Curriculum Vitae
of Professor
Vladimir P. Gerdt

May 15, 2017

Personal Data 

Born:
 

January 21, 1947, in Engels, Russia

Married to:

Evgenia Almazova

Children:

Two sons, Peter and Anton

Citizenship:

Russia
Address:

Laboratory of Information Technologies (LIT)
Joint Institute for Nuclear Research (JINR)
141980 Dubna
Russia

Telephones:

+7-49621-63437 at work; +7-49621-20899 at home

Fax:

+7-49621-65145

E-mail:

gerdt@jinr.ru

URL:

http://compalg.jinr.ru/CAGroup/Gerdt/, http://invo.jinr.ru.

Education:

M.S. in Theoretical Physics, Saratov State University, 1971[*].
Ph.D. in Theoretical and Mathematical Physics, JINR, 1976
D.Sc. in Physics and Mathematics, JINR, 1992.
Prof. in Mathematics and Computer Science by speciality ``Application of Computer Techniques, Mathematical Modelling and Mathematical Methods to Scientific Research'', JINR, 1997.

[*] I also did graduate studies in Theoretical Physics at the Physical Department of the Moscow State University (1969-1971).

Languages:

On the scale: rudimentary, poor, good, very good and excellent, my written and oral abilities in the following languages are:
Russian: excellent; English: very good; German: poor, French: rudimentary.

Positions:

Engineer-Programmer, Dept. of Radiation Safety, JINR, 1971-75.
Junior Research Worker, Dept. of Radiation Safety, JINR, 1975-77.
Research Worker, LIT, JINR, 1977-80.
Senior Research Worker, LIT, JINR, 1980-83.
Head of Computer Algebra Research Group (after 2007: Research Group on Algebraic and Quantum Computation), LIT, JINR, 1983-present.

Research Interests:

Computer Algebra, Symbolic and Algebraic Computation, Algebraic Analysis of Nonlinear Differential Equations, Solving Polynomial Equations, Design, Analysis and Implementation of (Algebraic) Algorithms, Computer Algebra Application to Mathematics and Physics, Quantum Computing, Adaptation to High-Performance and Exaflops Computing.

Current Research:
Involutive methods and algorithms applied to systems of polynomial and differential equations; computer-algebraic methods in simulation of quantum computation.

 

 

New Methods Developed 

 

  1. A computer-aided method for integrability analysis of nonlinear evolution equations, exploring the symmetry approach proposed by a group of Russian mathematicians under leadership A.B.Shabat. The computer-based part of the method was developed in 1984 for one-component equations and generalized in 1987 for multi-component ones
    together with A.Yu.Zharkov.

  2. An algorithmic method for generating and solving linear ordinary differential equation with elliptic coefficients and spectral parameter, which are integrable in terms of the elliptic functions. This method can be considered as generalization of constructive ideas of French mathematicians Hermite and Halphan on the basis of modern, high sophisticated, technique has been elaborated for investigating periodical solutions of integrable nonlinear evolution equations. Developed in 1989 together with N.A.Kostov.

  3. A computer algebra tool for integrability analysis, classification and construction of higher order Lie-Bäcklund evolutionary symmetries for multi-parametric families of polynomial-nonlinear evolution equations. This tool designed in the form of two separate modules written in the computer algebra language Reduce. It is the only tool which allows to generate polynomial systems in arbitrary parameters, equivalent to the integrability conditions, and to solve them. Developed in 1990-1991 together with A.Yu.Zharkov.

  4. A method of reduction, or splitting, homogeneous multivariate polynomial systems. It is based on a new concept of homogeneity, more general one than the well-known concept of Gamma-homogeneity has been intensively used for complexity analysis of Buchberger's algorithm for Gröbner bases construction for a polynomial ideals. The homogeneity reduction comb ined with the Gröbner bases technique, or with any other algorithmic method for "triangularization" of polynomial systems, increases its efficiency dramatically.

  5. An algorithmic approach to construction of Lie algebras and superalgebras given by a finite set of generators and defining relations. In this method a complete set of relations, that is a Gröbner basis, is constructed by means of sequential (Lie-)multiplications of the
    relations by single generators, first, and reductions modulo the current set of relations, second. The algorithm was developed and implemented in C together with V.V.Kornyak.

  6. An algorithmic method for the involution analysis of polynomial, linear differential and difference ideals. It is based on a concept of restricted monomial division defined on finite monomial sets. Involutive divisions form an important class of such restricted divisions. Every involutive division provides for each monomial a self-consistent partitioning the whole set of variables into two disjoined subsets called multiplicative and non-multiplicative. Given an admissible ordering, that partitioning is prescribed also to polynomials in terms of their leading monomials. Every specific partition provides its own algorithmic scheme for construction of an involutive Gröbner basis by doing non-multiplicative prolongations and multiplicative reductions. Among the other things the method gives one more efficient algorithm for construction of Gröbner bases. The underlying algorithms for completion to involution of polynomial and linear differential systems have been implemented in Reduce, C/C++ (GINV package) and Maple. The method is under further development and implementation in collaboration with Yu.A.Blinkov and D.Robertz.

  7. A computer algebra method for computation and separation of the complete set of constraints for generalized Hamiltonian dynamical systems of polynomial type. The method is based on combining of the classical Dirac method with (involutive) Gröbner bases. This yields the full algorithmization of the constraint computation as well as their separation in the first and second classes.

  8. An algorithmic approach to generation of finite difference approximations for partial differential equations and systems of such equations based on combination of the finite volume method with difference elimination by means of Gröbner bases. The method developed in 2005-2006 together with Yu.A.Blinkov and V.V.Mozzhilkin.

  9. A computer-algebra based method to analyze consistency of finite difference approximations to systems of partial differential equations. The method combines algorithmic techniques of differential and difference algebra and based on the new notion of strong consistency which means inheritance at the discrete level of algebraic properties of the differential equations. The method developed in 2010 for linear PDE systems together with D.Robertz, and then extended in 2011 to nonlinear systems.

 

 

Lecture Courses Given for Students and Young Scientists 

  1. Analytical Computations by Computer. Karel University, Petrozavodsk, U.S.S.R. Autumn 1981.
  1. Analytical Computations by Computer and its Application to High Energy Physics. XY International School on High Energy Physics for Young Scientists, Dubna, U.S.S.R. Nov.-Dec. 1982.
  1. Lie Methods in Differential Equations. University of Leipzig, GDR. Spring 1987.
  1. Computer Algebra Systems. All-Union School on Analytic Computations in Mechanics, Moscow, U.S.S.R. Autumn 1987.
  1. Computer Algebra Application to High Energy Physics. International School on the Problems of Use of Computers in Physical Research, Dubna, U.S.S.R. Autumn 1988.
  1. Introduction to Computer Algebra. Far-East University, Vladivostok, U.S.S.R. Autumn 1989.
  1. Gröbner Bases. Nankai Institute of Mathematics, Tianjin, China. Spring 1991.
  1. Applications of Symbolic Computation. Far-East University, Vladivostok, Russia. Autumn 1991.
  1. Perturbation Methods in Mechanics. Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden. Spring 1993.
  1. Lie Symmetry Analysis of Partial Differential Equations. Department of Mathematics and Computer Science, University of Greifswald, Germany. Spring 1993.
  1. Computer Algebra and Polynomial Equations, University of Limoges, France. Autumn 1994.
  1. Computer Algebra and Solving Polynomial Equations, University of Pereslavl. Spring 1997, Russia.
  1. Introduction to Programming in C/C++, University of Applied Sciences, Ravensburg-Weingarten, Winter Semester, 2000-2001.
  1. Applied Computer Algebra, University of Applied Sciences, Ravensburg-Weingarten, Winter Semester, 2000-2001.
  1. Elements of Computer Mathematics, University of Applied Sciences, Ravensburg-Weingarten, Winter Semester, 2000-2001.
  1. Introduction to Programming in C, University of Rostock, Winter Semester, 20002-2003.
  1. Programming Techniques / Algorithms and Data Structures, University of Rostock, Winter and Summer Semesters, 20002-2003.
  1. Elements of Computer Mathematics, University of Rostock, Summer Semester, 20002-2003.
  1. Introduction to Quantum Computing, University of Rostock, Summer Semester, 20002-2003.
  1. Introduction to Programming in C/C++, University of Applied Sciences, Ravensburg-Weingarten, Winter Semester, 2004-2005.
  1. Elements of Computer Mathematics, University of Applied Sciences, Ravensburg-Weingarten, Winter Semester, 2004-2005.
  1. Introduction to Quantum Computing, University of Applied Sciences, Ravensburg-Weingarten, Winter Semester, 2004-2005.

  2. Computer Mathematics and Fuzzy Systems, University of Applied Sciences, Ravensburg-Weingarten, Winter Semester, 2005-2006.

  3. Elements of Quantum Computation and Information, University of Applied Sciences, Ravensburg-Weingarten, Winter Semester, 2005-2006.

  4. Introduction to Quantum Informatics, University of Applied Sciences, Ravensburg-Weingarten, Summer Semester, 2007.

  5. Fuzzy Logics and Fuzzy Control with Mathematica, University of Applied Sciences, Ravensburg-Weingarten, Summer Semester, 2007.

  6. Introduction to Quantum Physics, University of Applied Sciences, Ravensburg-Weingarten, Summer Semester, 2007.

  7. Applied Computer Algebra, Ravensburg-Weingarten, Summer Semester, 2007.

  8. Introduction to Quantum Computation with Application of Computer Algebra, Rheinisch-WestfÄalische
    Technische Hochschule, Aachen, Winter Semester, 2008-2009.

  9. Fuzzy Logic and Fuzzy Control with Application of Computer Algebra, Rheinisch-WestfÄalische Technische Hochschule, Aachen, Winter Semester, 2009-2010.

  10. Theory and Applications of Involutive Bases, University of Kassel, Winter Semester, 2010-2011.

  11. Introduction to Differential Algebra, Winter Semester, 2010-2011.

  12. Introduction to Quantum Computation with Application of Computer Algebra, Winter Semester, 2011-2012.

  13. Constrained Dynamics, Winter Semester, 2012-2013.

 

Advising Students and PhD Theses 

  • Mr.Alexey Yu. Zharkov, Master Project, 1979, Three-Loop Computation of Anomalous Dimension and Renormalization Constant of the Ghost Propagator in Quantum Chromodynamics.
  • Mr.Valery V. Polyansky, Master Project, 1981, Analytic Calculation of Solution of the Chew-Low Equations with Reduce.
  • Dr. Alexey Yu. Zharkov, Ph.D., 1985, Methods of Computer Algebra in Investigation of Nonlinear Difference and Evolution Equations.
  • Ms. Franziska Kohley, Master Practicum, 1988, Symbolic Computation of Jordan Form for a Matrix with Elements from Q.
  • Mr. Kersten Schöbel, Master Practicum, 1988, Symbolic Computation of Matrix Eigenvalues and Eigenvectors.
  • Mr. Thomas Henke, Master Practicum, 1989, Algebraic Algorithms for Computation of Characteristic Polynomial of Matrices.
  • Mr. Sven Muecke, Master Practicum, 1989, Symbolic Computation of the Minimal Matrix Characteristic Polynomial.
  • Mr. Michael Ohme, Master Practicum, 1989, Symbolic Computation of Functions in Matrices.
  • Dr. Nikolay A. Kostov, Ph.D., 1990, Investigation of Integrable Models of Interacting Nonlinear Waves.
  • Mr. Vladimir V. Menkov, Master Project, 1991, Symbolic Computation in Clifford Algebras.
  • Dr. Nikolay V.Khutornoy, Ph.D., 1994, Algebraic Algorithms for Investigation of Polynomial Equation Systems and their Implementation in REDUCE.
  • Dr. Yuri A.Blinkov, Ph.D., 1995, Involutive Algorithms for Investigation of Nonlinear Algebraic and Differential Equations.
  • Dr. Victor N.Robuk, Ph.D., 1995, Algorithms for Construction of Finitely Presented Lie Algebras and their Application to Integrability Analysis of Nonlinear Partial Differential Equations.
  • Mr. Andrey V.Karol, Ph.D. student since 2003, GRID Computing applied to Solving Polynomial Systems
    over Finite Fields.
  • Mr. Denis A.Yanovich, Ph.D., 2004, Algorithms and Programs of Computing Involutive Bases and their Application to Solving Nonlinear Algebraic Systems.
  • Mr. Semyon A.Evlakhov, Ph.D. student since 2007, Computation and Analysis of Invariants for the Two-Qubit Density Matrix.
  • Mr. Sergei N.Tychkov, Master Project, 2008, Computer Algebra Approaches to Computing Hyperdeterminants.
  • Mr. Mikhail V.Zinin, Ph.D., 2013, Symbolic Algorithms and Programs or Computing Boolean Gröbner.
  • Mr. Konstantin B. Marinov, Master Project, 2015, Implementation in Maple of the Original Version of Algorithm F5 for Computation of Gröbner Bases.

 

Consulting Theses for Doctorship of Sciences 

  • Dr. Yuri A.Blinkov. 2009. Involutive Methods to Analyze Models Described by Systems of Algebraic and Differential Equations.

 

Current Foreign Collaborators 

 

Research and Teaching Visits 

  • Nov.-Dec. 81. Invited Lecturer, Department of Mathematics and Physics, Karel University, Petrozavodsk, U.S.S.R.
  • May-June 87. Invited Lecturer, Department of Computer Science, University of Leipzig, GDR.
  • Sept. 89. Invited Docent, Department of Mathematics and Computer Science, Far-East University, Vladivostok, U.S.S.R.
  • Apr.-May 91. Invited Professor, Nankai Institute of Mathematics, Tianjin, China.
  • Sept. 91. Invited Professor, Far-East University, Vladivostok, Russia.
  • Jun.-Jul. and Sept.-Oct. 91. Senior Research Visitor, Department of Computer Science, University of Leipzig, Germany.
  • Nov.92-May 93. Senior Visiting Scientist and Lecturer, Department of Mechanics, Royal Institute of Technology, Stockholm, Sweden.
  • Jun. 93. Invited Professor, Department of Mathematics and Informatics, University of Greifswald, Germany.
  • Sept.-Dec. 94. Invited Professor, Department of Mathematics, University of Limoges, France.
  • Jan.-Mar. 95. Invited Professor, Computer Science Laboratory, University Lille I, France.
  • Sept.-Oct. 96. Invited Professor, Institute of Physics, University of Liege, Belgium.
  • Apr.-Jun. 97. Invited Professor, Institut für Algorithmen und Kognitive Systeme, University of Karlsruhe, Germany.
  • Sept.-Nov. 97. Invited Professor, Department of Mathematics and Informatics, University of Greifswald, Germany.
  • Mar. 99. Invited Professor, Department of Mathematics, University of Catania, Italy.
  • Apr.-July 99. Invited Professor, Department of Mathematics and Informatics, University of Greifswald, Germany.
  • Oct.00-Apr.01. Invited Professor. University of Applied Sciences, Ravensburg-Weingarten, Germany.
  • Sept.02-Aug.03. Invited Professor, Department of Computer Science, University of Rostock, Germany.
  • Oct.04-Apr.05. Invited Professor, University of Applied Sciences, Ravensburg-Weingarten, Germany.
  • Oct.05-Apr.06. Invited Professor, University of Applied Sciences, Ravensburg-Weingarten, Germany.
  • Mar.-Aug.07. Invited Professor, University of Applied Sciences, Ravensburg-Weingarten, Germany.
  • Oct.08-Mar.09. Invited Professor, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany.
  • Oct.09-Mar.10. Invited Professor, Rheinisch-Westfälische Technische Hochschule, Aachen, Germany.
  • Oct.10-Mar.11. Invited Professor, University of Kassel, Kassel, Germany.
  • May 11. Invited Professor, Laboratory if Informatics (LIP6), Pierre and Marie Curie University (UPMC), Paris, France.
  • Oct.11-Mar.12. Invited Professor, University of Kassel, Kassel, Germany.

 

Professional Activities 

  • Sept. 79. Organizing Committee of International Conference on Computer Algebra, Dubna, U.S.S.R.
  • Sept. 82. Organizing Committee of II International Conference on Computer Algebra, Dubna, U.S.S.R.
  • Sept. 85. Organizing Committee of III International Conference on Computer Algebra, Dubna, U.S.S.R.
  • June 87. Program Committee of EUROCAL'87, Leipzig, GDR.
  • July 88. Program Committee of ISSAC-88, Rome, Italy.
  • May 90. Organizing Committee of IV International Conference on Computer Algebra, Dubna, U.S.S.R.
  • July 91. Program Committee of ISSAC'91, Bonn, Germany.
  • June 93. Scientific Committee of the IMACS Symposium on Symbolic Computation, Lille, France.
  • July 93. Co-Chair of ISSAC'93, Kiev, Ukraine.
  • March 94. Program Committee of International Conference on Interval and Computer-Algebraic Methods in Science and Engineering, St-Petersburg, Russia.
  • July 94. Program Committee of International Workshop on New Computer Technologies in Control Systems, Pereslavl-Zalessky, Russia.
  • August 95. Program Committee of 2nd International Workshop on New Computer Technologies in Control Systems, Pereslavl-Zalessky, Russia.
  • July 96. Program Committee of 3rd International Workshop on New Computer Technologies in Control Systems, Pereslavl-Zalessky, Russia.
  • May 97. Scientific Committee of International Symposium on Differential Algebraic Equations, Grenoble, France.
  • June 97. Co-chair of International Workshop on Symbolic-Numeric Analysis of Differential Equations, Prague, Chech Republic.
  • July 1997. Program Committee Co-chair of the 3rd IMACS-ACA Conference on Application of Computer Algebra, Maui, Hawaii, USA.
  • Feb. 1998. Program Committee of International Conference on Gröbner Bases, Linz, Austria.
  • March 1998. Program Committee of the 6th Rhein Workshop on Computer Algebra, St-Augustin, Germany.
  • April 1998. Co-chair of the 1st International Workshop on Computer Algebra in Scientific Computing, Saint-Petersburg, Russia.
  • May-June 1999. Co-chair of the 2nd International Workshop on Computer Algebra in Scientific Computing, Munich, Germany.
  • October 2000. Co-chair of the 3rd International Workshop on Computer Algebra in Scientific Computing, Samarkand, Uzbekistan.
  • June 2001. Chair of the 5th International Workshop on Computer Algebra and its Application to Physics, Dubna, Russia.
  • September 2001. Co-chair of the 4th International Workshop on Computer Algebra in Scientific Computing, Konstanz, Germany.
  • March 2002. Programm Committee co-chair of the International Workshop on Under- and Over-Determined Systems of Algebraic or Differential Equations, Karlsruhe, Germany.
  • March 2002. Program Committee of the 8th Rhein Workshop on Computer Algebra, Mannheim, Germany.
  • August 2002. Co-chair of the 5th International Workshop on Computer Algebra in Scientific Computing, Foros, Crimea, Ukraine.
  • Sept.-Oct. 2002. Organizing Committee of the 5th International Congress on Mathematical Modelling, Dubna, Russia.
  • Oct. 2002. Program Committee of the International Symposium "Logic, Mathematics and Computer Science", Linz, Austria.
  • July-Aug. 2003. Organizing Committee of the 2rd International Workshop "Quantum Physics and Information", Dubna, Russia.
  • Sept. 2003. Co-chair of the 6th International Workshop on Computer Algebra in Scientific Computing, Passau, Germany.
  • July 2004. Co-chair of the 7th International Workshop on Computer Algebra in Scientific Computing, Saint Petersburg, Russia.
  • July 2004. Program co-chair of the 10th International Conference on Applications of Computer Algebra, Beaumont, Texas, U.S.A.
  • April 2005. Program Committee of the International Conference "Algorithmic Algebra and Logic 2005", Passau, Germany.
  • May 2005. Advisory Committee of X International Workshop on Advanced Computing and Analysis Techniques in Physics Research, Zeuthen, Germany.
  • June 2005. Organizing Committee of the International Workshop "Symbolic Calculations and Exact Methods in Mathematical Physics", Kyiv, Ukraine.
  • June-July 2005. Organizing Committee of the 3rd International Workshop "Quantum Physics and Information", Dubna, Russia.
  • Sept. 2005. Co-chair of the 8th International Workshop on Computer Algebra in Scientific Computing, Kalamata, Greece.
  • June 2006. Co-chair of the 12th International Conference on Applications of Computer Algebra, Varna, Bulgaria.
  • Sept. 2006. Co-chair of the 9th International Workshop on Computer Algebra in Scientific Computing, Chisinau, Moldova.
  • July 2007. Chair of the Poster Committee of ISSAC’07, Waterloo, Canada.
  • Sept. 2007. Co-chair of the 10th International Workshop on Computer Algebra in Scientific Computing, Bonn, Germany.
  • March 2007. Co-chair of the International Conference on Differential Algebra and Related Computer Algebra, Catania, Italy.
  • July 2008. Co-chair of the 14th International Conference on Applications of Computer Algebra / ACA- 2008, RISC, Castle of Hagenberg, Austria.
  • November 2008. Advisory Committee of 11th International Workshop on Advanced Computing and Analysis Techniques in Physics Research / ACAT-2008, Sicily, Italy.
  • April 2009. Program Committee of the 2nd International Workshop on Polynomial Computer Algebra / PCA-2009, St.Petersburg, Russia.
  • July 2009. Organizing Committee of the 4th International Conference "Mathematical Modelling and Computational Physics / MMCP-2009'', Dubna, Russia.
  • September 2009. Co-chair of the 11th International Workshop on Computer Algebra in Scientific Computing / CASC-2009, Kobe, Japan.
  • October 2009. Program Committee of the 2nd International Workshop on Computer Algebra and Differential Equations / CADE-2009, Pamplona, Spain.
  • April 2010. Program Committee of the 3rd International Workshop on Polynomial Computer Algebra / PCA-2010, St.Petersburg, Russia.
  • July 2010. Program Committee of the International Conference on Symbolic Computation and its Applications, Maribor, Slovenia.
  • September 2010. Co-chair of the 12th International Workshop on Computer Algebra in Scientific Com puting / CASC-2010, Tsakhkadzor, Armenia.
  • September 2011. Co-chair of the 13th International Workshop on Computer Algebra in Scientific Computing / CASC-2011, Kassel, Germany.
  • September 2012. Co-chair of the 14th International Workshop on Computer Algebra in Scientific Computing / CASC-2012, Maribor, Slovenia.
  • May 2013. Program Committee of the 5th International Workshop on Polynomial Computer Algebra / PCA-2013, St.Petersburg, Russia.
  • July 2013. Organizing Committee of the 6th International Conference \Mathematical Modelling and Computational Physics / MMCP-2013", Dubna, Russia.
  • September 2013. Co-chair of the 15th International Workshop on Computer Algebra in Scienti c Computing / CASC-2013, Berlin, Germany.
  • September 2013. Scienti c Committee of the 21th International Conference on Applied and Industrial Mathematics / CAIM-2013, Bucharest, Romania.
  • April 2014. Program Committee of the 6th International Workshop on Polynomial Computer Algebra / PCA-2014, St.Petersburg, Russia.
  • September 2014. Co-chair of the 16th International Workshop on Computer Algebra in Scienti c Computing / CASC-2014, Warsaw, Poland.
  • April 2015. Program Committee of the 7th International Workshop on Polynomial Computer Algebra / PCA-2015, St.Petersburg, Russia.
  • July 2015. Program Committee of the 40th International Symposium on Symbolic and Algebraic Computation / ISSAC-2015, Bath, England.
  • July 2015. Organizing Committee of the 6th International Conference \Mathematical Modelling and Computational Physics / MMCP-2015", High Tatra Mountains, Slovakia.
  • September 2015. Co-chair of the 17th International Workshop on Computer Algebra in Scienti c Computing / CASC-2015, Aachen, Germany.
  • September 2016. Co-chair of the 18th International Workshop on Computer Algebra in Scientic Computing / CASC-2016, Bucharest, Romania.

 

Coordination of International Research Projects 

  1. Adjoint coordinator of the INTAS-93-0030 project "Computer Algebra, Symbolic and Combinatorial Tools in Differential Algebra and Differential Equations, with impact in Fundamental Physics and Control Theory" with 10 research teams from EC countries and 7 research team from NIS countries.
  1. Scientific coordinator of the claster A: Computer Assisted Mathematics of the INTAS-93-0893 project "ERSIM-FSU Cooperative Network in Informatics and Applied Mathematics" with 10 research teams EC countries and 10 rearch teams from NIS countries.

 

Coordination of National Research Projects 

  1. RFBR 98-01-00101 (1998-2000) "Involutivity Analysis of Constrained Dynamical Systems".
  1. RFBR 01-01-00708 (2001-2003) "Computer methods for involutivity analysis of differential equations and their application to gauge field theories".
  1. RFBR 04-01-00784 (2004-2006) "Computer-based completion of nonlinear systems to involution and its application to generalized Hamiltonian dynamics and to generation of fnite-difference schemes for partial differential equations".
  1. RFBR 07-01-00660 (2007-2009) "Computer-based compatibility analysis of equation syetems with application to quantum computation, gauge models of field theory and numerical solving of partial differential equations".
  1. RFBR 10-01-00200 (2010-2012) "Computer algebra modeling of quantum computation and discrete systems".
  1. RFBR 13-01-00668 (2013-2015) "Development of computer algebra methods for modelling entanglement of multiparticle quantum systems and systems with constraints''.

 

Memberships 

  • ACM - Association for Computing Machinery.
  • SIGSAM - ACM Special Interest Group on Symbolic and Algebraic Manipulation.
  • Editorial Board of Journal of Symbolic Computation (Academic Press).
  • Advisory Board of Computer Science Journal of Moldova.
  • Special Computer Algebra Group of German Societies on Computer Science.

 

Referee - Reviewer 

  • Journal of Symbolic Computation.
  • Programming and Computer Software.
  • Physics of Particles and Nuclei Letters.
  • Russian Foundation for Basic Research.
  • Russian Science Foundation.

 

Editorial Works 

  1. (With E.W.Mayr and E.V.Vorozhtsov) Computer Algebra in Scientific Computing / CASC 2009, Lecture Notes in Computer Science, 5743, Springer-Verlag, 2009.
  2. (With W.Koeppf, E.W.Mayr and E.V.Vorozhtsov) Computer Algebra in Scientific Computing/ CASC 2010, Lecture Notes in Computer Science, 6244, Springer-Verlag, 2010.
  3. (With W.Koeppf, E.W.Mayr and E.V.Vorozhtsov) Computer Algebra in Scienti c Computing/ CASC 2011, Lecture Notes in Computer Science, 6885, Springer-Verlag, 2011.
  4. (With W.Koeppf, E.W.Mayr and E.V.Vorozhtsov) Computer Algebra in Scienti c Computing/ CASC 2012, Lecture Notes in Computer Science, 7442, Springer-Verlag, 2012.
  5. (With W.Koeppf, E.W.Mayr and E.V.Vorozhtsov) Computer Algebra in Scienti c Computing/ CASC 2013, Lecture Notes in Computer Science, 8136, Springer-Verlag, 2013.
  6. (With W.Koeppf, E.W.Mayr and E.V.Vorozhtsov) Computer Algebra in Scienti c Computing/ CASC 2014, Lecture Notes in Computer Science, 8860, Springer-Verlag, 2014.

Publications 

Articles in Books, Journals, Proceedings

  1. (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. 
  1. ((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.
  1. (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. 
  1. (With V.A.Meshcheryakov) Local Form of the Solution of the Chew-Low Equations, Teor. Mat. Fiz., 24, 2, 1975, 155-163. 
  1. (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. 
  1. (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. 
  1. (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.  
  1. (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. 
  1. 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 
  1. 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. 
  1. 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. 
  1. (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. 
  1. (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. 
  1. 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. 
  1. 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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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.  
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (With A.S.Ilchev, V.K.Mitrjushkin, I.K.Sobolev and A.M.Zadorozh, Nuclear Physics B265 [FS15], 1986, 145-160. 
  1. (With D.Yu.Grigor'ev) Computer Algebra Algorithms, Systems and Applications, In: "Computer Algebra. Symbolic and Algebraic Computation", Mir Publishers, Moscow, 1986, 373-383. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (With D.V.Shirkov) New Trends in Computer Science. Computer Algebra, In: "Computers in Modern Science", Nauka Publishers, Moscow, 1988, 35-48. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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.  
  1. (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. 
  1. (With A.Yu.Zharkov) Computer Classification of Integrable Coupled KdV-Like Systems, Journal of Symbolic Computation, 10, 1990, 203-207. 
  1. (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. 
  1. (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 
  1. 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. 
  1. (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.   
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. 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. 
  1. (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. 
  1. (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. 
  1. 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. 
  1. (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. 
  1. (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. 
  1. (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
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. Homogeneity of Integrability Conditions for Multiparametric Families of Polynomial-Nonlinear Evolution Equations, Mathematics and Computers in Simulation, 42, 1996, 399-408. 
  1. (With V.V.Kornyak) Construction of Finitely Presented Lie Algebras and Superalgebras, Journal of Symbolic Computation, 21, 1996, 337-349. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. (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. 
  1. Gröbner Bases and Involutive Methods for Algebraic and Differential Equations, Mathematics and Computers in Modelling, 25, No. 8/9, 1997, 75-90. 
  1. (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. 
  1. (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. 
  1. (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
  1. (With Yu.A.Blinkov) Minimal Involutive Bases, Mathematics and Computers in Simulation 45, 1998, 543-560.
    URL: http://arXiv.org/abs/math.RA/9912029
  1. (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.  
  1. (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. 
  1. (With Yu.A.Blinkov) Involutive Monomial Divisions, Russian Journal "Programming and Computer Software", 24, No.6, 1998, 283-285.  
  1. 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.  
  1. (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.  
  1. (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.  
  1. (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.  
  1. 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.  
  1. 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 
  1. (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.  
  1. 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.  
  1. (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.  
  1. (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.  
  1. (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. 
  1. On an Algorithmic Optimization in Computation of Involutive Bases. Russian Journal "Programming and Computer Software", Vol. 28, No. 2, 2002, 62-65.  
  1. Involutive Division Technique: Some Generalizations and Optimizations. Journal of Mathematical Sciences 108(6), 2002, 1034-1051. URL: http://arXiv.org/abs/math.SC/9912030.  
  1. (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
  1. (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
  1. (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. 
  1. (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. 
  1. (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. 
  1. (With G. Carra'Ferro) Improved Kolchin-Ritt Algorithm. Programming and Computer Software, Vol.29, No.2, 2003, 83-87. 
  1. (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
  1. (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. 
  1. (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. 
  1. (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
  1. (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. 
  1. Gröbner Bases in Perturbative Calculations. Nuclear Physics B (Proc. Suppl.) 135, 2004, 232-237.
    URL: http://arXiv.org/hep-ph/0501053
  1. (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. 
  1. 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. 
  1. (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. 
  1. (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. 
  1. (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.  
  1. (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. 
  1. (With D.Robertz) Computation of Gröbner Bases for Systems of Linear Difference Equations. Computeralgebra, Rundbrief Nr.37, GI_DMV_GAMM, 2005, 8-13. 
  1. (With Yu.A.Blinkov) On Computing Janet Bases for Degree Compatible Orderings. Proceedings of the 10th Rhine Workshop on Computer Algebra (Basel, Switzerland, March 16-17, 2006), J.Draisma and H.Kraft (Eds.), University of Basel, 2006, pp.107--117 URL: http://arXiv:math.AC/0603161
  1. On Computation of Gröbner Bases for Linear Difference Systems. Nuclear Instruments and Methods in Physics Research 559(1), 2006, 211--214. URL: http://arXiv.org/math-ph/0509050.  
  1. (With D.Robertz) A Maple Package for Computing Gröbner Bases for Linear Recurrence Relations. Nuclear Instruments and Methods in Physics Research 559(1), 2006, 215--219. URL: http://arXiv:cs.SC/0509070.  
  1. (With V.M.Severyanov) A Software Package to Construct Polynomial Sets over Z2 for Determining the Output of Quantum Computation. Nuclear Instruments and Methods in Physics Research A 559(1), 2006, 215--219. 260-264. URL: arXiv:quant-ph/0509064. 
  1. (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 

  1. (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.  

  1. (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.  

  1. (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.

  2. (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

  3. (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.

  4. (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

  5. 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.

  6. (With A.M.Khvedelidze and D.M.Mladenov) . On application of involutivity analysis of differential equations to constrained dynamical systems. Symmetries and Integrable Systems, Selected Papers of the Seminar, 2000--2005, A.N.Sissakian (ed.), vol.1, Dubna, JINR, pp.132--150, 2006. arXiv:hep-th/0311174.

  7. (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.

  8. (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.

  9. (With A.Gusev, M.Kaschiev, V.Rostovtsev, V.Samoylov, T.Tupikova, Y.Uwano, S.Vinitsky) On Symbolic- Numerical Representation of Evolution Operator for Finite-Dimensional Quantum Systems. Particles and Nuclei, Letters, Vol. 4, No.2, 2007, 253-259.

  10. (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.

  11. (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.

  12. (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– 133.

  13. (With A.M.Khvedelidze, Yu.G.Palii.) Deducing the constraints in the light-cone SU(3) Yang-Mills mechanics via Gr¨obner 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.

  14. (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 symposium, University of South Africa, Pretoria, 2007, pp.219-232.

  15. On Completion to Involution Based on Janet Division. Computer Algebra and Differential Equations, Acta Academiae Aboensis, Ser. B, Vol. 67, no. 2, 2007, pp.1-11.

  16. (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. B, Vol. 67, no. 2, 2007, pp.28-38.

  17. (With M.V.Zinin) On computation of Gr¨obner bases over F2. Computer Algebra and Differential Equations, Acta Academiae Aboensis, Ser. B, Vol. 67, no. 2, 2007, pp.59-68.

  18. (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.

  19. (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.

  20. (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 radial equations for a Hydrogen-like atom in a homogeneous magnetic field. Computer Physics Communications 178, 301–330, 2008.

  21. On Decomposition of Algebraic PDE Systems into Simple Subsystems. Acta Appl. Math. 101, 2008, 39–51.

  22. Gröbner Bases Applied to Systems of Linear Difference Equations. Physics of Particles and Nuclei Letters Vol.5, No.3, 2008, 425–436. arXiv:cs.SC/0611041

  23. (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.

  24. (With Yu.A.Blinkov) Specialized Computer Algebra System GINV. Programming and Computer Software, Vol. 34, No. 2, 2008, 112–123.

  25. (With M.V.Zinin) Involutive Method for Computing Gröbner Bases over F2. Programming and Computer Software, Vol.34, No. 4, 2008, 191–203.

  26. (With M.V.Zinin) A Pommaret Division Algorithm for Computing Gröbner Bases in Boolean Rings. Proceedings of ISSAC 2008, ACM Press, pp.95–102.

  27. (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.

  28. (With M.V.Zinin) Role of Involutive Criteria in Computing Boolean Gröbner Bases. Programming and Computer Software, Vol.35, No.2, 2009, 90–97.

  29. (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.

  30. (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, pp.17–24.

  31. (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.

  32. (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 (Eds.), LNCS 5743, Springer-Verlag, Berlin, 2009, pp.106-117.

  33. (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, Springer-Verlag, Berlin, 2009, pp.334-349.

  34. 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.

  35. (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.

  36. (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.

  37. (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.

  38. Algebraically Simple Involutive PDEs and Cauchy Problem. Journal of Mathematical Sciences, Vol.168, No.3, 2010, 362-367.

  39. (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

  40. (with D.Stefanescu and S.Yevlakhov) Estimations of Positive Roots of Polynomials. Journal of Math ematical Sciences, Vol.168, No.3, 2010, 468-474.

  41. (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.

  42. (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.

  43. (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.

  44. (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.

  45. (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 (Eds.), LNCS 6264, Springer-Verlag, Berlin, 2010, pp.106-122. arXiv:cond-mat.mes-hall/1004.4202

  46. (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).

  47. (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.

  48. (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.

  49. (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.

  50. (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.

  51. (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

  52. 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

  53. (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.

  54. (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

  55. (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

  56. (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

  57. (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.

  58. 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

  59. (With D.Robertz) Computation of Difference Gröbner Bases. Computer Science Journal of Moldova, 20(2), 2012, 203-226. arXiv:cs.SC/1206.3463

  60. (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.

  61. (with S.Gogilidze, A.Khvedelidze, D.Mladenov, V.Sanadze). Entanglement of spins under strong laser in uence. Physica Scripta, T153, 2013, 014026 (5pp). arXiv:quant-ph/1306.2074

  62. (with A.Prokopenya) Simulation of Quantum Error Correction by Means of QuantumCircuit Package. Programming and Computer Software, Vol.39, No.3, 2013, 143-149.

  63. (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

  64. (with P.Amodio, Yu.A.Blinkov and R.La Scala) On Consistency of Finite Di erence 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- 60. arXiv:math.NA/1307.0914

  65. (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 (Eds.), LNCS 8136, Springer, Cham, 2013, pp.116-129.

  66. (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

  67. (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.

  68. (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

  69. (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

  70. (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.

  71. (with D.Michels, D.Lyakhov, G.Sobottka and A.Weber) On Partial Analytical Solution to the Kirchhoff Equation. In: "Computer Algebra in Scienti c Computing / CASC 2015", V.P.Gerdt, W.Koepff, W.M.Seiler, E.V.Vorozhtsov (Eds.), LNCS 9301, Springer, Cham, 2015, pp.320-331.

  72. (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

  73. (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.

  74. (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.

  75. (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.

  76. (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

  77. (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.

  78. (with Yu.A.Blinkov, K.B.Marinov) Computer Algebra Based Discretization of Quaslinear Evolution Equations. Programming and Computer Software, 43(2), 2017, 84-89.

Communications of Joint Institute for Nuclear Research

  1. (With V.A.Meshcheryakov) New Type of Sum Rules for p N - Scattering in Subthreshold Region, JINR R2- 7222, Dubna, 1973.
  2. (With V.A.Meshcheryakov) Local Study of Rest Points of the Chew-Low Type Equation, JINR R2-7976, Dubna, 1974.
  3. (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.
  4. Local Uniformization of Amplitude of Elastic Hadron-Hadron Scattering, JINR 2-9709, Dubna, 1976.
  5. (With O.V.Tarasov and D.V.Shirkov) Analytical Calculations by Computer in Physics and Mathematics, JINR R2-11547, Dubna, 1978.
  6. 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.
  7. (With A.Yu.Zharkov) Elementary Fraction Decomposition of Rational Functions in System REDUCE-2, JINR R5-82-187, Dubna, 1982.
  8. (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.
  9. (With A.B.Shvachka and A.Yu.Zharkov) Classification of Integrable High-Order KdV-Like Equations, JINR R5-84-489, Dubna, 1984.
  10. (With A.Yu.Zharkov) On Asymptotic Expansion of General Solution of Chew-Low Equations, JINR R5-84-431, Dubna, 1984.
  11. (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.
  12. (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.
  13. (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.
  14. (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.
  15. (With M.G.Meshcherykov and D.V.Shirkov) Computers in Theoretical Physics, JINR R2-86-848, Dubna, 1986.
  16. (With A.Yu.Zharkov) Solving the Polynomial Equations Arising in Classification of Integrable Coupled KdV-like Systems, JINR R5-89-231, Dubna, 1989.
  17. (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.
  18. (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.
  19. (With A.Yu.Zharkov) Algorithms for Investigating Integrability of Quasi-linear Evolution Systems with Non-degenerated Main Matrix, JINR R5-91-225, Dubna, 1991.
  20. (With P.Tiller) A Reduce Program for Symbolic Computation of Puiseux Expansions, JINR E5-91-401, Dubna, 1991.
  21. (With W.Lassner) Verifying Isomorphisms of Finite Dimensional Lie Algebras by Gröbner Basis Technique, JINR E5-92-145, Dubna, 1992.
  22. Computer Algebra Methods in Investigation of Integrability of Nonlinear Evolution Equations, JINR 11-92-258, Dubna, 1992.

Preprints and Technical Reports

  1. Computer Algebra and Nonlinear Equations: Recent Achievements, Publication IT-270, Laboratoire d'Informatique Fondamentale de Lille, Lille, 1995.
  2. (With Yu.A.Blinkov) Involutive Polynomial Bases, Publication IT-271, Laboratoire d'Informatique Fondamentale de Lille, Lille, 1995.

Papers Submitted/Accepted for Publication

  1. (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. Submitted to Applied Mathematics and Computation.
  2. (with D.A.Lyakhov and D.Michels) Algorithmic Veri cation of Linearizability for Ordinary Differential Equations. Proceedings of ISSAC 2017 (University of Kaiserslautern, Kaiserslautern, Germany, July 25-28, 2017), to appear.
  3. (with D.A.Lyakhov, A.Weber and D.Michels) Symbolic-Numeric Integration of Dynamical Cosserat Equations. Submitted to CASC 2017 (September 18-22, 2017, Beijing, China).
  4. (with A.A.Gusev, O.Chuluunbaatar, G.Chuluunbaatar, S.I.Vinitsky, V.L.Derbov,A.Góźdź ) Symbolic- Numerical Algorithm for Generating Interpolation Multivariable Hermite Polynomials of High-Accuracy Finite Element Method. Submitted to CASC 2017 (September 18-22, 2017, Beijing, China).
  5. (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. Submitted to CASC 2017 (September 18-22, 2017, Beijing, China).

Work in Progress

  1. (with Yu.A.Blinkov and D.Michels) Strongly consistent finite difference approximations to Navier- Stokes equations.
  2. (with Yu.A.Blinkov) Compact Involutive Bases.
  3. (with Yu.A.Blinkov and K.B.Marinov) Algorithmically generated implicit difference schemes for the KdV equation.

 

 

 

Last modified:   May 31, 2017   by   Alla Bogolubskaya