for universities. 8th edition., 2017 (Published online) zbmath.org/?q=an:06763203
2016
47.
Lyudmila Romakina, “Svetlana Ribbons with Intersecting Axes in a Hyperbolic Plane of Positive Curvature”, Journal for Geometry and Graphics, 20:2 (2016), 209–224www.heldermann.de/JGG/JGG20/JGG202/jgg20016.htm
48.
Lyudmila N. Romakina, “Inversion with respect to a hypercycle of a hyperbolic plane of positive curvature”, Journal of Geometry, 107:1 (2016), 137–149
Lyudmila Romakina, “The Area of a Generalized Polygon without Parabolic Edges of a Hyperbolic Plane of Positive Curvature”, Asian Journal of Mathematics and Computer Research, 10:4 (2016), 293–310www.ikpress.org/abstract/5199
52.
L.N. Romakina, “Ellipticheskie ortrisy rasshirennoi giperbolicheskoi ploskosti”, Matematika: Fundamentalnye i prikladnye issledovaniya i voprosy obrazovaniya, materialy mezhdunarodnoi nauchno-prakticheskoi konferentsii (Ryazan, 26-28 aprelya 2016 g.), Ryazanskii gosudarstvennyi universitet imeni S.A. Esenina, Ryazan, 2016, 27–31
53.
L. N. Romakina, “Diskussiya o giperbolicheskoi geometrii. Otvet professoru V.V. Mironovu”, EVRAZIISKOE NAUChNOE OB'EDINENIE, 2016, no. 2(14), 7–10
54.
L. N. Romakina, “Ploschadi vpisannykh v gipertsikl pravilnykh mnogougolnikov giperbolicheskoi ploskosti polozhitelnoi krivizny”, Innovatsionnaya nauka, 2016, no. 6(3), 20–23
L. N. Romakina, “Partitions of a hyperbolic plane of positive curvature by correct horocyclic $n$-trapezes”, Chebyshevskii Sb., 16:3 (2015), 376–416
60.
L. N. Romakina, “Classification of tetrahedrons with not hyperbolic sides in a hyperbolic space of positive curvature”, Chebyshevskii Sb., 16:2 (2015), 208–221
Lyudmila Romakina, “About a Trapeze of the Type Hee(I) on a Hyperbolic Plane of Positive Curvature”, Asian Journal of Mathematics and Computer Research, 2:4 (2015), 1–11www.ikpress.org/abstract/3683
64.
Lyudmila Romakina, “An Eye as the Tool of a Choice of the Euclidean Metric for the Description of Real Physical Space”, Journal of Basic and Applied Research International, 9:3 (2015), 147–154www.ikpress.org/abstract/4148
65.
L. N. Romakina, “Razvitie predstavlenii o geometrii okruzhayuschego prostranstva”, EVRAZIISKOE NAUChNOE OB'EDINENIE, 1:10(10), Effektivnye issledovaniya sovremennosti (2015), 18–21
66.
L. N. Romakina, “Trapetsii kopsevdoevklidovoi ploskosti”, Vspominaya uchitelya, sbornik nauchnykh trudov, posvyaschënnyi 85-letiyu Galiny Vasilevny Kiotinoi, eds. L. N. Romakina, Izdatelstvo Saratovskogo universiteta, 2015, 79–84
67.
L. N. Romakina, “Klassifikatsiya tetraedrov trekhmernogo giperbolicheskogo prostranstva polozhitelnoi krivizny”, ALGEBRA, TEORIYa ChISEL I DISKRETNAYa GEOMETRIYa: SOVREMENNYE PROBLEMY I PRILOZhENIYa, Materialy XIII Mezhdunarodnoi konferentsii, posvyaschennoi vosmidesyatipyatiletiyu so dnya rozhdeniya professora Sergeya Sergeevicha Ryshkova (Tula, 25–30 maya 2015 g.), Tulskii gosudarstvennyi pedagogichekii universitet im. L.N. Tolstogo, Tula, 2015, 319–322
2014
68.
L. N. Romakina, “Carpets on simple $4$-contours on the hyperbolic plane of positive curvature”, Discrete Math. Appl., 24:2 (2014), 109–121
69.
L. N. Romakina, “Parabolic parallelograms of the plane $\widehat H$”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 14:1 (2014), 20–28
2015
70.
L. N. Romakina, “On the area of a trihedral on a hyperbolic plane of positive curvature”, Siberian Adv. Math., 25:2 (2015), 138–153
L. N. Romakina, “The theorem of the area of a rectangular trihedral of the hyperbolic plane of positive curvature”, Dal'nevost. Mat. Zh., 13:1 (2013), 127–147
73.
L. N. Romakina, “Hyperbolic parallelograms of the plane $\widehat H$”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 13:3 (2013), 43–52
2014
74.
L. N. Romakina, “Fan triangulations of a hyperbolic plane of positive curvature”, Siberian Adv. Math., 24:3 (2014), 204–221
2013
75.
L. N. Romakina, “Analogs of a formula of Lobachevsky for angle of parallelism on the hyperbolic plane of positive curvature”, Sib. Èlektron. Mat. Izv., 10 (2013), 393–407
76.
L. N. Romakina, “The chord length of a hypercycle in a hyperbolic plane of positive curvature”, Siberian Math. J., 54:5 (2013), 894–904
2016
77.
L. N. Romakina, “Cycles of the hyperbolic plane of positive curvature”, J. Math. Sci. (N. Y.), 212:5 (2016), 605–621
Romakina L.N., Geometriya giperbolicheskoi ploskosti polozhitelnoi krivizny : v 4-kh ch. Ch. 2: Preobrazovaniya i prostye razbieniya, eds. V avtorskoi redaktsii, Izdatelstvo Saratovskogo universiteta, Saratov, 2013
80.
L. N. Romakina, “O ploschadi ellipticheskogo chetyrekhugolnika Sakkeri na giperbolicheskoi ploskosti polozhitelnoi krivizny”, Matematika. Mekhanika, 2013, no. 15, 66–69
81.
L. N. Romakina, M. A. Bondareva, “Ob odnom metricheskom svoistve ovalnykh linii giperbolicheskikh ploskostei”, Matematika. Mekhanika, 15, Izd-vo Sarat. un-ta, Saratov, 2013, 70–73https://www.elibrary.ru/item.asp?id=23617358
2012
82.
L. N. Romakina, “Oval lines of the hyperbolic plane of positive curvature”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 12:3 (2012), 37–44
83.
L. N. Romakina, “Simple partitions of a hyperbolic plane of positive curvature”, Sb. Math., 203:9 (2012), 1310–1341
L. N. Romakina, “Finite closed 5-loops of extended hyperbolic plane”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 11:1 (2011), 38–49
2010
86.
L. N. Romakina, “Finite closed 3(4)-loops of extended hyperbolic plane”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 10:3 (2010), 14–26
87.
L.N. Romakina, “Razbieniya giperbolicheskoi ploskosti polozhitelnoi krivizny, porozhdennye pravilnym n-konturom”, TEORIYa OTNOSITELNOSTI, GRAVITATsIYa I GEOMETRIYa, Trudy mezhdunarodnoi konferentsii “Petrov 2010 anniversary symposium on general relativity and gravitation”. (Kazan, 1–6 noyabrya 2010 g.), eds. Sostaviteli: A. V. Aminova, S. V. Sushkov., Kazanskii (Privolzhskii) federalnyi universitet, Kazan, 2010, 227–232
88.
L. N. Romakina, “Analog mozaiki na giperbolicheskoi ploskosti polozhitelnoi krivizny”, Matematika. Mekhanika, 2010, no. 12, 69–72
2008
89.
Romakina L.N., Geometrii koevklidovoi i kopsevdoevklidovoi ploskostei, OOO Izd-vo “Nauchnaya kniga”, Saratov, 2008, 279 pp.
2000
90.
L. N. Romakina, “Izotropnye kongruentsii biaksialno-flagovogo prostranstva giperbolicheskogo tipa”, Differentsialnaya geometriya mnogoobrazii, 31 (2000), 65–73
1999
91.
L. N. Romakina, “Theory of curves in a biaffine flag space of hyperbolic type”, Russian Math. (Iz. VUZ), 43:9 (1999), 79–80
Presentations in Math-Net.Ru
1.
Ортосхемы расширенного гиперболического
пространства L. N. Romakina XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai Mikhailovich May 30, 2018 16:30
2025
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