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
2.
L. N. Romakina, I. V. Ushakov, “Chaos game in an extended hyperbolic plane”, Theoret. and Math. Phys., 215:3 (2023), 793–804
3.
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
4.
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, 156–159 https://kpfu.ru/portal/docs/F_970833811/ITON_2023.pdf
5.
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
6.
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, 340–342 http://poivs.tsput.ru/conf/international/XXII/files/Conference2023S.pdf?v=3
7.
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
8.
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, 943–946 https://www.springer.com/gp/book/9783030634025#
9.
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
10.
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
11.
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
12.
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
13.
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, 52–55 https://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
16.
Lyudmila N. Romakina, “Construction of cubic curves with a node”, Beitr Algebra Geom, 60:4 (2019), 761–781 https://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
18.
L. N. Romakina, “Svetovye petli na sferakh v rasshirennom giperbolicheskom prostranstve”, Dinamika. 2019. Yaroslavl : tezisy dokladov konferentsii. (Yaroslavl, 10–12 oktyabrya 2019 g.), Yaroslavl : YarGU, 2019, 88–91 https://lomonosov-msu.ru/file/event/5741/eid5741_attach_34bca7d13ad90787fd2cde9c393c8b8788cb41c3.pdf
19.
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
23.
Lyudmila Romakina, Leonid Bessonov, and Angelina Chernyshkova, “Modeling of curls of Agnesi in non-Euclidean planes”, AIP Conference Proceedings. American Institute of Physics, 2037 (2018), 020022-1–020022-6 http://aip.scitation.org/toc/apc/2037/1, https://doi.org/10.1063/1.5078477
24.
L. Romakina, “To a question on the existence of regular mosaics on a hyperbolic plane of positive curvature”, Miskolc Mathematical Notes, 19:2 (2018), 1117–1132 http://mat76.mat.uni-miskolc.hu/mnotes/article/2104
25.
L. N. Romakina, “Koordinaty seredin neparabolicheskikh otrezkov giperbolicheskoi ploskosti polozhitelnoi krivizny v kanonicheskom repere pervogo tipa”, Matematika. Mekhanika, 20, 2018, 70–72
26.
L. N. Romakina, “Ellipticheskie R-orbity vtorogo poryadka na rasshirennoi giperbolicheskoi ploskosti”, Evraziiskoe nauchnoe ob'edinenie, 1:10(44) (2018), 32–34 https://esa-conference.ru/wp-content/uploads/files/pdf/Romakina-Lyudmila-Nikolaevna3.pdf
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), 20–31 https://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
37.
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
38.
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
41.
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
42.
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
43.
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
47.
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
48.
L. N. Romakina, “Diskussiya o giperbolicheskoi geometrii. Otvet professoru V.V. Mironovu”, EVRAZIISKOE NAUChNOE OB'EDINENIE, 2016, no. 2(14), 7–10
49.
L. N. Romakina, “Ploschadi vpisannykh v gipertsikl pravilnykh mnogougolnikov giperbolicheskoi ploskosti polozhitelnoi krivizny”, Innovatsionnaya nauka, 2016, no. 6(3), 20–23
L. N. Romakina, “O ploschadi ellipticheskogo oritsiklicheskogo n-rebernika giperbolicheskoi ploskosti polozhitelnoi krivizny”, Matematika. Mekhanika, 2016, no. 18, 43–45
52.
L. N. Romakina, “Partitions of a hyperbolic plane of positive curvature by correct horocyclic $n$-trapezes”, Chebyshevskii Sb., 16:3 (2015), 376–416
53.
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
57.
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
58.
L. N. Romakina, “Razvitie predstavlenii o geometrii okruzhayuschego prostranstva”, EVRAZIISKOE NAUChNOE OB'EDINENIE, 1:10(10), Effektivnye issledovaniya sovremennosti (2015), 18–21
59.
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
60.
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
61.
L. N. Romakina, “Carpets on simple $4$-contours on the hyperbolic plane of positive curvature”, Discrete Math. Appl., 24:2 (2014), 109–121
62.
L. N. Romakina, “Parabolic parallelograms of the plane $\widehat H$”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 14:1 (2014), 20–28
63.
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
66.
L. N. Romakina, “Hyperbolic parallelograms of the plane $\widehat H$”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 13:3 (2013), 43–52
67.
L. N. Romakina, “Fan triangulations of a hyperbolic plane of positive curvature”, Siberian Adv. Math., 24:3 (2014), 204–221
68.
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
69.
L. N. Romakina, “The chord length of a hypercycle in a hyperbolic plane of positive curvature”, Siberian Math. J., 54:5 (2013), 894–904
70.
L. N. Romakina, “Cycles of the hyperbolic plane of positive curvature”, J. Math. Sci. (N. Y.), 212:5 (2016), 605–621
71.
L. N. Romakina, “O ploschadi ellipticheskogo chetyrekhugolnika Sakkeri na giperbolicheskoi ploskosti polozhitelnoi krivizny”, Matematika. Mekhanika, 2013, no. 15, 66–69
72.
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
73.
L. N. Romakina, “Simple partitions of a hyperbolic plane of positive curvature”, Sb. Math., 203:9 (2012), 1310–1341
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
83.
Romakina L.N., Geometrii koevklidovoi i kopsevdoevklidovoi ploskostei, OOO Izd-vo “Nauchnaya kniga”, Saratov, 2008 , 279 pp.
Proceedings
84.
L. N. Romakina, I. V. Ushakov,, “The Chaos game with arbitrary jump in an extended hyperbolic plane”, INTEGRABLE SYSTEMS &
NONLINEAR DYNAMICS
(ISND–2023) 4th
International Conference on INTEGRABLE SYSTEMS &
NONLINEAR DYNAMICS (Yaroslavl, September 25−29, 2023), Yaroslavl: YarSU, 2023, 123–124 https://lomonosov-msu.ru/file/event/8178/eid8178_attach_aa69e05e67bb6b924ef4401e9cd307ecf88b5997.pdf
85.
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, 86–88 https://lomonosov-msu.ru/file/event/6251/eid6251_attach_6196e3b7acf3be664a5374d942dbfff78b412c06.pdf
86.
L. N. Romakina, “O vybore evklidovoi modeli dlya opisaniya geometrii okruzhayuschego prostranstva”, Materialy mezhdunarodnoi konferentsii po algebre, analizu i geometrii, posvyaschennoi yubileyam vydayuschikhsya professorov Kazanskogo universiteta, matematikov Petra Alekseevicha (1895-1944) i Aleksandra Petrovicha (1926-1998) Shirokovykh (Kazan, 26 iyunya – 2 iyulya 2016 g.), Kazanskii universitet; izd-vo Akademii nauk RT, Kazan, 2016, 86kpfu.ru/main_page?p_sub=58462&p_member=25528&p_conf_lang=
Preprints
87.
Lyudmila N. Romakina, Construction of Cubic Curves with a Node (preprint), Preprint opublikovannoi stati, polnaya versiya kotoroi dostupna dlya prosmotra po ssylke https://rdcu.be/buOiI, 2018 , 21 pp. https://www.researchgate.net/publication/325987248_Construction_of_Cubic_Curves_with_a_Node
Miscellaneous
88.
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
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
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