Publications
Articles in Books, Journals, Proceedings
- (With V.E.Aleinikov and M.M.Komochkov) Neutron Spectra Outside the Proton Accelerator Shielding, Neutron Monitoring for Radiation Protection Purposes, Vol.I, IAEA, Vienna, 1973, 31-46.
- ((With V.A.Meshcheryakov and V.I.Zhuravlev)N - Scattering S Waves and the Value of theσ commutator in the Static Model, Sov. J. Nucl. Phys. (Yad. Fiz. 20, 4, 1974, 756-761), 20 (4), 1975, 405-407.
- (With V.E.Aleinikov and M.M.Komochkov) Neutron Energy Spectra Outside the Shielding of High Energy Proton Accelerators, Proceedings of All-Union Meeting on Accelerators of Charged Particles, Vol.II, Nauka Publishers, Moscow, 1975, 240-242.
- (With V.A.Meshcheryakov) Local Form of the Solution of the Chew-Low Equations, Teor. Mat. Fiz., 24, 2, 1975, 155-163.
- (With V.E.Aleinikov and G.N.Timoshenko) Measurement of the Spectra of High Energy Protons from the Shielding of 680 Mev Synchrocyclotron, Sov. Atomic Energy, 41, 5, 1976, 332-334.
- (With V.I.Inozemtsev and V.A.Meshcheryakov) Uniformization of the Forward-Scattering Amplitude at High Energy, Lettere al Nuovo Cimento, 15, 1976, 321-328.
- (With V.E.Aleinikov and M.M.Komochkov) Some Regularities in Formation of the Neutron Spectra Outside the Shielding of Proton Accelerators, Sov. Atomic Energy, 42, 4, 1977, 305.
- (With V.A.Meshcheryakov) Uniformization of the Forward Scattering Amplitude in the Quark Model, In: "Processes of Multiple Production and Inclusive Reactions at High Energy", Institute of High Energy Physics, Serpukhov, 1977, 333-340.
- On Application of Computer Algebra Systems for Computation of Feynman Integrals, Proceedings of International Meeting on Programming and Mathematical Methods for Solving the Physical Problems, (Dubna, September 20-23, 1977), JINR D10,11-11264, Dubna, 1978, 166-174
- Analytical Computation of the Invariant Curve of the Chew-Low Equations, U.S.S.R. Comput. Maths. Math. Phys. (Zh. Vychisl. Mat. & Mat. Fiz., 19, 6, 1979, 1602-1608), 19, 6, 1979, 257-266.
- Local Construction of General Solution of the Chew-Low Equation by Computer, Proceedings of International Conference on Systems and Techniques of Analytical Computing and Their Applications to Theoretical Physics (Dubna, September 18-21, 1979), JINR D11-80-13, 1980, 159-169.
- (With O.V.Tarasov and D.V.Shirkov) Analytic Calculations on Digital Computers for Applications in Physics and Mathematics, Sov. Phys. Usp. (Usp. Fiz. Nauk, 130, 1980, 113-147), 23(1), 1980, 59-77.
- (With A.Karimkhodzhaev and R.N.Faustov) Hadronic Vacuum Polarization and Test of Quantum Electrodynamics at Low Energies, In: "Problems in Theory of Gravity and Elementary Particles", K.P.Staniukovich (Ed.), Atomizdat Publishers, Moscow, 1980, 172-181.
- Analytical Calculations in High Energy Physics by Computer, Computer Physics Communications, 20, 1980, 85-90. Global Structure of the General Solution of the Chew-Low Equations, Sov. Theor. Math. Phys. (Teor. Mat. Fiz., 48, 3, 1981, 346-355), 48, 3, 1982, 790-796.
- Global Structure of the General Solution of the Chew-Low Equations, Sov. Theor. Math. Phys. (Teor. Mat. Fiz., 48, 3, 1981, 346-355), 48, 3, 1982, 790-796.
- (With A.Yu.Zharkov) Solution of Chew-Low Equations in the Quadratic Approximation, Sov. Theor. Math. Phys. (Teor. Mat. Fiz., 52, 3, 1982, 384-392), 52, 3, 1983, 868-874.
- (With A.B.Shvachka and A.Yu.Zharkov) Investigation of Nonlinear Evolution Equations Using Analytical Calculation Systems, Proceedings of the Second International Conference on Systems and Techniques of Analytical Computing and Their Applications in Theoretical Physics (Dubna, September 21-23, 1982), JINR D11-83-511, Dubna, 1983, 114-119.
- (With A.Yu.Zharkov) A REDUCE Package for Solving of Ordinary Differential Equations, Proceedings of the Second International Conference on Systems and Techniques of Analytical Computing and Their Applications in Theoretical Physics (Dubna, September 21-23, 1982), JINR D11-83-511, Dubna, 1983, 171-177.
- (With A.Yu.Zharkov) Iterative Method of Construction of General Solution of the Chew-Low Equation, Proceedings of the Second International Conference on Systems and Techniques of Analytical Computing and Their Applications in Theoretical Physics (Dubna, September 21-23, 1982), JINR D11-83-511, Dubna, 1983, 232-241.
- (With A.P.Kryukov, A.Ya.Rodionov and A.Yu.Zharkov) An Algorithm of Elementary Fraction Decomposition of Rational Functions and Its Implementation in System REDUCE, Proceedings of the Second International Conference on Systems and Techniques of Analytical Computing and Their Applications in Theoretical Physics (Dubna, September 21-23, 1982), JINR D11-83-511, Dubna, 1983, 178-182.
- (With O.V.Tarasov) Analytical Computations by Computer and its Application to High Energy Physics, Proceedings of the XY International School on High Energy Physics for Young Scientists (Dubna, November 23 - December 2, 1982), JINR D2,4-83-179, Dubna, 1983, 481-504.
- (With V.K.Mitrjushkin) Phase Transitions in the Euclidean and Hamiltonian Approaches to Lattice Gauge Theories at a Finite Temperature, JETP Lett. (Pis'ma Zh. Eksp. Teor. Fiz. 37, 8, 1983, 400-403), 37, 8, 1983, 474-478.
- (With A.Yu.Zharkov) Cubic Approximation and Local Limitations on the Functional Arbitrariness in the General Solution of the Chew-Low Equations, Sov. Theor. Math. Phys. (Teor. Mat. Fiz., 55, 3, 1983, 469-474), 52, 3, 1983, 626-639.
- (With A.S.Ilchev and V.K.Mitrjushkin) Phase Transitions in Abelian Higgs Models on a Lattice, Sov. J. Nucl. Phys. (Yad. Fiz., 40, 1984, 1097-1104), 40, (4), 1985, 698-702.
- (With A.Yu.Zharkov) Methods of Investigating and Solving Differential Equations by Means of Algebraic Computation, In: "Systems for Analytical Transformations in Mechanics", Gorky, 1984, 16-19.
- (With A.B.Shvachka and A.Yu.Zharkov) FORMINT - a Program for the Classification of Integrable Nonlinear Evolution Equations, Computer Physics Communications, 34, 1985, 303-311.
- (With A.S.Ilchev, V.K.Mitrjushkin and A.M.Zadorozhny) SU(2) Lattice Gauge -- Higgs Model, Zeitschrift für Physik C - Particles and Fields, 29, 1985, 363-369.
- (With A.B.Shvachka and A.Yu.Zharkov) Computer Algebra Application for Classification of Integrable Non-Linear Evolution Equations, Journal of Symbolic Computation, 1, 1, 1985, 101-107.
- (With A.Yu.Zharkov) On Computer Algebra Application to Classification of Integrable Systems of Nonlinear Evolution Equations, Proceedings of the Third International Conference on Computer Algebra and its Applications to Theoretical Physics (Dubna, September 17-20, 1985), JINR D11-85-791, Dubna, 1985, 225-330.
- (With N.A.Kostov, R.P.Raychev and R.P.Roussev) Algebraic Models in Nuclear Physics and Group Theory Computation with Using of Computer Algebra Systems, Proceedings of the Third International Conference on Computer Algebra and its Applications to Theoretical Physics (Dubna, September 17-20, 1985), JINR D11-85-791, Dubna, 1985, 376-381.
- (With A.S.Ilchev, V.K.Mitrjushkin, I.K.Sobolev and A.M.Zadorozh, Nuclear Physics B265 [FS15], 1986, 145-160.
- (With D.Yu.Grigor'ev) Computer Algebra Algorithms, Systems and Applications, In: "Computer Algebra. Symbolic and Algebraic Computation", Mir Publishers, Moscow, 1986, 373-383.
- (With V.K.Mitrjushkin and A.M.Zadorozhny) The Phase Structure of the SU(3) Lattice Gauge-Higgs Model, Physics Letters 172B, 1, 1986, 65-70.
- (With A.S.Ilchev and V.K.Mitrjushkin) Lattice U(1) Higgs—Gauge Theory, Sov. J. Nucl. Phys. (Yad. Fiz., 43, 1986, 736-746), 43 (3), 1986, 468-473.
- (With O.V.Tarasov and D.V.Shirkov) Analytical Computations by Computer in Theoretical Physics, In: "Problems of Cybernetics. Computer Application to Quantum Field Theory", Moscow, 1987, 146-154.
- (With V.K.Mitrjushkin and A.M.Zadorozhny) Phase Structure of Gauge-Higgs Lattice Theory, Proceedings of International Seminar "Quarks-86" (Tbilisi, April 15-17, 1986), Moscow, 1987, 300-307.
- (With A.A.Bogoliubskaya and O.V.Tarasov) On Forming of Libraries for Computer Algebra Systems SCHOONSCHIP and REDUCE, In: "Applied Packages. Analytical Transformations", Nauka Publishers, Moscow, 1988, 83-90.
- (With R.N.Fedorova, N.N.Govorun and V.P.Shirikov) Software for Analytical Computation, In: "Modern Problems of Applied Mathematics and Mathematical Physics", Nauka Publishers, Moscow, 1988, 150-160.
- (With D.V.Shirkov) New Trends in Computer Science. Computer Algebra, In: "Computers in Modern Science", Nauka Publishers, Moscow, 1988, 35-48.
- (With O.V.Tarasov and D.V.Shirkov) Computer Algebra Application to High Energy Physics, Proceedings of International School on the Problems of Use of Computers in Physical Research (Dubna, 28 November - 3 December, 1988), JINR D10-89-70, Dubna, 1989, 134-178.
- (With R.N.Fedorova, N.N.Govorun and V.P.Shirikov) Computer Algebra in Physical Research of Joint Institute for Nuclear Research, In: "EUROCAL'87", Lecture Notes in Computer Science 378, Springer-Verlag, 1989, 1-10.
- (With A.B.Shabat, S.I.Svinolupov and A.Yu.Zharkov) Computer Algebra Application to Investigating Integrability of Nonlinear Evolution Systems, In: "EUROCAL'87", Lecture Notes in Computer Science 378, Springer-Verlag, 1989, 81-92.
- (With A.Yu.Zharkov) Computer Classification of Integrable Seventh Order MKdV-Like Equations, In: "EUROCAL'87", Lecture Notes in Computer Science 378, Springer-Verlag, 1989, 93-94.
- (With N.A.Kostov and Z.T.Kostova) Computer Algebra and Computation of Puiseux Expansions of Algebraic Functions, In: "EUROCAL'87", Lecture Notes in Computer Science 378, Springer-Verlag, 1989, 206-207.
- (With N.A.Kostov) Computer Algebra in the Theory of Ordinary Differential Equations of Halphen Type, In: "Computer and Mathematics", E.Kaltofen and S.M.Watt (Eds.), Springer-Verlag, New York, 1989, 279-288.
- (With N.A.Kostov and A.Y.Spasov) Investigation of Four Wave Interaction in j 4 Theory Using Computer Algebra, In: "Solitons and Applications", V.G.Makhankov, V.K.Fedyanin and O.K.Pashaev (Eds.), World Scientific Publishing Co., Singapore, 1990, 114-119.
- (With N.A.Kostov and A.Yu.Zharkov) Nonlinear Evolution Equations and Solving Algebraic Systems: the Importance of Computer Algebra, In: "Solitons and Applications", V.G.Makankov, V.K.Fedyanin and O.K.Pashaev (Eds.), World Scientific Publishing Co., Singapore, 1990, 120-128.
- (With A.Yu.Zharkov) Computer Classification of Integrable Coupled KdV-Like Systems, Journal of Symbolic Computation, 10, 1990, 203-207.
- (With A.Yu.Zharkov) Computer Generation of Necessary Integrability Conditions for Polynomial-Nonlinear Evolution Systems, Proceedings of "ISSAC'90", International Symposium on Symbolic and Algebraic Computation, ACM Press, Addison-Wesley Publishing Company, 1990, 250-254.
- (With N.V.Khutornoy and A.Yu.Zharkov) Lie-Bäcklund Symmetries of Coupled Nonlinear Schrödinger Equations, Proceedings of "ISSAC'91", International Symposium on Symbolic and Algebraic Computation, ACM Press, Addison-Wesley Publ. Company, 1991, 313-314
- Integrability of Polynomial-Nonlinear Evolution Equations and Computer Algebra, In: "Nonlinear Evolution Equations and Dynamical Systems", V.G.Makhankov and O.K.Pashaev (Eds.), Springer-Verlag, Berlin, 1991, 121-123.
- (With V.E.Kovtun and V.N.Robuk) Genetic Codes of Lie Algebras and Nonlinear Evolution Equations, In: "Nonlinear Evolution Equations and Dynamical Systems", V.G.Makhankov and O.K.Pashaev (Eds.), Springer-Verlag, Berlin, 1991, 124-126.
- (With I.R.Akselrod, V.E.Kovtun and V.N.Robuk) Construction of a Lie Algebra by a Subset of Generators and Commutation Relations, In: "Computer Algebra in Physical Research", D.V.Shirkov, V.A.Rostovtsev and V.P.Gerdt (Eds.), World Scientific Publ.Co., Singapore, 1991, 306-312.
- (With N.V.Khutornoy and A.Yu.Zharkov) Solving Algebraic Systems Which Arise as Necessary Integrability Conditions for Polynomial-Nonlinear Evolution Equations, In: "Computer Algebra in Physical Research", D.V.Shirkov, V.A.Rostovtsev and V.P.Gerdt (Eds.), World Scientific Publ.Co., Singapore, 1991, 321-328.
- (With L.M.Berkovich, Z.T.Kostova and M.L.Nechaevsky) Integration of Some Classes of Linear Ordinary Differential Equations, In: "Computer Algebra in Physical Research", D.V.Shirkov, V.A.Rostovtsev and V.P.Gerdt (Eds.), World Scientific Publ.Co., Singapore, 1991, 350-356.
- (With O.V.Tarasov and D.V.Shirkov) Symbolic and Formula Processing in HEP, In: "Computing in High Energy Physics'91", Y.Watase and F.Abe (Eds.), Universal Academy Press Inc., Tokyo, 1991, 373-382.
- Computer Algebra Tools for Higher Symmetry Analysis of Nonlinear Evolution Equations, In: "Programming Environments for High-Level Scientific Problem Solving", P.W.Gaffney and E.N.Houstis (Eds.), North-Holland, 1992, 107-115.
- (With N.V.Khutornoy and A.Yu.Zharkov) Gröbner Basis Technique, Homogeneity and Solving Polynomial Equations, Proceedings of the 1992 International Workshop on Mathematics Mechanization (Beijing, China, July 16-18, 1992), Wu Wen-Tsün and Cheng Min-De (Eds.), International Academic Publishers, Beijing, China, 1992, 38-51.
- (With L.M.Berkovich, Z.T.Kostova and M.L.Nechaevsky) Second Order Reducible Linear Differential Equations, In: "Applied Packages. Software for Methematical Simulation", Nauka Publishers, Moscow, 1992, 9-24.
- Computer Algebra, Symmetry Analysis and Integrability of Nonlinear Evolution Equations, In: "Physics Computing'92", R.A. de Groot and J.Nadrchal (Eds.), World Scientific Publ.Co., Singapore, 1993, 52-59; International Journal of Modern Physics C, v.4, No.2, 1993, 279-286.
- (With N.V.Khutornoy and A.Yu.Zharkov) ASYS: A Computer Algebra Package for Analysis of Systems of Nonlinear Algebraic Equations, Russian Journal "Programming and Computer Software", No.2, 1993, 69-75.
- (With W.Lassner) Isomorphism Verification for Complex and Real Lie Algebras by Gröbner Basis Technique, In: "Modern Group Analysis: Advanced Analytical and Computational Methods in Mathematical Physics", N.H. Ibragimov et al. (Eds.), Kluwer Academic Publishers, Amsterdam, 1993, 245-254.
- (With N.V.Khutornoy and A.Yu.Zharkov) ASYS2: a New Version of Computer Algebra Package ASYS for Analysis and Simplification of Polynomial Systems, Proceedings of the Rhein Workshop on Computer Algebra (Karlsruhe, Germany, March 22-24, 1994), J.Calmet (Ed.), Institute of Algorithms and Cognitive Systems, University of Karlsruhe, 1994, 162-178
- (With N.Khutornoy and W.Lassner) Computer Detecting of Lie Algebra Isomorphisms, In: "Programming and Mathematical Technique in Physics", Yu.Yu.Lobanov and E.P.Zhidkov (Eds.), World Scientific, Singapore, 1994, 108-113.
- (With N.V.Khutornoy and A.Yu.Zharkov) Implementation of Zero-Dimensional Gröbner Bases Transformation from One Order into Another, Proceedings of the International Workshop on New Computer Technologies in Control Systems (Perslavl-Zalessky, Russia, July 11-15, 1994), Program Systems Institute, Pereslavl-Zalessky, 1994, 36-43.
- (With V.V.Kornyak) Lie Algebras and Lie Superalgebras Defined by a Finite Number of Relations: Computer Analysis, Journal of Nonlinear Mathematical Physics, v.2, No.3/4, 1995, 367-373.
- (With V.V.Kornyak) Computer Analysis of Finitely Presented Lie Superalgebras, In: "New Computing Techniques in Physics Research IV", B. Denby and D. Perret-Gallix (Eds.), World Scientific, Singapore, 1996, pp. 289-294.
- Homogeneity of Integrability Conditions for Multiparametric Families of Polynomial-Nonlinear Evolution Equations, Mathematics and Computers in Simulation, 42, 1996, 399-408.
- (With V.V.Kornyak) Construction of Finitely Presented Lie Algebras and Superalgebras, Journal of Symbolic Computation, 21, 1996, 337-349.
- (With V.F.Edneral, D.V.Shirkov and N.N.Vasiliev) {\em Computer Algebra as Applied to Science and Engineering, Russian Journal "Programming and Computer Software", 22, 6, 1996, 296-306.
- (With V.N.Robuk and V.M.Severyanov) On Construction of Finitely Presented Lie Algebras, Russian Journal of Computational Mathematics and Mathematical Physics (Zh. Vychisl. Mat. \& Mat. Fiz.), 36, 11, 1996, 1493-1505.
- (With V.V.Kornyak) An Implementation in C of an Algorithm for Construction of Finitely Presented Lie Superalgebras, Computer Science Journal of Moldova, V 4, No. 3, 1996, 399-427.
- (With V.V.Kornyak) A Program for Constructing the Complete Set of Relations, Basis Elements and Their Commutator Table for Finitely Presented Lie Algebras and Superalgebras, Russian Journal "Programming and Computer Software", 23, 1997, 164-172.
- Gröbner Bases and Involutive Methods for Algebraic and Differential Equations, Mathematics and Computers in Modelling, 25, No. 8/9, 1997, 75-90.
- (With V.V.Kornyak) A Program for Constructing Finitely Presented Lie Algebras and Superalgebras, Nuclear Instruments & Methods in Physics Research A 389, 1997, 370-373.
- (With V.V.Kornyak) An Algorithm for Analysis of the Structure of Finitely Presented Lie Algebras and Superalgebras, Discrete Mathematics and Theoretical Computer Science 1, 1997, 217-228.
- (With Yu.A.Blinkov) Involutive Bases of Polynomial Ideals, Mathematics and Computers in Simulation 45, 1998, 519-542.
URL: http://arXiv.org/abs/math.RA/9912027.
- (With Yu.A.Blinkov) Minimal Involutive Bases, Mathematics and Computers in Simulation 45, 1998, 543-560.
URL: http://arXiv.org/abs/math.RA/9912029.
- (With M.Berth and G.Czichowski) Involutive Divisions in Mathematica: Implementation and Some Applications, Proceedings of the 6th Rhein Workshop on Computer Algebra (Sankt-Augustin, Germany, March 31 - April 3, 1998), J.Calmet (Ed.), Institute for Algorithms and Scientific Computing, GMD-SCAI, Sankt-Augustin, 1998, pp.74-91.
- (With M.Berth and G.Czichowski) Completion of Monomial Sets to Involution with Mathematica, International Conference "Computer Algebra in Scientific Computing" (April 20-24, St.Petersburg, Russia), Extended Abstracts, Euler International Mathematical Institute, St.Petersburg, 1998, pp. 58-63.
- (With Yu.A.Blinkov) Involutive Monomial Divisions, Russian Journal "Programming and Computer Software", 24, No.6, 1998, 283-285.
- Completion of Linear Differential Systems to Involution, In: "Computer Algebra in Scientific Computing \/ CASC'99", V.G.Ganzha, E.W.Mayr and E.V.Vorozhtsov (Eds.), Springer-Verlag, Berlin, 1999, pp. 115-137. URL: http://arXiv.org/abs/math.AP/9909114.
- (With S.A.Gogilidze) Constrained Hamiltonian Systems and Gröbner Bases, In: "Computer Algebra in Scientific Computing \ CASC'99", V.G.Ganzha, E.W.Mayr and E.V.Vorozhtsov (Eds.), Springer-Verlag, Berlin, 1999, pp. 138-146. URL: http://arXiv.org/abs/math.AP/9909113.
- (With V.V.Kornyak, M.Berth and G.Czichowsky) Construction of Involutive Monomial Sets for Different Involutive Divisions, In: "Computer Algebra in Scientific Computing \ CASC'99", V.G.Ganzha, E.W.Mayr and E.V.Vorozhtsov (Eds.), Springer-Verlag, Berlin, 1999, pp. 147-157. \\ URL: http://arXiv.org/abs/math.SC/9912031.
- (With M.G.Dmitriev and M.V.Nesterova) Polynomial-Nonlinear Boundary Problems with Inexactly Known Boundary Conditions and their Approximate Solving by Means of Gröbner Bases. Russian Journal "Fundamental and Applied Mathematics" 5, 1999, 675-686.
- Computer Algebra and Constrained Dynamics. In: "Problems of Modern Physics", A.N.Sisakian and D.I.Trubetskov (Eds.), JINR D2-99-263, 2000, pp. 164-171.
- On the Relation Between Pommaret and Janet Bases, In: "Computer Algebra in Scientific Computing / CASC 2000", V.G.Ganzha, E.W.Mayr, E.V.Vorozhtsov (Eds.), Springer-Verlag, Berlin, 2000, pp.164-171. arXiv:math.AC/0004100
- (With Yu.A.Blinkov and D.A.Yanovich) Fast Search for the Janet Divisor. Russian Journal "Programming and Computer Software", Vol. 27, No. 1, 2001, 22-24.
- Involutivity Applied to Differential Equations. Proceedings of International Conference "Differential Equations and Computer Algebra Systems" (Brest, Belarus, September 19-22, 2000), Brest State University, 2001, pp. 10-15.
- (With M.Berth) Computation of Involutive Bases with Mathematica. Proceedings of the Third International Workshop on Mathematica System in Teaching and Research (Sieldce, Poland, September 5-7, 2001), Institute of Mathematics \& Physics, University of Podlasie, 2001, pp. 29-34.
- (With Yu.A.Blinkov and D.A.Yanovich) Computation of Janet Bases. I.Monomial Bases. In: "Computer Algebra in Scientific Computing / CASC 2001", V.G.Ganzha, E.W.Mayr, E.V.Vorozhtsov (Eds.), Springer-Verlag, Berlin, 2001, pp. 233-247.
- (With Yu.A.Blinkov and D.A.Yanovich) Computation of Janet Bases. II.Polynomial Bases. In: "Computer Algebra in Scientific Computing / CASC 2001", V.G.Ganzha, E.W.Mayr, E.V.Vorozhtsov (Eds.), Springer-Verlag, Berlin, 2001, pp. 249-263.
- On an Algorithmic Optimization in Computation of Involutive Bases. Russian Journal "Programming and Computer Software", Vol. 28, No. 2, 2002, 62-65.
- Involutive Division Technique: Some Generalizations and Optimizations. Journal of Mathematical Sciences 108(6), 2002, 1034-1051. URL: http://arXiv.org/abs/math.SC/9912030.
- (With Yu.A.Blinkov) Janet Bases of Toric Ideals. In: "Computer Algebra and its Application to Physics CAAP-2001", V.P.Gerdt (Ed.), JINR E5,11-2001-279, Dubna, 2002, pp. 71-82; Proceedings of the 8th Rhine Workshop on Computer Algebra (Mannheim, Germany, March 21-22, 2002), H.Kredel, W.K.Seiler (Eds.), University of Mannheim, 2002, 125-135. arXiv:math.AC/0501180
- (With A. M. Khvedelidze and D. M. Mladenov) Analysis of Constraints in Light-cone Version of SU(2) Yang-Mills Mechanics. In: "Computer Algebra and its Application to Physics / CAAP-2001", V.P.Gerdt (Ed.), JINR E5,11-2001-279, Dubna, 2002, pp. 83-92. URL: http://arXiv.org/hep-th/0209107.
- (With D.A.Yanovich) Parallelism in Computing Janet Bases. In: "Computer Algebra and its Application to Physics / CAAP-2001", V.P.Gerdt (Ed.), JINR E5,11-2001-279, Dubna, 2002, pp. 93-103; Proceedings of the Workshop on Under- and Overdetermined Systems of Algebraic or Differential Equations (Karlsruhe, March 18-19, 2002), J.Calmet, M.Hausdorf, W.M.Seiler (Eds.), Institute of Algorithms and Cognitive Systems, University of Karlsruhe, 2002, 47-56.
- (With G. Carra'Ferro) Extended Characteristic Sets of Finitely Generated Differential Ideals. In: "Computer Algebra in Scientific Computing / CASC 2002", V.G.Ganzha, E.W.Mayr, E.V.Vorozhtsov (Eds.). Institute of Informatics, Technical University of Munich, Garching, 2002, pp. 29-36.
- (With D.A.Yanovich) Implementation of the FGLM Algorithm and Finding Roots of Polynomial Involutive Systems. Programming and Computer Software, Vol.29, No.2, 2003, 72-74.
- (With G. Carra'Ferro) Improved Kolchin-Ritt Algorithm. Programming and Computer Software, Vol.29, No.2, 2003, 83-87.
- (With M.Znojil and D.A.Yanovich) New exact solutions for polynomial oscillators in large dimensions. Journal of Physics A: Mathematical and General 36, 2003, 6531-6545. URL: http://arXiv.org/math-ph/0302046.
- (With Yu.A.Blinkov, C.F.Cid, W.Plesken and D.Robertz) The Maple Package "Janet": I.Polynomial Systems. In: "Computer Algebra in Scientific Computing / CASC 2003", V.G.Ganzha, E.W.Mayr, E.V.Vorozhtsov (Eds.). Institute of Informatics, Technical University of Munich, Garching, 2003, pp.31-40.
- (With Yu.A.Blinkov, C.F.Cid, W.Plesken and D.Robertz) The Maple Package "Janet": II.Linear Partial Differential Equations. In: "Computer Algebra in Scientific Computing / CASC 2003", V.G.Ganzha, E.W.Mayr, E.V.Vorozhtsov (Eds.). Institute of Informatics, Technical University of Munich, Garching, 2003, pp.41-54.
- (With M.Znojil and D.A.Yanovich) On Exact Solvability of Anharmonic Oscillators in Large Dimensions. In: "Computer Algebra in Scientific Computing / CASC 2003", V.G.Ganzha, E.W.Mayr, E.V.Vorozhtsov (Eds.). Institute of Informatics, Technical University of Munich, Garching, 2003, pp.143-162.
URL: http://arXiv.org/math-ph/0310012.
- (With D.A.Yanovich) Parallel Computation of Involutive and Gröbner Bases. In: "Computer Algebra in Scientific Computing / CASC 2004", V.G.Ganzha, E.W.Mayr, E.V.Vorozhtsov (Eds.). Institute of Informatics, Technical University of Munich, Garching, 2004, pp.185-194.
- Gröbner Bases in Perturbative Calculations. Nuclear Physics B (Proc. Suppl.) 135, 2004, 232-237.
URL: http://arXiv.org/hep-ph/0501053.
- (With D.A.Yanovich) Parallel Computation of Janet and Gröbner Bases over Rational Numbers. Programming and Computer Software, Vol.31, No.2, 2005, 73-80.
- Involutive Algorithms for Computing Gröbner Bases. In "Computational Commutative and Non-Commutative Algebraic Geometry", S.Cojocaru, G.Pfister
and V.Ufnarovski (Eds.), NATO Science Series, IOS Press, 2005, pp. 199-225.
URL: http://arXiv.org/math.AC/0501111.
- (With Yu.A.Blinkov) Janet-like Monomial Division. in: "Computer Algebra in Scientific Computing / CASC 2005", V. G. Ganzha, E. W. Mayr, E. V. Vorozhtsov (Eds.), LNCS 3781, Springer-Verlag, Berlin, 2005, pp. 174--183.
- (With Yu.A.Blinkov) Janet-like Gröbner Bases. in: "Computer Algebra in Scientific Computing / CASC 2005", V. G. Ganzha, E. W. Mayr, E. V. Vorozhtsov (Eds.), LNCS 3781, Springer-Verlag, Berlin, 2005, pp. 184--195.
- (With A.Gusev, M.Kaschiev, V.Rostovtsev, V.Samoylov, T.Tupikova, Y.Uwano and S.Vinitsky) Symbolic-Numerical Algorithm for Solving the Time-Dependent Shrödinger Equation by Split-Operator Method. In: "Computer Algebra in Scientific Computing / CASC 2005", V. G. Ganzha, E. W. Mayr, E. V. Vorozhtsov (Eds.), LNCS 3781, Springer-Verlag, Berlin, 2005, pp. 244--258.
- (With D.A.Yanovich) Experimental Analysis of Involutive Criteria. In: "Algorithmic Algebra and Logic", A.Dolzmann, A.Seidl and T.Sturm (Eds.), BOD Norderstedt, Germany, pp. 105-109.
- (With D.Robertz) Computation of Gröbner Bases for Systems of Linear Difference Equations. Computeralgebra, Rundbrief Nr.37, GI_DMV_GAMM, 2005, 8-13.
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(With Yu.A.Blinkov and V.V.Mozzhilkin) Gröbner Bases and Generation of Difference Schemes for Partial Differential Equations. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 2 (2006) 051, 26 pages. URL: arXiv:math.RA/0605334
(With S.I. Vinitsky, A.A. Gusev, M.S. Kaschiev, V.A. Rostovtsev, V.N. Samoylov, T.V. Tupikova, Y. Uwano) Symbolic algorithm for factorization of evolution operator for time-dependent Schroedinger equation. Programming and Computer Software, Vol. 32, No. 2, 2006, 103–-113.
(With D.A.Yanovich) Effectiveness of Involutive Criteria in Computation of Polynomial Janet Bases. Programming and Computer Software, Vol. 32, No. 3, 2006, 134–-138.
(With A.Gusev, M.Kaschiev, V.Rostovtsev, V.Samoylov, T.Tupikova, S.Vinitsky) A Symbolic-Numerical Algorithm for Solving the Eigenvalue Problem for a Hydrogen Atom. In: “Computer Algebra in Scientific Computing / CASC 2006", V. G. Ganzha, E.W. Mayr, E. V. Vorozhtsov (Eds.), LNCS 4194, Springer-Verlag, Berlin, 2006, pp. 205--218.
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(With A.Khvedelidze, Yu.Palii). Towards an Algorithmization of the Dirac Constraints Formalism. In: “Global Integrability of Field Theories”, J.Calmet, W.M.Seiler, R.W.Tucker (Eds.), Cocroft Institute, Daresbury (UK), 2006, pp.135–154. arXiv:math-ph/0611021
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(With V.M.Severyanov) An Algorithm for Constructing Polynomial Systems Whose Solution Space Characterizes Quantum Circuits. In: “Quantum Informatics 2005”, Yu.I.Ozhigov (Ed.), Proceedings of SPIE, Volume 6264, 626401, 2006.
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(With R.Horan, A.Khvedelidze, M.Lavelle, D.McMullan, Yu.Palii). On the Hamiltonian reduction of geodesic motion on SU(3)to SU(3)/SU(2). Journal of Mathematical Physics, Vol.47, No. 10, 2006, 112902 (27 pages). arXiv:hep-th/0511245
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Involutive methods applied to algebraic and differential equations. In: “Constructive algebra and Systems Theory”, B.Hanzon, M.Hazewinkel (Eds.), Royal Netherland Academy of Arts and Sciences, Amsterdam, 2006, pp.245-250.
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(With A.M.Khvedelidze and D.M.Mladenov). On application of
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(With R.Kragler, A.N.Prokopenya). Mathematica Package for Construction of Circuit Matrices in Quantum Computation. In: “Computer Algebra Systems in Teaching and Research CASTR 2007”, University of Podlasie, Scieldce, Poland, 2007, pp.135-144.
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(With V.M.Severyanov) C# Package for Assembling Quantum Circuits and Generating Associated Polynomial Sets. Physics of Particles and Nuclei Letters, Vol.4, No.2, 2007, 225–230.
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(With A.Gusev, M.Kaschiev, V.Rostovtsev, V.Samoylov, T.Tupikova, Y.Uwano, S.Vinitsky) On Symbolic-
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(With O.Chuluunbaatar, A.Gusev, M.Kaschiev, V.Rostovtsev, V.Samoylov, T.Tupikova, S.Vinitsky). Symbolic-Numeric Algorithm for Computing Matrix Elements of Parametric Eigenvalue Problem. Programming and Computer Software, Vol. 33, No. 2, 105-116, 2007.
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(With Yu.A.Blinkov). On Selection Strategy for Nonmultiplicative Prolongations at Construction of Janet Bases. Programming and Computer Software, Vol. 33, No. 3, 147-153, 2007.
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(With O.Chuluunbaatar, A.Gusev, M.Kaschiev, V.Rostovtsev, V.Samoylov, T.Tupikova, S.Vinitsky). Symbolic-Numerical Algorithm for Solving the Eigenvalue Problem for Hydrogen Atom in the Magnetic Field: Cylindrical Coordinates. In: “Computer Algebra in Scientific Computing CASC 2007”, V.G.Ganzha, E.W.Mayr, E.V.Vorozhtsov (Eds.) LNCS 4770, Springer-Verlag, Berlin, 2007, pp. 118–
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(With A.M.Khvedelidze, Yu.G.Palii.) Deducing the constraints in the light-cone SU(3) Yang-Mills mechanics via Gröbner bases. In: “Computer Algebra in Scientific Computing / CASC 2007”, V.G.Ganzha, E.W.Mayr, E.V.Vorozhtsov (Eds.) LNCS 4770, Springer-Verlag, Berlin, 2007, pp. 145–159.
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(With R.Kragler, A.N.Prokopenya). On computer algebra application to simulation of quantum computation.
Models and Methods in Few-and Many-Body Systems. Proceedings of the DST-UNISA-JINR
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On Completion to Involution Based on Janet Division. Computer Algebra and Differential Equations,
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(With R.Kragler, A.N.Prokopenya). A Mathematica Package for Construction of Circuit Matrices in
Quantum Computation. Computer Algebra and Differential Equations, Acta Academiae Aboensis, Ser.
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(With M.V.Zinin) On computation of Gröbner bases over F2. Computer Algebra and Differential
Equations, Acta Academiae Aboensis, Ser. B, Vol. 67, no. 2, 2007, pp.59-68.
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(With O.Chuluunbaatar, A.A.Gusev, V.A.Rostovtsev, T.V.Tupikova, S.I.Vinitsky, A.G.Abrashkevich,
M.S.Kaschiev, V.V.Serov). POTHMF, a program to compute matrix elements of the coupled radial
equations for a Hydrogen-like atom in a homogeneous magnetic field. Computer Algebra and Differential
Equations, Acta Academiae Aboensis, Ser. B, Vol. 67, no. 2, 2007, pp.69-78.
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(With Yu.A.Blinkov) On computer algebra-aided stability analysis of difference schemes generated by
means of Gröbner bases. Computer Algebra and Differential Equations, Acta Academiae Aboensis,
Ser. B, Vol. 67, no. 2, 2007, pp.168-177.
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(With O.Chuluunbaatar, A.A.Gusev, S.I.Vinitsky, A.G. Abrashkevich, M.S.Kaschiev, V.V.Serov). POTHMF: A program for computing potential curves and matrix elements of the coupled adiabatic
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On Decomposition of Algebraic PDE Systems into Simple Subsystems. Acta Appl. Math. 101, 2008,
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Gröbner Bases Applied to Systems of Linear Difference Equations. Physics of Particles and Nuclei
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(With A.M.Khvedelidze, Yu.G.Palii.) Light-cone Yang-Mills mechanics: SU(2) vs. SU(3). Theoretical
and Mathematical Physics 155(1), 2008, 557-566.
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(With Yu.A.Blinkov) Specialized Computer Algebra System GINV. Programming and Computer Software,
Vol. 34, No. 2, 2008, 112–123.
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(With M.V.Zinin) Involutive Method for Computing Gröbner Bases over F2. Programming and Computer
Software, Vol.34, No. 4, 2008, 191–203.
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(With M.V.Zinin) A Pommaret Division Algorithm for Computing Gröbner Bases in Boolean Rings.
Proceedings of ISSAC 2008, ACM Press, pp.95–102.
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(With Nguyen Van Hieu, Nguyen Bich Ha, O. Chuluunbaatar, A.A. Gusev, Yu. G. Palii and Nguyen
Van Hop) Analytical Asymptotic Expressions for the Green’s Function of the Electron in a Single-Level
Quantum Dot at the Kondo and the Fano Resonances. Journal of the Korean Physical Society, Vol.
53, No. 6, 2008, 3645–3649.
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(With M.V.Zinin) Role of Involutive Criteria in Computing Boolean Gröbner Bases. Programming and
Computer Software, Vol.35, No.2, 2009, 90–97.
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(With M.Eliashvili, A.M.Khevedelidze) On precession of entangled spins in a strong laser field. Physics
of Atomic Nuclei, Vol.72, No.5, 2009, 1-8.
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(With Yu.A.Blinkov and M.V.Zinin) On computation of Boolean involutive bases. Proceedings of
the 2nd International conference “Polynomial Computer Algebra”, POMI RAS, St.Petersburg, 2009,
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(with Yu.A.Blinkov) Involution and Difference Schemes for the Navier-Stokes Equations. In: “Computer Algebra in Scientific Computing / CASC
2009'', V.P.Gerdt, E.W.Mayr, E.V.Vorozhtsov (Eds.), LNCS 5743, Springer-Verlag, Berlin, 2009, pp.94-105.
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(with R.Kragler, A.N.Prokopenya) A Mathematica Package for Simulation of Quantum Computation. In: "Computer Algebra in Scientific Computing / CASC 2009", V.P.Gerdt, E.W.Mayr, E.V.Vorozhtsov
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(with S.I. Vinitsky, O. Chuluunbaatar, A.A. Gusev, V.A. Rostovtsev) Symbolic-Numerical Algorithms
for Solving Parabolic Quantum Well Problem with Hydrogen-Like Impurity. In: \Computer Algebra
in Scientific Computing / CASC 2009", V.P.Gerdt, E.W.Mayr, E.V.Vorozhtsov (Eds.), LNCS 5743,
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On Completion of Nonlinear Differential Systems to Involution. Proceedings of the 4th World Conference on 21st Century Mathematics, A.D.R.Choudary (ed.), Lahore, Pakistan, 2009, pp.79-87.
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(with M.V.Zinin) An algorithmic approach to solving polynomial equations associated with quantum
circuits. Physics of Particles and Nuclei Letters, Vol.6, No.7, 2009, 521-525.
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(with R.Kragler, A.N.Prokopenya) A Mathematica Program for Constructing Quantum Circuits and
Computing Their Unitary Matrices. Physics of Particles and Nuclei Letters, Vol.6, No.7, 2009, 526-529.
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(with O.Chuluunbaatar, A.A.Gusev, M.S.Kaschiev, V.A.Rostovtsev, Y.Uwano, S.I.Vinitsky) Multi-
Layer Evolution Schemes for the Finite-Dimensional Quantum Systems in External Fields. Physics of
Particles and Nuclei Letters, Vol.6, No.7, 2009, 550-553.
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Algebraically Simple Involutive PDEs and Cauchy Problem. Journal of Mathematical Sciences, Vol.168,
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(with A.Khvedelidze and Yu.Palii) On the ring of local invariants for a pair of entangles qubits. Journal
of Mathematical Sciences, Vol.168, No.3, 2010, 368-378. arXiv:quant-ph/1007.0968
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(with D.Stefanescu and S.Yevlakhov) Estimations of Positive Roots of Polynomials. Journal of Math
ematical Sciences, Vol.168, No.3, 2010, 468-474.
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(with A.N.Prokopenya) On Some Algorithms of Computing Unitary Matrices for Quantum Circuits. Programming and Computer Software, Vol.36, No.2, 2010, 111-116.
(with Yu.A.Blinkov and M.V.Zinin) On Computing Boolean Involutive Bases. Programming and Com
puter Software, Vol.36, No.2, 2010, 117-123.
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(with D.Robertz) Consistency of Finite Difference Approximations for Linear PDE Systems and its
Algorithmic Verification. Proceedings of ISSAC 2010, ACM Press, 2010, pp.53-59.
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(with T.Bächler, M.Lange-Hegermann and D.Robertz). Thomas Decomposition of Algebraic and Differential Systems. In: "Computer Algebra in Scientific Computing / CASC 2010", V.P.Gerdt,
W.Koepff, E.W.Mayr, E.V.Vorozhtsov (Eds.), LNCS 6264, Springer-Verlag, Berlin, 2010, pp.31-54.
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(with A.A. Gusev, O. Chuluunbaatar, V.A. Rostovtsev, S.I. Vinitsky, V.L. Derbov and V.V. Serov)
Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models. In: “Computer Algebra in Scientific Computing / CASC 2010", V.P.Gerdt, W.Koepff, E.W.Mayr, E.V.Vorozhtsov
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(with A.N.Prokopenya) Simulation of the quantum algorithm for order finding with the QuantumCircuit
package. Vestnik of Brest Technical University, Series Physics, Mathematics, Informatics, No.5, 2010, 78-83 (in Russian).
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(with A.Khvedelidze and Yu.Palii) Constraints on SU(2) ⊗SU(2) invariant polynomials for entangled
qubit pair. Physics of Atomic Nucleii, Vol. 74, No. 6, 2011, 893-900.
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(with Yu.A.Blinkov) Involutive Division Generated by an Antigraded Monomial Ordering. In: “Computer Algebra in Scientific Computing / CASC
2011'', V.P.Gerdt, W.Koepff, E.W.Mayr, E.V.Vorozhtsov (Eds.), LNCS 6885, Springer-Verlag, Berlin, 2011, pp.158-174.
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(with A.A. Gusev, S.I. Vinitsky, O. Chuluunbaatar and V.A. Rostovtsev) Symbolic-Numerical Algorithms to Solve the Quantum Tunneling Problem for a Coupled Pair of Ions. In: “Computer Algebra in Scientific Computing / CASC
2011'', V.P.Gerdt, W.Koepff, E.W.Mayr, E.V.Vorozhtsov (Eds.), LNCS 6885, Springer-Verlag, Berlin, 2011, pp.175-191.
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(with A.Khvedelidze and Yu.Palii) Separability of Two-Qubit State in Terms of Local Invariants. Physics of Particles and Nuclei Letters Vol.8, No.5, 2011, 451-454.
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(with A.Khvedelidze, D.Mladenov and Yu.Palii). SU(6) Casimir Invariants and SU(2) ⊗ SU(3) Scalars for a Mixed Qubit-Qutrit States. Journal of Mathematical Sciences, Vol. 179, No. 6, 2011, 690-701. arXiv:quant-ph/1106.4905
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Consistency Analysis of Finite Difference Approximations to PDE Systems. Proceedings of MMCP 2011 (July 3-8, 2011, Stara Lesna, High Tatra Mountains, Slovakia), G.Adam, J.Busa, M.Hnatic (Eds.), LNCS 7175, Springer, Heidelberg, 2012, pp.28-42. arXiv:math.AP/1107.4269
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(with A.N. Prokopenya) The Circuit Model of Quantum Computation and its Simulation with Mathematica. Proceedings of MMCP 2011 (July 3-8, 2011, Stara Lesna, High Tatra Mountains, Slovakia), G.Adam, J.Busa, M.Hnatic (Eds.), LNCS 7175, Springer, Heidelberg, 2012, pp.43-55.
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(with T.Bächler, M.Lange-Hegermann and D.Robertz). Algorithmic Thomas Decomposition of Algebraic and
Differential Systems. Journal of Symbolic Computation, 47(10), 1233-1266, 2012. arXiv:math.AC/1108.0817
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(with A.Hashemi and B.M.-Alizadeh) A Variant of Gerdt`s Algorithm for Computing Involutive Bases. Herald of Peoples' Friendship University of Russia: Series Mathematics, Information Sciences, Physics, No.2, 2012, 43-54. arXiv:math.RA/1108.3261
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(with A.Hashemi) Comprehensive Involutive Systems. In: “Computer Algebra in Scientific Computing / CASC
2012'', V.P.Gerdt, W.Koepff, E.W.Mayr, E.V.Vorozhtsov (Eds.), LNCS 7442, Springer-Verlag, Berlin, 2012, pp.98-116. arXiv:cs.SC/1206.0181
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(with A.Gusev, S.Vinitsky, O.Chuluunbaatar, L. Le Hai, V. Rostovtsev) Symbolic-Numerical Algorithm for
Calculations of High-|m| Rydberg States and Decay Rates. In: "Computer Algebra in Scientific Computing / CASC
2012'', V.P.Gerdt, W.Koepff, E.W.Mayr, E.V.Vorozhtsov (Eds.), LNCS 7442, Springer-Verlag, Berlin, 2012, pp.155-171.
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On investigation of finite difference approximations to partial differential equations systems. Electronic journal ''System analysis in science and education'' (in Russian). http://www.sanse.ru/archive/24
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(With D.Robertz) Computation of Difference Gröbner Bases. Computer Science Journal of Moldova, 20(2), 2012, 203-226. arXiv:cs.SC/1206.3463
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(With A.Hashemi) On the Use of Buchberger Criteria in G2V Algorithm for Calculating Gröbner Bases. Programming and Computer Software, Vol.39, No.2, 2013, 81-90.
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(with S.Gogilidze, A.Khvedelidze, D.Mladenov, V.Sanadze). Entanglement of spins under strong laser
infuence. Physica Scripta, T153, 2013, 014026 (5pp). arXiv:quant-ph/1306.2074
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(with A.Prokopenya) Simulation of Quantum Error Correction by Means of QuantumCircuit Package.
Programming and Computer Software, Vol.39, No.3, 2013, 143-149.
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(with A.Hashemi and B.M.-Alizadeh) An Involutive Bases Algorithm Incorporating F5 Criterion. Journal
of Symbolic Computation, 59, 2013, 1-20. arXiv:math.AC/1306.6811
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(with P.Amodio, Yu.A.Blinkov and R.La Scala) On Consistency of Finite Difference Approximations
to the Navier-Stokes Equations. In: "Computer Algebra in Scientific Computing / CASC 2013",
V.P.Gerdt, W.Koepff, E.W.Mayr, E.V.Vorozhtsov (Eds.), LNCS 8136, Springer, Cham, 2013, pp.46-
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(with A.Prokopenya) Simulation of Quantum Error Correction with Mathematica. In:"Computer
Algebra in Scientific Computing / CASC 2013", V.P.Gerdt, W.Koepff, E.W.Mayr, E.V.Vorozhtsov
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(with A.Khvedelidze and Yu.Palii) Describing the orbit space of global unitary actions for mixed qudit
states. Journal of Mathematical Sciences, Vol.200, No.6, 2014, 682-689. arXiv:quant-ph/1311.4649
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(with D.Michels, D.Lyakhov, G.Sobottka and A.Weber) Lie Symmetry Analysis for Cosserat Rods.
In: "Computer Algebra in Scientifc Computing / CASC 2014", V.P.Gerdt, W.Koepff, W.M. Seiler,
E.V.Vorozhtsov (Eds.), LNCS 8860, Springer, Cham, 2014, pp.324-334.
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(with R.La Scala) Noetherian Quotient of the Algebra of Partial Difference Polynomials and Gröobner
Bases of Symmetric Ideals. Journal of Algebra, Vol. 423, 2015, 1233-1261. arXiv:math.AC/1304.7967
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(with A.Khvedelidze and Yu.Palii) Constructing SU(2) x U(1) orbit space for qutrit mixed states. Journal of Mathematical Sciences, Vol. 209, No. 6, 2015, 878-889. arXiv:quant-ph/1408.6697
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(with A.A.Gusev, S.I.Vinitsky, V.L.Derbov, A.Góźdź and A. Pędrak ) Symbolic algorithm for generating irreducible bases of point groups in the space of SO(3) group. In: "Computer Algebra in Scientific
Computing / CASC 2015", V.P.Gerdt, W.Koepff, W.M.Seiler, E.V.Vorozhtsov (Eds.), LNCS 9301,
Springer, Cham, 2015, pp.166-181.
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(with D.Michels, D.Lyakhov, G.Sobottka and A.Weber) On Partial Analytical Solution to the Kirchhoff Equation. In: "Computer Algebra in Scientic Computing / CASC 2015", V.P.Gerdt, W.Koepff,
W.M.Seiler, E.V.Vorozhtsov (Eds.), LNCS 9301, Springer, Cham, 2015, pp.320-331.
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(with D.Robertz) Lagrangian constraints and Differential Thomas decomposition. (2015), http://dx.doi.org/10.1016/j.aam.2015.09.005. arXiv:math.DS/1509.01464
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(with A.A.Gusev, L.L.Hai, V.L. Derbov, S.I.Vinitsky, O.Chuluunbaatar) Symbolic-Numeric Algorithms
for Solving BVPs for a System of ODEs of the Second Order: Multichannel Scattering and Eigenvalue
Problems. In: "Computer Algebra in Scientific Computing / CASC 2016", V.P.Gerdt, W.Koepff,
W.M.Seiler, E.V.Vorozhtsov (Eds.), LNCS 9890, Springer, Cham, 2016, pp.212-227.
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(with A.A.Gusev, S.I.Vinitsky, V.L.Derbov, A.Góźdź and A. Pędrak, A.Szulerecka and A.Dobrowolski)
Symbolic algorithm for generating irreducible rotational-vibrational bases of point groups. In: \Computer
Algebra in Scientific Computing / CASC 2016", V.P.Gerdt, W.Koepff, W.M.Seiler, E.V.Vorozhtsov
(Eds.), LNCS 9890, Springer, Cham, 2016, pp.228-242.
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(with D.Michels, D.Lyakhov, Z.Hossain, I.Riedel-Kruse and A.Weber) On the General, Analytical
Solution of the Kinematic Cosserat Equations. In: \Computer Algebra in Scientific Computing /
CASC 2016", V.P.Gerdt, W.Koepff, W.M.Seiler, E.V.Vorozhtsov (Eds.), LNCS 9890, Springer, Cham,
2016, pp.367-380.
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(with A.Khvedelidze and Yu.Palii) On the ring of local unitary invariants for mixed X-states of two
qubits. Zapiski Nauchnyh Seminarov POMI 448, 2016, 107-123. arXiv:quant-ph/1603.03262
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(with A.A.Gusev, S.I.Vinitsky, O.Chuluunbaatar, V.L.Derbov) Symbolic numerical algorithms and
programs for the solution of boundary-value problems of dynamics of few-body quantum systems. In the
Proceedings of the 9th International Scientific Conference "Distributed Computer and Communication
Networks: Control, Computation, Communications (DCCN-2016), V.M.Vishnevskiy, K.E.Samouylov
(Eds.), Vol.2, Mathematical Modelling Simulation and Control Problems, Moscow, 2016, pp.100-108.
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(with Yu.A.Blinkov, K.B.Marinov) Computer Algebra Based Discretization of Quaslinear Evolution
Equations. Programming and Computer Software, 43(2), 2017, 84-89.
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(with P.Amodio, Yu.A.Blinkov and R.La Scala) Algebraic construction and numerical behavior of a
new s- consistent difference scheme for the 2D Navier-Stokes equations. Applied Mathematics and Computation, 314, 2017, 408-421.
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(with R.Bradford, J.H.Davenport, M.England, H.Errami, D.Grigoriev, Ch.Hoyt, M.Kosta, O.Radulescu, T.Sturm and A.Weber). A Case Study on the Parametric Occurrence
of Multiple Steady States. Proceedings of ISSAC 2017, ACM Press, 2017, pp.45-52. arXiv:cs.SC/1704.08997
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(with D.A.Lyakhov and D.Michels) Algorithmic Verification of Linearizability for Ordinary Differential Equations. Proceedings of ISSAC 2017, ACM Press, 2017, pp.285-292. arXiv:math.CA/1702.03829
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(with A.A.Gusev, O.Chuluunbaatar, G.Chuluunbaatar, S.I.Vinitsky, V.L.Derbov, A.Góźdź) Symbolic
Numerical Algorithm for Generating Interpolation Multivariate Hermite Polynomials of High-Accuracy
Finite Element Method. In: "Computer Algebra in Scientific Computing / CASC 2017", V.P.Gerdt,
W.Koepff, W.M.Seiler, E.V.Vorozhtsov (Eds.), LNCS 10490, Springer, Cham, 2017, pp.135-150.
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(with A.A.Gusev, O.Chuluunbaatar, G.Chuluunbaatar, S.I.Vinitsky, V.L.Derbov, A.Góźdź) Symbolic
Numerical Algorithms for Solving the Parametric Self-Adjoint 2D Elliptic Boundary-Value Problem
Using High-Accuracy Finite Element Method. In: "Computer Algebra in Scientific Computing / CASC
2017", V.P.Gerdt, W.Koepff, W.M.Seiler, E.V.Vorozhtsov (Eds.), LNCS 10490, Springer, Cham, 2017,
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(with D.A.Lyakhov, A.G.Weber and D.L.Michels) Symbolic-Numeric Integration of Dynamical Cosserat
Equations. In: "Computer Algebra in Scientific Computing / CASC 2017", V.P.Gerdt, W.Koepff,
W.M.Seiler, E.V.Vorozhtsov (Eds.), LNCS 10490, Springer, Cham, 2017, pp.301-312. arXiv:math.AP/1704.01309
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(with Yu.A.Blinkov and K.B.Marinov) Generation and analysis of a new implicit difference scheme
for the Korteveg-de Vries equation. (Proceedings of Mathematical Modeling and Computational Physics 2017,
July 3--7, Dubna, Russia. EPJ Web of Conferences 173, 2018, 03006.doi.org/10.1051/epjconf/201817303006
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(with S.Gusev, S.Vinitsky, O.Chuluunbaatar, G.Chuluunbaatar, V.Derbov, A.Góźdź, P.Krassovitskiy).
Interpolation Hermite Polynomials For Finite Element Method. (Proceedings of Mathematical Modeling and Computational
Physics 2017, July 3--7, Dubna, Russia. EPJ Web of Conferences 173, 2018, 03009. doi.org/10.1051/epjconf/201817303009
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(with A.Gusev, S.Vinitsky, O.Chuluunbaatar, G.Chuluunbaatar, V.Derbov, A.Góźdź, P.Krassovitskiy).
High-Accuracy Finite Element Method: Benchmark Calculations. (Proceedings of Mathematical Modeling and
Computational Physics 2017, July 3--7, Dubna, Russia. EPJ Web of Conferences 173, 2018, 03010. doi.org/10.1051/epjconf/201817303010
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(with Yu.Blinkov, D.Lyakhov and D.Michels) A Strongly Consistent Finite Difference Scheme
for Steady Stokes Flow and its Modified Equations. In: "Computer Algebra in Scientific Computing / CASC 2018'',
V.P.Gerdt, W.Koepff, W.M.Seiler, E.V.Vorozhtsov (Eds.), LNCS 11077, Springer, Cham, 2018, pp.67--81. arXiv:math.NA/1807.00328
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(with A.Deveikis, A.A.Gusev, S.I.Vinitsky, A.Góźdź and A.Pędrak)
Symbolic Algorithm for Generating of Orthonormal Bargmann and Moshinsky Basis for SU(3) group.
In: "Computer Algebra in Scientific Computing / CASC 2018'', V.P.Gerdt, W.Koepff, W.M.Seiler, E.V.Vorozhtsov (Eds.),
LNCS 11077, Springer, Cham, 2018, pp.131--145.
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(with A.A.Gusev, O.Chuluunbaatar, G.Chuluunbaatar, S.I.Vinitsky, V.L.Derbov, A.Góźdź and
P.M. Krassovitskiy) Symbolic-Numerical Algorithms for Solving Elliptic Boundary-Value Problems Using Multivariate
Simplex Lagrange Elements. In: "Computer Algebra in Scientific Computing / CASC 2018'', V.P.Gerdt, W.Koepff,
W.M.Seiler, E.V.Vorozhtsov (Eds.), LNCS 11077, Springer, Cham, 2018, pp.197--213.
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(with M.Lange-Hegermann, D.Robertz) The MAPLE package TDDS for Thomas decomposition
of systems of nonlinear PDEs. Computer Physics Communications, 234, 2019, 202--215. arXiv:physics.comp-ph/1801.09942
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(with D.L.Michels,Yu.A.Blinkov,D.A.Lyakhov). On the consistency analysis of finite
difference approximations. Journal of Mathematical Sciences, 240, 5, 2019, 665--677.
Zapiski Nauchnyh Seminarov POMI, 468, 2018, 249--266.
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(with Xiaojing Zhang,Yury A. Blinkov) Algebraic Construction of a Strongly Consistent,
Permutationally Symmetric and Conservative Difference Scheme for 3D Steady Stokes Flow. Symmetry, 11, 269, 2019
(15 pages). DOI: 10.3390/sym11020269
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(with Algirdas Deveikis, Alexander Gusev, Vladimir Gerdt, Sergue Vinitsky, Andrzej Góźdź,
Aleksandra Pędrak and Cestmir Burdik) Symbolic-Numerical Algorithm for Large Scale Calculations the Orthonormal
SU(3) BM Basis. In: "Computer Algebra in Scientific Computing / CASC 2019'', M. England et al (Eds.),
LNCS 11661, Springer, Cham, 2019, pp.91--106.
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(with Yu.A.Blinkov, E.A.Kotkova and I.A.Pankratov) Construction and analysis of a new implicit
difference scheme for the 2D Boussinesq paradigm equation. In: "Computer Algebra in Scientific Computing / CASC 2019'',
M. England et al (Eds.), LNCS 11661, Springer, Cham, 2019, pp.152--163.
(with D.Robertz) Algorithmic approach to strong consistency analysis of finite
difference approximations to PDE systems. Proceedings of ISSAC 2019 (Beihang University, Beijing, China,
July 15-18, 2019), Publications Dept., ACM, New York, USA, 2019, pp.163--170.
(with M.D.Malykh, L.A.Sevastyanov, Yu Ying) On the properties of numerical solutions of dynamical
systems obtained using the midpoint method. Discrete & Continuous Models: Applied Computational
Science. Vol. 27, No 1, 2019, 1-22. DOI: 10.22363/2312-9735-2019-27-1-1-22 .
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(with E.A.Kotkova and V.V.Vorob'ev) Teleportation of Bell states performed on quantum computer of IBM. Particles and Nuclei, Letters, Vol.16, No.6, 2019, 975-984.
(with D.A.Lyakhov, D.Michels) On the Algorithmic Linearizability for Nonlinear Ordinary Differential Equations. Journal of Symbolic Computation, 98, 2020, 3-22. Doi.org/10.1016/j.jsc.2019.07.004.
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(with R.Bradford, J.H.Davenport, M.England, H.Errami, D.Grigoriev, Ch.Hoyt, M.Kosta, O.Radulescu, T.Sturm and A.Weber) Identifying the Parametric Occurrence of Multiple Steady States for Biological Networks. Journal of Symbolic Computation, 98, 2020, 84-119. arXiv:cs.SC/1902.04882 Doi.org/10.1016/j.jsc.2019.07.008
Communications of Joint Institute for Nuclear Research
- (With V.A.Meshcheryakov) New Type of Sum Rules for p N - Scattering in Subthreshold Region, JINR R2- 7222, Dubna, 1973.
- (With V.A.Meshcheryakov) Local Study of Rest Points of the Chew-Low Type Equation, JINR R2-7976, Dubna, 1974.
- (With V.E.Aleinikov, M.A.Ignatenko and V.I.Zovbun) Radiation Situation in the Area of the Canal of Slow Beam Which Is Extracted from the 10 Gev Synchrophasotron, JINR 16-8583, Dubna, 1975.
- Local Uniformization of Amplitude of Elastic Hadron-Hadron Scattering, JINR 2-9709, Dubna, 1976.
- (With O.V.Tarasov and D.V.Shirkov) Analytical Calculations by Computer in Physics and Mathematics, JINR R2-11547, Dubna, 1978.
- With F.Kh.Abdullaev and J.S.Vaklev) The Role of Nonlinearity in a Model with a Strange Attractor, JINR R4-80-446, Dubna, 1980.
- (With A.Yu.Zharkov) Elementary Fraction Decomposition of Rational Functions in System REDUCE-2, JINR R5-82-187, Dubna, 1982.
- (With N.A.Kostov and A.B.Shvachka) Investigation of Nonlinear Water Waves Using Computer Algebra System REDUCE-2, JINR E11-83-750, Dubna, 1983.
- (With A.B.Shvachka and A.Yu.Zharkov) Classification of Integrable High-Order KdV-Like Equations, JINR R5-84-489, Dubna, 1984.
- (With A.Yu.Zharkov) On Asymptotic Expansion of General Solution of Chew-Low Equations, JINR R5-84-431, Dubna, 1984.
- (With N.A.Kostov, P.P.Raychev and R.P.Russev) Calculation of the Matrix Elements of the Hamiltonian of the Interacting Vector Boson Model Using Computer Algebra. Basic Concepts of the Interacting Vector Boson Model and Matrix Elements of the SU(3) -Quadrupole Operator, JINR E4-85-262, Dubna, 1985.
- (With N.A.Kostov, P.P.Raychev and R.P.Russev) Calculation of the Matrix Elements of the Hamiltonian of the Interacting Vector Boson Model Using Computer Algebra. Matrix Elements of the Hamiltonian and Some U(6)- Clebsh-Gordon Coefficients, JINR E4-85-263, Dubna, 1985.
- (With N.A.Kostov, P.P.Raychev and R.P.Russev) Calculation of the Matrix Elements of the Hamiltonian of the Interacting Vector Boson Model Using Computer Algebra. Matrix Elements of the Hamiltonian -Analytical Results, JINR E4-85-264, Dubna, 1985.
- (With A.S.Ilchev, V.K.Mitrjushkin and A.M.Zadorozhny) On the Phase Structure of Lattice SU(2) Gauge-Higgs Theory, JINR E2-85-104, Dubna, 1985.
- (With M.G.Meshcherykov and D.V.Shirkov) Computers in Theoretical Physics, JINR R2-86-848, Dubna, 1986.
- (With A.Yu.Zharkov) Solving the Polynomial Equations Arising in Classification of Integrable Coupled KdV-like Systems, JINR R5-89-231, Dubna, 1989.
- (With N.A.Kostov, Z.T.Kostova and I.P.Yudin) Algebraic-Numeric Calculations of Proton Trajectories in Bending Magnets of Synchrotron Accelerator, JINR E11-89-755.
- (With L.M.Berkovich, Z.T.Kostova and M.L.Nechaevsky) Computer Algebra Generating Related 2nd Order Linear Differential Equation, JINR E5-90-509, Dubna, 1990.
- (With A.Yu.Zharkov) Algorithms for Investigating Integrability of Quasi-linear Evolution Systems with Non-degenerated Main Matrix, JINR R5-91-225, Dubna, 1991.
- (With P.Tiller) A Reduce Program for Symbolic Computation of Puiseux Expansions, JINR E5-91-401, Dubna, 1991.
- (With W.Lassner) Verifying Isomorphisms of Finite Dimensional Lie Algebras by Gröbner Basis Technique, JINR E5-92-145, Dubna, 1992.
- Computer Algebra Methods in Investigation of Integrability of Nonlinear Evolution Equations, JINR 11-92-258, Dubna, 1992.
Preprints and Technical Reports
- Computer Algebra and Nonlinear Equations: Recent Achievements, Publication IT-270, Laboratoire d'Informatique Fondamentale de Lille, Lille, 1995.
- (With Yu.A.Blinkov) Involutive Polynomial Bases, Publication IT-271, Laboratoire d'Informatique Fondamentale de Lille, Lille, 1995.
Papers Submitted/Accepted for Publication
-
Work in Progress
- A strongly consistent finite difference scheme for the 3D incompressible Navier - Stokes equations.
- (with Yu.A.Blinkov) Compact and Computationally Efficient Involutive Bases.
- (with K.K.Sharma, P.V.Gerdt) Milestone Developments in Quantum Information and No-Go Theorems.
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