Editor Profile

Prof. Dr. hab. Anatolij K. Prykarpatski, Ph.D.
Full Professor
Present
Cracov University of Technology
Krakow
Poland

Name: Prykarpatski
First name: Anatolij
Nationality: Poland
Gender: Male
Birthdate: October 07, 1953
Place: Town Boryslav of Lviv region, Ukraine
Prefered languages: English, mediocry Francais
Professional email: pryk.anat@cybergal.com
Private email: pryk.anat@ua.fm
AFFILIATION:
The Department of Applied Mathematics at the Cracov University of Technology,
Krakow, Poland
Position: Full Professor of Mathematical Physics
Title: Professor of Mathematical Physics - (1995 - nominated by the Ministry of Education and Science of Ukraine, Kyiv, Ukraine; 2002 - nominated by the Ministry of Education, Warsaw, Poland
EDUCATION
Student: (1970-1975) - the Ivan Franko Lviv State University, the Physics Department, 1 Universytetska Str., Lviv city, 79000 Ukraine (Master Degree)
Graduate Student: (1977-1980)- the Dept. of Mathematical Physics at the Institute of Mathematics of the National Academy of Sciences of Ukraine, 3 Tereshchenkivska Str., Kyiv 01601 UkrSSR- Ph.D. in Differential Equations and Mathematical Physics, 30.10.1980: Thesis: "The integrability investigation of the ordinary Riccati and some partial differential equations of mathematical physics")
Doctor of Mathematics and Physics Habilitation: Thesis: "Investigation of nonlinear dynamical systems of statistical and mathematical physics by functional-operator methods";
17.06.1987- at the Laboratory of Theoretical Physics of the Joint Institute for Nuclear Research, Dubna, Moscow region, 141980, Russia, USSR.
PROFESSIONAL EXPERIENCE
Visisting Professor: (2023-2024) - The Department of Mathematical Sciences at the UAE-University, Al Ain, UAE
Professor: (2018-present) The Department of Applied Mathematics at the Cracov University of Technology, Krakow, Poland
Visisting Professor: (2019, Spring Semester) - Dept. of Mathematical Sciences at the New Jersey Institute of Technology of Newark NJ, USA, and the Dept. of Applied Mathematics and Computer Science at the Rutgers University, New Brunswick NJ, USA
Visisting Professor: (2017, Summer Semester) - Dept. of Mathematical Sciences at the New Jersey Institute of Technoilogy of Newark, NJ USA
Visisting Professor: (2015, Summer Semester) -Dept. of Mathematical Sciences at the New Jersey Institute of Technoilogy of Newark, NJ USA
Visisting Professor: (2015, May-June) - Department of Physics at the Massachusette Institute of Technology (MIT), Boston, MA, USA
Visiting Professor: (2015, Spring Semester) - the Mathematics Department at the Haceteppe University of Ankara, Turkey
Visiting Professor: (2013, Spring Semester) - the Mathematics and Physics Departments of the Hacettepe University of Ankara, Turkey
Visiting Professor: (2010, Spring Semester)- the Mathematics, Physics Departments of Turku University, Turku, Finland
- Differential Gepmetric and Algebraic Methods;
- Dynamical systems Theory;
- Applied Mathematics and Mathematical Physics;
- Quantum Mathematics in Computer Science and Applications
- Mathematics
- Physics
- Computer Science
- Dynamaical Systems of Mathematical Physics
- Differential Equations
- Spectral Theory and Inverse Spectral Analysis
- Differential Geometric Structures on Manifolds
- Operator Methods and Variational Analysis
- Lie-Algebraic Methods and Symmetry Analysis
- Ergodic Theory and Applications
- Complex Manifolds and Analytical Structures
- Linearization Covering Technique and its Application to Integrable Nonlinear Differential Systems, Symmetry, Integrability and Geometry: Methods and Applications, SIGMA 14 (2018), 02, 15 pages, "On the (by: Anatolij K. Prykarpatski)
- Generalized multidimensional Boole type transformations, their discretization and ergodicity, Chaotic Modeling and Simulation, CMSIM 3: 369-376, 2018; (by: Anatolij K. Prykarpatski) Theory of Multidimensional Delsarte--Lions Transmutation Operators. I, Ukrainian Mathematical Journal, 2019, Volume 70, Issue 12, pp 1913--1952 Theory of Multidimensional Delsarte--Lions Transmutation Operators. II, Ukrainian Mathematical Journal, 2019, Volume 71, Issue 2, pp 345---361 (with A.M. Samoilenko and others) Ergodic deformations of nonlinear Hamilton systems and local homeomorphism of metric spaces, Journal of Mathematical Sciences, 2019, Vol. 241, No.1, p. 27-35 (with T. Banakh) Quantum Current Algebra Symmetries and Integrable Many-Particle Schredinger Type Quantum Hamiltonian Operators, Symmetry, 2019, 11, 975; doi:10.3390/sym11080975 (with Dominik Prorok) New fractional nonlinear integrable Hamiltonian systems, Applied Mathematics Letters 88 (2019) 41--49, (with Oksana Ye. Hentosh and others) A.M. Samoilenko, Ya.A. Prykarpatsky, D. Blackmore, and A.K. Prykarpatsky, The theory of multidimensional Delsarte-Lions transmuattion operators. I"", Ukrainian Mathematical Journal, 70(12) (2019), 1913-1952;
- A.M. Samoilenko, Ya.A. Prykarpatsky, D. Blackmore, and A.K. Prykarpatsky, "The theory of multidimensional Delsarte-Lions transmuattion operators. II", Ukrainian Mathematical Journal, 71(6) (2019), 921-953
- Orest D. Artemovych, Denis Blackmore, Anatolij K. Prykarpatski. "Non-associative structures of commutative algebras related with quadratic Poisson brackets", European Journal of Mathematics (2020) 6:208--231; https://doi.org/10.1007/s40879-020-00398-w
- Orest D. Artemovych, Alexander A. Balinsky, Anatolij K. Prykarpatski, "Hamiltonian operators and related differential-algebraic Balinsky-Novikov, Riemann and Leibniz type structures on nonassociative noncommutative algebras", Proceedings of the International Geometry Center, Vol. 12, no. 4 (2019) pp. 1--49
- Alexander A. Balinsky, Denis Blackmore, Radosław Kycia and Anatolij K. Prykarpatski, "Geometric Aspects of the Isentropic Liquid Dynamics and Vorticity Invariants", Entropy 2020, 22, 1241; doi:10.3390/e22111241
- N. N. Bogolubov, Jr., D. Prorok and A. K. Prykarpatski, "Integrability Aspects of the Current Algebra Representation and the Factorized Quantum Nonlinear Schrodinger Type Dynamical Systems", Particles and Nuclei, 2020, Vol. 51, No. 4, pp. 434--442.
- Ludwik Byszewski, Denis Blackmore, Alexander A. Balinsky, Anatolij K. Prykarpatski and Mirosław Lustyk, "Solvability, Completeness and Computational Analysis of A Perturbed Control Problem with Delays", Mathematics and Statistics 8(2): 187-200, 2020; DOI: 10.13189/ms.2020.080215
- Anatolij K.Prykarpatski, "On symmetry analysis of differential systems on functional manifolds", J. Math.Anal.Appl.490 (2020), 124326
- Lev I. Ivankiv, Yarema A. Prykarpatsky, Valeriy H. Samoilenko and Anatolij K. Prykarpatski, "Quantum Current Algebra Symmetry and Description of Boltzmann Type Kinetic Equations in Statistical Physics", Symmetry 2021, 13, 1452. https://doi.org/10.3390/sym13081452
- Anatolij K. Prykarpatski and Alexander A. Balinsky, "On Symmetry Properties of Frobenius Manifolds and Related Lie-Algebraic Structures", Symmetry 2021, 13, 979. https://doi.org/10.3390/sym13060979
- Balinsky A.A., Prykarpatski A.K. "On the Finite Dimensionality of Closed Subspaces in Lp(M, dm) \ Lq(M, dn)". Axioms, 2021, 10, 275. https://doi.org/ 10.3390/axioms10040275
- Blackmore D.; Balinsky, A.A.; Kycia, R. and Prykarpatski A.K., " Entropy and Ergodicity of Boole-Type Transformations". Entropy 2021, 23, 1405. https://doi.org/10.3390/ e23111405
- Prykarpatsky, Y.A.; Urbaniak, I.; Kycia, R.A.; Prykarpatski, A.K. "Dark Type Dynamical Systems: The Integrability Algorithm and Applications.", Algorithms 2022, 15, 266. https://doi.org/10.3390/a15080266
- A. Balinsky, V. V. Gafiychuk, B. Yu. Kyshakevych, and A. K. Prykarpatsky, "On the dynamics of matrix models for immune clonal netwots", Journal of Mathematical Sciences, Vol. 263, No. 2, May, 2022; DOI 10.1007/s10958-022-05920-x
- Denis Blackmore, Mykola M Prytula and Anatolij K Prykarpatski, "Quasi-linearization and stability analysis of some self-dual, dark equations and a new dynamical system", Commun. Theor. Phys. 74 (2022) 105007 (8pp)
- Denis Blackmore, Yarema Prykarpatsky, Mykola M. Prytula, Denys Dutykh and Anatolij K. Prykarpatski, "On the integrability of a new generalized Gurevich-Zybin dynamical system, its Hunter-Saxton type reduction and related mysterious symmetries", Analysis and Mathematical Physics (2022), 12:66; https://doi.org/10.1007/s13324-022-00662-0
- Prykarpatski, A.K.; Balinsky, A.A. Special Issue Editorial: "Symmetry of Hamiltonian Systems: Classical and Quantum Aspects", Symmetry 2023, 15, 96. https:// doi.org/10.3390/sym15010096
- Prykarpatski, A.K. "Quantum Current Algebra in Action: Linearization, Integrability of Classical and Factorization of Quantum Nonlinear Dynamical Systems." Universe 2022, 8, 288. https://doi.org/10.3390/universe8050288
- Hentosh O. E., Prykarpatsky Ya.A., Balinsky A.A. and Prykarpatski A.K. "Geometric structures on orbits of loop diffeomorphism groups and related heavenly type Hamiltonian systems", Ukrainian Mathematical Journal, Vol. 74, No. 8, January, 2023; DOI 10.1007/s11253-023-02129-2
- Prykarpatski, A.K.; Pukach, P.Y.; Vovk, M.I. Symplectic Geometry Aspects of the Parametrically-Dependent Kardar--Parisi--Zhang Equation of Spin Glasses Theory, Its Integrability and Related Thermodynamic Stability. Entropy 2023, 25, 308. https://doi.org/10.3390/e25020308
- Balinsky A.A., Prykarpatski, A.K.; Pukach, P.Y.; Vovk, M.I. On the symplectic structure deformations related to the Monge-Ampere equation on the Kahler Manifold. Ukr. Mathem. Journal, 2023, 75(1), p. 28-37
- Prykarpatski Anatolij K. and Bovdi Victor A. The Courant Type Algebroids, the Coadjoint Orbits, and Related Integrable Flows. Geometric Methods in Physics XL, Trends in Mathematics, https://doi.org/10.1007/978-3-031-62407-0_31
- Prykarpatski, A.K.; Dilnyi, V.M.; Pukach, P.Y.; Vovk, M.I. Supersymmetric Integrable Hamiltonian Systems, Conformal Lie Superalgebras K(1, N = 1, 2, 3), and Their Factorized SemiSupersymmetric Generalizations. Symmetry 2024, 16, 1441. https://doi.org/10.3390/sym16111441
- Balinsky, A.A., Bovdi, V.A., Prykarpatski, A.K. On the Quantum Deformations of Associative Sato Grassmannian Algebras and the Related Matrix Problems (2024) Symmetry, 16 (1), art. no. 54: DOI: 10.3390/sym16010054
- Oksana Hentosh and Anatolij Prykarpatski. Rational factorization of Hamiltonian flows in the space dual to the Lie algebra of fractional integro-differential operators and Benney - type integrable htydrodynamic systems. Journal of Mathematical Sciences, Vol. 279, N3, 2024, 308-329; DOI 10.1007/s10958-024-07016-0
- Balinsky, A.A.; Bovdi, V.A.; Prykarpatski, A.K. On the Quantum Deformations of Associative Sato Grassmannian Algebras and the Related Matrix Problems. Symmetry 2024, 16, 54. https://doi.org/ 10.3390/sym16010054
- Prykarpatski Anatolij K. , Pukach Petro Y., and Vovk Myroslava I. On the Dual Representation of the Congruence Kernels and the Related Delsarte Type Transmutations of Multidimensional Differential Operators. Springer Nature Switzerland AG 2024: M. Ptak et al. (eds.), Operator and Matrix Theory, Function Spaces, and Applications, Operator Theory: Advances and Applications 295, https://doi.org/10.1007/978-3-031-50613-0_
- Balinsky, A.A., Prykarpatski, A.K., Pukach, P.Y., Vovk, M.I. On the Deformations of Symplectic Structure Related to the Monge--Ampere Equation on the Kehler Manifold P 2(ℂ). Ukrainian Mathematical Journal, 2023, 75, pp. 29-39; DOI: 10.1007/s11253-023-02183-w
- Anatolij K. Prykarpatski and Victor A. Bovdi. The Courant Type Algebroids, the Coadjoint Orbits, and Related Integrable Flows. Springer Nature Switzerland AG P. Kielanowski et al. (eds.), Geometric Methods in Physics XL, Trends in Mathematics, 2024, 441-452; https://doi.org/10.1007/978-3-031-62407-0_31
- Hentosh, O.E., Prykarpatskyy, Y.A., Balinsky, A.A., Prykarpatski, A.K. Geometric Structures on the Orbits of Loop Diffeomorphism Groups and Related Heavenly-Type Hamiltonian Systems. II (2023) Ukrainian Mathematical Journal, 74 (9), 2023, 1348-1368. DOI: 10.1007/s11253-023-02140-7
- Hentosh, O.E., Prykarpatskyy, Y.A., Balinsky, A.A., Prykarpatski, A.K. Geometric Structures on the Orbits of Loop Diffeomorphism Groups and Related Heavenly-Type Hamiltonian Systems. I (2023) Ukrainian Mathematical Journal, 74 (8), 2023, pp. 1175-1208. DOI: 10.1007/s11253-023-02129-2
- Prykarpatski, A.K., Bovdi, V.A. On Some Aspects of the Courant-Type Algebroids, the Related Coadjoint Orbits and Integrable Systems. (2024) Symmetry, 16 (1), art. no. 76, DOI: 10.3390/sym16010076
- K. Prykarpatski1 and A. A. Balinsky. The two-dimensional Boole-type transform and its ergodicity. Journal of Mathematical Sciences, Vol. 278, No. 6, February, 2024, 1055-1076; DOI 10.1007/s10958-024-06977-6
- Anatolij K. Prykarpatski, Victor A. Bovdi, Myroslava I. Vovk and Petro Ya. Pukach. On parametric generalizations of the Kardar-Parisi-Zhang equation and their integrability. Journal of Physics: Conference Series 2667 (2023) 012043; doi:10.1088/1742-6596/2667/1/012043
- Anatolij K. Prykarpatski. On the electron spin and spectrum energy problems within the Fock many temporal and Feynman proper time paradigms. Journal of Physics: Conference Series 2482 (2023) 012017; doi:10.1088/1742-6596/2482/1/012017
- Myroslava I. Vovk, Petro Ya. Pukach, Volodymyr M. Dilnyi, Anatolij K. Prykarpatski. Hilbert Space Decomposition Properties of Complex Functions and Their Applications. Contemporary Mathematics, Volume 4 Issue 4(2023), 702-708 http://ojs.wiserpub.com/index.php/CM/
- Prykarpatski, A.K.; Pukach, P.Y.; Vovk, M.I. Symplectic Geometry Aspects of the ParametricallyDependent Kardar--Parisi--Zhang Equation of Spin Glasses Theory, Its Integrability and Related Thermodynamic Stability. Entropy. 2023, 25, 308. https://doi.org/ 10.3390/e25020308
- Orest D. Artemovych, Denis L. Blackmore, Radoslaw A. Kycia, and Anatolij K. Prykarpatski. New Dubrovin-type integrability theory applications of differential rings. Contemporary Mathematics, Volume 789, 2023, 19-39; https://doi.org/10.1090/conm/789/15838
- Anatolij K. Prykarpatski, Victor A. Bovdi. On the Lie-Algebraic Integrability of the Calogero-Degasperis Dynamical System and Its Generalizations. Contemporary Mathematics, Volume 4 Issue 4(2023), 750-768; http://ojs.wiserpub.com/index.php/CM/
- Anatolij K. Prykarpatski, Petro Ya. Pukach, and Myroslava I. Kopych The Parametrically Extended Kardar--Parisi--Zhang Equation, Its Dark-Type Generalization, and Integrability. Springer Nature Switzerland AG 2023: Kielanowski et al. (eds.), Geometric Methods in Physics XXXIX, Trends in Mathematics, (2023), 233-254. https://doi.org/10.1007/978-3-031-30284-8_21
- Myroslava I Vovk, Petro Ya Pukach and Anatolij K Prykarpatski. A remark on a perturbed Benjamin-Bona-Mahony type equation and its complete integrability. Ann Math Phys, 6(1): 021-025. DOI: https://dx.doi.org/10.17352/amp.000071
- A charged hadronic string model within the R.P.Feynman paradigm and vacuum field the ory approach 2025, Journal of Physics - Conference Series; https://iopscience.iop.org/article/10.1088/1742-6596/2987/1/012009;
- The Courant type algebroids, the coadjoint orbits, and related integrable flows. Geometric Methods in Physics XL : Workshop, Białowieża, Poland, 2023; Prykarpatski, Anatolij K. and Pukach, Petro Y. and Vovk, Myroslava i.; https://link.springer.com/chapter/10.1007/978-3-031-62407-0_31
- On the dual representation of the Congruence Kernels and the related Delsarte type transmutations of multidimensional differential operators. Operator and Matrix Theory, Function Spaces, and Applications : International Workshop on Operator Theory and its Applications 2022, Kraków, Poland; https://link.springer.com/chapter/10.1007/978-3-031-50613-0_13
- On the quantum deformations of associative sato grassmannian algebras and the related matrix problems. (by: Balinsky, Alexander A. and Bovdi, Victor A. and Prykarpatski, Anatolij) ; https://www.mdpi.com/2073-8994/16/1/54
- Rational factorization of Hamiltonian flows in the space dual to the Lie algebra of fractional integrodifferential operators and Benney-type integrable hydrodynamic systems (by: Hentosh, Oksana and Prykarpatski, Anatolij), Journal of Mathematical Sciences; https://link.springer.com/article/10.1007/s10958-024-07016-0
- On some aspects of the courant-type algebroids, the related coadjoint orbits and integrable systems. (by: Prykarpatski, Anatolij and Bovdi, Victor A.) Symmetry, 2024; www.mdpi.com/2073-8994/16/1/76
- Supersymmetric integrable Hamiltonian Systems, conformal Lie superalgebras K(1,N =1,2,3), and their factorized semi-supersymmetric generalizations. (By: Prykarpatski, Anatolij and Dilnyi, Volodymyr and Pukach, Petro Ya.and Vovk, Myroslava I. Symmetry, 2024; https://www.mdpi.com/2073-8994/16/11/1441
- Wstęp do równań fizyki matematycznej, Wydawnictwo PK, 2023 (by: Prykarpatski, Anatolij and Kycia, Radosław Antoni); isbn = {978-83-67188-54-8
- New Dubrovin-type integrability theory applications of differential rings (by: Artemovych, Orest D. and Blackmore, Denis L. and Kycia, Radosław A. and Prykarpatski, Anatolij K.) in: The Diverse World of PDEs Algebraic and Cohomological Aspects : Alexandre Vinogradov Memorial Conference Diffieties, Cohomological Physics, and Other Animals. 2023; Contemporary Mathematics; doi:10.1090/conm/789/15838, isbn: 978-1-4704-7409-6 (eBook); https://www.ams.org/books/conm/789/
- The parametrically extended Kardar--Parisi--Zhang equation, its dark-type generalization, and integrability. (by: Prykarpatski, Anatolij K. and Pukach, Petro Ya. and Kopych, Myroslava I.) Geometric Methods in Physics XXXIX, 2023; https://link.springer.com/chapter/10.1007/978-3-031-30284-8_21
- On the deformations of symplectic structure related to the Monge--Ampere equation on the Kohler manifold P2(ℂ)}. Ukrainian Mathematical Journal, 2023; https://link.springer.com/article/10.1007/s11253-023-02183-w#rightslink
- Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. I. (by: Hentosh, O. E. and Prykarpatskyy, Ya. A. and Balinsky, A. A. and Prykarpatski, A. K.), Ukrainian Mathematical Journal, 2023; https://link.springer.com/article/10.1007/s11253-023-02129-2
- Geometric structures on the orbits of loop diffeomorphism groups and related heavenly-type Hamiltonian systems. II. (by: Hentosh, O. E. and Prykarpatskyy, Ya. A. and Balinsky, A. A. and Prykarpatski, A. K.), Ukrainian Mathematical Journal, 2023; https://link.springer.com/article/10.1007/s11253-023-02140-7
- On the Lax-type Hamiltonian flows in the space dual to the Lie algebra of fractional integrodifferential operators. (by: Hentosh, Oksana and Prykarpatski, Anatolij), Nonlinear Oscillations, 2023 https://imath.kiev.ua/~nosc/web/show_article.php?article_id=1422
- On parametric generalizations of the Kardar-Parisi-Zhang equation and their integrability. (by: Prykarpatski, Anatolij and Bovdi, Victor A. and Vovk, Myroslava I. and Pukach, Petro Ya.), Journal of Physics - Conference Series, 2023; https://iopscience.iop.org/article/10.1088/1742-6596/2667/1/012043}
- On the Lie-algebraic integrability of the Calogero-Degasperis dynamical system and its generalizations (by: Prykarpatski, Anatolij and Bovdi, Victor A.), Contemporary Mathematics, 2023, https://ojs.wiserpub.com/index.php/CM/article/view/2955
- On the electron spin and spectrum energy problems within the Fock many temporal and Feynman proper time paradigm (by: Prykarpatski, Anatolij K.), Journal of Physics - Conference Series, 2023; https://iopscience.iop.org/article/10.1088/1742-6596/2482/1/012017
- Symplectic geometry aspects of the parametrically-dependent Kardar-Parisi-Zhang equation of spin glasses theory, its integrability and related thermodynamic stability, Entropy, 2023; https://www.mdpi.com/1099-4300/25/2/308}
- A remark on a perturbed Benjamin-Bona-Mahony type equation and its complete integrability (by: Vovk, Myroslava I and Pukach, Petro Ya and Prykarpatski, Anatolij K.), Annals of Mathematics and Physics, 2023; https://www.peertechzpublications.org/journals/annals-of-mathematics-and-physics/articles/volume-6/issue-1}
- Hilbert space decomposition properties of complex functions and their applications (by: Vovk, Myroslava I. and Pukach, Petro Ya. and Dilnyi, Volodymyr and Prykarpatski, Anatolij), Contemporary Mathematics, 2023; https://ojs.wiserpub.com/index.php/CM/article/view/2386
- Quantum current algebra in action: linearization, integrability of classical and factorization of quantum nonlinear dynamical systems (by: Prykarpatski, Anatolij K.), Universe, 2022; https://www.mdpi.com/books/book/6455}
- On the dynamics of matrix models for immune clonal networks (by: Balinsky, A. A. and Gafiychuk, V. V. and Kyshakevych, B. Yu. and Prykarpatsky, A. K.) Journal of Mathematical Sciences, 2022, https://link.springer.com/article/10.1007/s10958-022-05920-x
- On the integrability of a new generalized Gurevich-Zybin dynamical system, its Hunter-Saxton type reduction and related mysterious symmetries (by: Blackmore, Denis and Prykarpatsky, Yarema and Prytula, Mykola M. and Dutykh, Denys and Prykarpatski, Anatolij K.), Analysis and Mathematical Physics, 2022 https://link.springer.com/article/10.1007/s13324-022-00662-0
- Quasi-linearization and stability analysis of some self-dual, dark equations and a new dynamical system (by: Blackmore, Denis and Prytula, Mykola M. and Prykarpatski, Anatolij K.), Communications in Theoretical Physics, 2022; https://iopscience.iop.org/article/10.1088/1572-9494/ac5d28
- Geometriczni struktury na orbitakh petlevykh grup dyfeomorfizmiv ta asocijovani integrovni Hamiltonovi systemy. 1. (by: Hentosh, O. Ye. and Prykarpatskyj, Y. A. and Balinskyj, O. A. and Prykarpatskyj, A. K), Ukrainskyj matematycznyj zhurnal, 2022; https://umj.imath.kiev.ua/index.php/umj/article/view/661
- Quantum current algebra in action: linearization, integrability of classical and factorization of quantum nonlinear dynamical systems (by: Prykarpatski, Anatolij K.), Universe, 2022}; https://www.mdpi.com/2218-1997/8/5/288
- Dark type dynamical systems: the integrability algorithm and applications (by: Prykarpatsky, Yarema A. and Urbaniak, Ilona and Kycia, Radosław A. and Prykarpatski, Anatolij K.), Algorithms, 2022; https://www.mdpi.com/1999-4893/15/8/266