optimality conditions,
degenerated control systems,
covering mappings,
mathematical models in economics,
equilibrium prices.
Subject:
Optimal control theory, extremal problems, nonlinear analysis, theory of covering mappings and its applications in mathematical economics
Main publications:
A.V. Arutyunov, N.G. Pavlova, “Topological properties of attainability sets of linear systems”, Differential Equations, 40:11 (2004), 1645–1648
N.G. Pavlova, “2-regularity and 2-normality conditions for systems with impulsive controls”, Yugoslav Journal of Operations Research, 17:2 (2007), 149–164
A.V. Arutyunov, S.E. Zhukovskiy, N.G. Pavlova, “Equilibrium price as a coincidence point of two mappings”, Zh. Vychisl. Mat. Mat. Fiz., 53:2 (2013), 225–237
A.V. Arutyunov, N.G. Pavlova, A.A. Shananin, “Equilibrium prices in an economic equilibrium model”, Matem. Mod., 28:3 (2016), 3–22
N.G. Pavlova, A.O. Remizov, “On isomorphisms of pseudo-Euclidean spaces with signature (p,n − p) for p = 2,3”, Linear Algebra and its Applications, 2018, № 541, 60–80
A. V. Arutyunov, S. E. Zhukovskiy, N. G. Pavlova, “Equilibrium price as a coincidence point of two mappings”, Comput. Math. Math. Phys., 53:2 (2013), 158–169
2.
N. G. Pavlova, “Study of the Continuous-Time Open Dynamic Leontief Model as a Linear Dynamical Control System”, Differ. Equ., 55:1 (2019), 113–119
3.
A. V. Arutyunov, N. G. Pavlova, A. A. Shananin, “New conditions for the existence of equilibrium prices”, Yugosl. J. Oper. Res., 28:1 (2018), 59–77
N. G. Pavlova, A. O. Remizov, “Geodesics on hypersurfaces in Minkowski space: singularities of signature change”, Russian Math. Surveys, 66:6 (2011), 1201–1203
5.
N. G. Pavlova, A. O. Remizov, “Completion of the classification of generic singularities of geodesic
flows in two classes of metrics”, Izv. Math., 83:1 (2019), 104–123
6.
N. G. Pavlova, “Necessary conditions for closedness of the technology set in dynamical Leontief model”, Eleventh International Conference “Management of large-scale system development” (MLSD) (Moskva, 1–3 oktyabrya 2018, IPU RAN), IEEE, 2018, 1–4
N. G. Pavlova, A. O. Remizov, “A complete classification of generic singularities of geodesic flows on 2-surfaces with pseudo-Riemannian metrics”, Russian Math. Surveys, 72:3 (2017), 577–579
10.
A. V. Arutyunov, N. G. Pavlova, “Topological properties of attainability sets of linear systems”, Differ. Equ., 40:11 (2004), 1645–1648
11.
N. D. Pazij, N. G. Pavlova, “Local analytic classification for quasi-linear implicit differential systems at transversal singular points”, J. Dyn. Control Syst., 28:3 (2022), 453–464
N. G. Pavlova, A. O. Remizov, “Hyperbolic Roussarie fields with degenerate quadratic part”, Russian Math. Surveys, 76:2 (2021), 366–368
13.
N. G. Pavlova, “Applications of the Theory of Covering Maps to the Study of Dynamic Models of Economic Processes with Continuous Time”, Mathematical Analysis With Applications (CONCORD-90, Ekaterinburg, Russia 2018), Springer Proc. in Math. & Stat., 318, Springer, 2020, 123–129
A. V. Arutyunov, N. G. Pavlova, A. A. Shananin, “Equilibrium prices in an economic equilibrium model”, Matem. Mod., 28:3 (2016), 3–22
15.
A. V. Arutyunov, N. G. Pavlova, “Equilibrium in market models described by differential equations”, Differ. Equ., 58:9 (2022), 1267–1276
16.
N. G. Pavlova, A. O. Remizov, “Oscillating and proper solutions of singular quasi-linear differential equations”, Adv. Syst. Sci. Appl., 22:4 (2022), 51–64
17.
A. V. Arutyunov, A. M. Kotyukov, N. G. Pavlova, “Equilibrium in Market Models with Known Elasticities”, Adv. Syst. Sci. Appl., 21:4 (2021), 130–144 "article.pdf"
18.
A. M. Kotyukov, S. O. Nikanorov, N. G. Pavlova, “Local Normal Forms of Autonomous Quasi-Linear Constrained Differential Systems”, Adv. Syst. Sci. Appl., 20:1 (2020), 119–127 "article.pdf"
19.
N. G. Pavlova, A. O. Remizov, “On isomorphisms of pseudo-Euclidean spaces with signature (p,n-p) for p = 2,3”, Linear Algebra Appl., 541 (2018), 60–80
20.
N. G. Pavlova, A. O. Remizov, “A brief survey on singularities of geodesic flows in smooth signature changing metrics on 2-surfaces”, Advances in Singularities and Foliations: Geometry, Topology and Applications (Salvador, Brazil, 2015), Springer Proc. in Math. & Stat., 222, Springer, 2018, 135–155
21.
N. G. Pavlova, “Zamknutost tekhnologicheskogo mnozhestva v dinamicheskikh proizvodstvennykh modelyakh”, Vestnik Tambovskogo un-ta. Seriya: estestv. i tekhn. nauki, 23:124 (2018), 666–673
22.
N. G. Pavlova, E. S. Belyakova, “O polozhenii ravnovesiya v modelyakh ekonomicheskogo ravnovesiya s tranzaktsionnymi izderzhkami”, Vestnik Tambovskogo un-ta. Seriya: estestv. i tekhn. nauki, 21:1 (2016), 9–16
23.
N. G. Pavlova, O. M. Bozhinskaya, “O topologicheskikh svoistvakh tekhnologicheskogo mnozhestva v dinamicheskoi modeli Leonteva s nepreryvnym vremenem”, Vestnik Tambovskogo un-ta. Seriya: estestv. i tekhn. nauki, 20:5 (2015), 1071–1078
24.
N. G. Pavlova, A. E. Bolotin, “Prilozhenie teorii nakryvayuschikh otobrazhenii k issledovaniyu modeli Errou–Debre s tranzaktsionnymi izderzhkami”, Vestnik Tambovskogo un-ta. Seriya: estestv. i tekhn. nauki, 19:2 (2014), 357–364
25.
N. G. Pavlova, A. E. Bolotin, “Dostatochnye usloviya suschestvovaniya polozheniya ravnovesiya v modeli “spros-predlozhenie””, Vestnik Tambovskogo un-ta. Seriya: estestv. i tekhn. nauki, 19:2 (2014), 349–356
26.
N. G. Pavlova, “Issledovanie ekonomicheskikh modelei metodami teorii nakryvayuschikh otobrazhenii”, Vestnik Tambovskogo un-ta. Seriya: estestv. i tekhn. nauki, 18:5-2 (2013), 2621–2624
27.
S. E. Zhukovskii, N. G. Pavlova, “O prilozhenii teorii nakryvayuschikh otobrazhenii k issledovaniyu nelineinoi modeli rynka”, Vestnik Tambovskogo un-ta. Seriya: estestv. i tekhn. nauki, 18:1 (2013), 47–48
28.
N. G. Pavlova, “Upravlyaemost traektorii v zadachakh optimalnogo upravleniya s fazovymi ogranicheniyami”, Vestnik Tambovskogo un-ta. Seriya: estestv. i tekhn. nauki, 16:4 (2011), 1140–1142
29.
N. G. Pavlova, “Usloviya optimalnosti i upravlyaemosti dlya dinamicheskikh impulsnykh sistem”, Vestnik Tambovskogo un-ta. Seriya: estestv. i tekhn. nauki, 15:4 (2010), 692–695
30.
N. G. Pavlova, “Lokalnaya upravlyaemost dinamicheskikh impulsnykh sistem”, Vestnik Tambovskogo un-ta. Seriya: estestv. i tekhn. nauki, 14:4 (2009), 714–715
31.
N. G. Pavlova, “Neobkhodimye usloviya ekstremuma dlya 2-normalnykh protsessov”, Vestnik RUDN. Seriya: Matematika, informatika, fizika., 2009, no. 1, 5–13 "Vestnik RUDN"
32.
A. V. Arutyunov, N. G. Pavlova, “Lokalnaya upravlyaemost dinamicheskikh sistem s impulsnymi upravleniyami”, Differents. uravneniya, 44:8 (2008), 1145–1146
33.
N. G. Pavlova, “2-regularity and 2-normality conditions for systems with impulsive controls”, Yugosl. J. Oper. Res., 17:2 (2007), 149–164
34.
N. G. Pavlova, “Neobkhodimye i dostatochnye usloviya ekstremuma dlya zadach optimalnogo impulsnogo upravleniya”, Vestnik Voronezhskogo un-ta. Seriya: fizika, matematika, 2007, no. 1, 105–111 "Vestnik VGU"
35.
A. M. Kotyukov, N. G. Pavlova, “complex system, equilibrium, covering map, coincidence point, elastisity”, UBS, 107 (2024), 6–27
36.
A. N. Kurbatskii, N. G. Pavlova, A. O. Remizov, “Singularities of geodesic flows and lines in pseudo-Finsler spaces. III”, Tambov University Reports. Series: Natural and Technical Sciences, 22:3 (2017), 539–551
37.
N. G. Pavlova, “On the application of the results of covering mappings theory for the study of dynamical models of economic processes”, Tambov University Reports. Series: Natural and Technical Sciences, 22:6 (2017), 1304–1308
38.
B. O. Volkov, O. A. Zagryadskii, N. G. Pavlova, A. O. Remizov, Elementy teorii dinamicheskikh sistem na ploskosti, Izd-vo MFTI, Moskva, 2024 , 104 pp. "Researchgate"
39.
N. G. Pavlova, A. O. Remizov, Introduction to Singularity Theory, MIPT, Moscow, 2022 , 181 pp. "Researchgate
40.
N. G. Pavlova, A. O. Remizov, “Correction to the article “Smooth functions, formal series and Whitney theorems ””, Math. Ed., 2020, no. 1(93), 69
41.
N. G. Pavlova, A. O. Remizov, “Smooth functions, formal series, Whitney theorems, finished”, Math. Ed., 2017, no. 3(83), 13–27
42.
N. G. Pavlova, A. O. Remizov, “Smooth Functions, Formal Series, and Whitney Theorems”, Math. Ed., 2016, no. 3(79), 49–65
