Publications & Presentations

Dr. Alexander B. Levin

List of Publications

Books

  1. Levin, A. B. Difference Algebra. Springer, New York, 2008. 522 pp. ISBN-10:  9781402069468. ISBN-13: 978-1402069468 
  2. Kondrateva, M. V.; Levin, A. B.; Mikhalev, A. V.; Pankratev E. V. Differential and Difference Dimension Polynomials. Kluwer Academic Publishers, Dordrecht-Boston-London, 1999, 436 pp. ISBN-10: ISBN-13: 978-9048151417

Book chapters 

  1. Levin, A. B. Computation of the Strength of Systems of Difference Equations via Generalized Groebner Bases. Groebner Bases in Symbolic Analysis, 43-73. Walter de Gruyter, Berlin - New York, 2007. ISBN: 311019323X, 9783110193237
  2. Levin, A. B. Difference Algebra. Handbook of Algebra, Vol. 4, 241 - 334. Elsevier, 2006. ISBN-13: 978-0-444-52213-9

Papers

  1. Levin, A. A New Type of Difference Dimension Polynomials. Accepted for publication in Mathematics in Computer Science, Vol. 16 (2022), 15 pp. Doi: https://doi.org/10.1007/s11786-022-00540-9  
  1. Levin, A. Reduction with Respect to the Effective Order and a New Type of Dimension Polynomials of Difference Modules. ISSAC’22. Proceedings of the 2022 International Symposium on Symbolic and Algebraic Computation, 55 – 62. DOI: https://doi.org/10.1145/3476446.3535497.
  1. Levin, A. Bivariate Kolchin-type dimension polynomials of non-reflexive prime difference-differential ideals. The case of one translation. Journal of Symbolic Computation, Vol. 102 (2021), 173 - 188. Doi:  https://doi.org/10.1016/j.jsc.2019.10.014
  2. Levin, A. Generalized Groebner Bases and New Properties of Multivariate Difference Dimension Polynomials. ISSAC '21: Proceedings of the 46th International Symposium on Symbolic and Algebraic Computation, July 2021, 273 – 280. Doi: https://doi.org/10.1145/3452143.3465544
  1. Evgrafov, A.; Levin, A. Dimension Polynomials and the Einstein’s Strength of Some Systems of Quasi-linear Algebraic Difference Equations. Mathematics in Computer Science, Vol. 14 (2020), 347 – 360. Doi: https://doi.org/10.1007/s11786-019-00430-7
  2. Levin, A. Some properties of multivariate differential dimension polynomials and their invariants. ISSAC '20: Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, July 2020, 320 – 327. Doi: https://doi.org/10.1145/3373207.3404013  
  1. Levin, A. Multivariate Difference–Differential Dimension Polynomials. Mathematics in Computer Science, Vol. 14 (2020), 361 – 374. Doi: https://doi.org/10.1007/s11786-019-00436-1
  2. Levin, A. Hilbert-Type Dimension Polynomials of Intermediate Difference-Differential Field Extensions. Lect. Notes in Comput. Sci. (Mathematical Aspects of Computer and Information Science), 11989 (2020), 64 -79. Doi: https://doi.org/10.1007/978-3-030-43120-4_7  
  1. A. Evgrafov, A; Goyal, S; Levin, A. Some properties and applications of multivariate dimension polynomials and their computation in Python. Proceedings of the 25th International Conference on Applications of Computer Algebra. Montreal, Canada, 2019, 43 – 44.
  2. A. Levin. Hilbert-type Functions of Non-reflexive Prime Difference Polynomial Ideals. Proceedings of the 25th International Conference on Applications of Computer Algebra. Montreal, Canada, 2019, 87 – 88.
  3. Levin, A. Bivariate Dimension Polynomials of Non-Reflexive Prime Difference-Differential Ideals. The Case of One Translation. Proceeding of the 43rd International Symposium on Symbolic and Algebraic Computation. New York, NY, 2018, 255 – 262
  4. Levin, A. Bivariate Dimension Polynomials of Non-Reflexive Prime Difference-Differential Ideals. The Case of One Translation. Proceeding of the 43rd International Symposium on Symbolic and Algebraic Computation. New York, NY, 2018, 255 – 262.  
  1. Levin, A. Some Properties and Invariants of Multivariate Difference-Differential Dimension Polynomials. Proceedings of the 24th International Conference on Applications of Computer Algebra. Santa de Compostela, Spain, 2018, 168 – 169. https://par.nsf.gov/servlets/purl/10066959
  1. Levin, A. Difference Dimension Quasi-polynomials. Advances in Appl. Math., 89 (2017), 1 – 17. Doi: https://doi.org/10.1016/j.aam.2017.02.003  
  1. Fuerst, C.; Levin, A. Relative Reduction and Buchberger’s Algorithm in Filtered Free Modules. Mathematics in Computer Science, Vol. 11 (2017), no. 3 - 4, 329 – 339. Doi: https://doi.org/10.1007/s11786-017-0317-1  
  1. Levin, A. Dimension Polynomials of Intermediate Fields of Inversive Difference Field Extensions. Lect. Notes in Comp. Sci., 9582 (2016), 362–376. Doi: https://doi.org/10.1007/978-3-319-32859-1_31  
  1. Levin, A. Dimension polynomials of difference local algebras. Advances in Appl. Math., 72 (2016), 166–174. Doi: https://doi.org/10.1016/j.aam.2015.09.011  
  1. Levin, A. On the ascending chain condition for mixed difference ideals. International Mathematics Research Notices, v. 2015, no. 10, 2830–2840. Doi:  https://doi.org/10.1093/imrn/rnu021   
  1. Levin, A. Multivariate Dimension Polynomials of Inversive Difference Field Extensions. Lecture Notes in Comput. Sci., 8372 (2014), 146–163. Doi: https://doi.org/10.1007/978-3-642-54479-8_7   
  1. Levin, A. B. Multivariate Difference-Differential Polynomials and New Invariants of Difference-Differential Field Extensions. ISSAC’22. Proceedings of the 2013 International Symposium on Symbolic and Algebraic Computation, 267–274. Doi: https://doi.org/10.1145/2465506.2465521
  1. Doench, C.; Levin, A. B. Bivariate Dimension Polynomials and New Invariants of Finitely Generated D-Modules. International Journal of Algebra and Computation, 23, no. 7 (2013) , 1625 - 1651. Doi: https://doi.org/10.1142/S0218196713500409
  2. Doench, C.; Levin, A. B. Computation of the Strength of PDEs of Mathematical Physics and their Difference Approximations. Doctoral Program Computational Mathematics. Numerical Analysis and Symbolic Computation. Austrian Acad.of Sci. DK-Report 2012-09, 39 pp. https://www.dk-compmath.jku.at/publications/dk-reports/2012-07-02/view
  1. Doench, C.; Levin, A. B. Computation of Bivariate Characteristic Polynomials of Finitely Generated Modules over Weyl Algebras. arXiv:1212.1833v1.
  2. Levin, A. B. Dimension polynomials of intermediate fields and Krull-type dimension of finitely generated differential field extensions. Mathematics in Computer Science, 4 (2010), no. 2-3, 143-150. Doi: https://doi.org/10.1007/s11786-010-0048-z
  3. Levin, A. B. Dimension Polynomials of Intermediate Differential Fields and the Strength of a System of Differential Equations with Group Action. Journal of Mathematical Sciences, 163, no. 5 (2009), 554-562. Doi: https://doi.org/10.1007/s10958-009-9693-7
  4. Levin, A. B. Computation of the Strength of Systems of Difference Equations via Generalized Groebner Bases. Groebner Bases in Symbolic Analysis. Walter de Gruyter, 2007, 43 - 73. Doi: https://doi.org/10.1515/9783110922752.43  
  1. Levin, A. B. Groebner bases with respect to several orderings and multivariable dimension polynomials. Journal of Symbolic Computation, 42 (2007), 561-578. Doi: https://doi.org/10.1016/j.jsc.2006.05.006

 28. Levin, A. B. Inversive Difference Modules and Solvability of Systems of Linear Difference Equations. Rocky Mountain Journal of Mathematics, 37, no. 2 (2007), 519-532. Doi:  https://doi.org/10.1216/rmjm/1181068764

  1. Levin, A. B. Groebner Bases with respect to Several Term Orderings and Multivariate Dimension Polynomials. ISSAC’07. Proceedings of the 2007 International Symposium on Symbolic and Algebraic Computation, 251-260. 
  1. Levin, A. B. Multivariable Difference Dimension Polynomials. Journal of Mathematical Sciences, 131, no. 6 (2005), 6060 - 6082. Doi: https://doi.org/10.1007/s10958-005-0461-z
  2. Bhutani, K.; Levin, A. B. Graceful Numbers. International Journal of Mathematics and Mathematical Sciences, 29 (2002), no. 8, 495 - 499. Doi: https://doi.org/10.1155/S0161171202007615
  1. Bhutani, K.; Levin, A. B. The Problem of Sawing a Chain. Journal of Recreational Mathematics, 31, no.1 (2002-2003), 32 - 35.
  2. Levin, A. B. On the Set of Hilbert Polynomials. Bulletin of the Australian Mathematical Society, 64 (2001), 291 - 305. Doi: https://doi.org/10.1017/S0004972700039952
  3. Levin, A. B. Multivariable Dimension Polynomials and New Invariants of Differential Field Extensions. International Journal of Mathematics and Mathematical Sciences, 27 (2001), no. 4, 201 - 214. https://www.emis.de/journals/HOA/IJMMS/Volume27_4/214.pdf
  4. Levin, A. B. Reduced Groebner bases, free difference-differential modules and difference-differential dimension polynomials. Journal of Symbolic Computation, 30 (2000), 357-382. Doi: https://doi.org/10.1006/jsco.1999.0412

36. Levin, A. B. Characteristic Polynomials of Finitely Generated Modules over Weyl Algebras. Bulletin of the Australian Mathematical Society, 61 (2000), no. 3, 387 - 403. Doi:  https://doi.org/10.1017/S0004972700022425

  1. Levin, A. B. Generalized Characteristic Sets and Multivariable Differential Dimension Polynomials. Collection of Papers of VI International IMACS Conference on Applications of Computer Algebra, St. Petersburg, Russia, 2000, 69-72.
  2. Levin, A. B. Characteristic Polynomials of Finitely Generated Modules over Weyl Algebras. Collection of Papers of VI International IMACS Conference on Applications of Computer Algebra, St. Petersburg, Russia, 2000, 23 - 28.
  3. Levin, A. B. Computation of Hilbert polynomials in two variables. Journal of Symbolic Computation, 28 (1999), 681 - 709. Doi: https://doi.org/10.1006/jsco.1999.0320
  4. Levin, A. B.; Mikhalev, A. V. Type and Dimension of Finitely Generated G-algebras. Contemporary Mathematics, 184 (1995), 275 - 280.
  5. Kondrateva, M. V.; Mikhalev, A. V.; Pankratev, E. V.; Levin, A. B. Computation of Dimension Polynomials. International Journal of Algebra and Computation, 3, no. 2 (1992), 117 - 137. Doi: https://doi.org/10.1142/S0218196792000098
  6. Levin, A. B.; Mikhalev, A. V. Dimension Polynomials of Filtered Differential G-modules and Extensions of Differential G-fields. Contemporary Mathematics, 131 (1992), Part 2, 469 – 489.
  7. Levin, A. B.; Mikhalev, A. V. Dimension Polynomials of Difference-Differential Modules and of Difference-Differential Field Extensions. Abelian Groups and Modules, no. 10 (1991), 56-82 (Russsian).
  8. Levin, A. B.; Mikhalev, A. V. Type and Dimension of Finitely Generated G-algebras. Collection of Papers of the International Conference on Algebra in the Memory of A. Shirshov. Barnaul, Russia, 1991, p. 70 (Russian).
  9. Levin, A. B. Type and Dimension of a Finitely Generated Module over a Twisted Group Algebra. Collection of Papers of the International Conference on Algebra in the Memory of A. Shirshov. Barnaul, Russia, 1991, p. 69 (Russian).
  10. Levin, A. B.; Mikhalev, A. V. Type and Dimension of Finitely Generated Vector G-spaces. Vestnik of Moscow University, Ser. I, 1991, no. 4, 72 - 74 (Russian). English translation: Moscow University Mathematics Bulletin, 46, no. 4, 51 - 52.
  11. Levin, A. B.; Mikhalev, A. V. Characteristic Polynomials of Filtered Modules over Twisted Group Rings. Collection of Papers of VI National Symposium on the Theory of Rings, Algebras, and Modules. Lvov, Ukraine, 1990, p. 80 (Russian).
  12. Levin, A. B. Dimension Polynomial of a Finitely Generated Difference Field Extension. Collection of Papers of VI National Symposium on the Theory of Rings, Algebras, and Modules. Lvov, Ukraine, 1990, p. 79 (Russian).
  13. Levin, A. B. The Use of Multilevel Problems in Precalculus and Calculus. Collection of Papers of the International Conference on Mathematics Education. Tula, 1989, 11 - 12 (Russian).
  14. Levin, A. B.; Mikhalev, A. V. Dimension Polynomials of Differential Modules. Abelian Groups and Modules, no. 9 (1989), 51 - 67 (Russian).
  15. Levin, A. B. Dimension Polynomials of Filtered G-modules. Moscow State University, VINITI. No. 6849-B88 (1988), 1 - 27 (Russian).
  16. Levin, A. B. Difference-Differential Dimension Polynomials. (Jointly with A. Mikhalev) Moscow State University, VINITI, no. 6848-B88 (1988), 1 - 64 (Russian).
  17. Levin, A. B.; Mikhalev, A. V. Dimension Polynomials of Filtered G-modules and of Finitely Generated G-field Extensions. Collection of Papers on Algebra. Moscow State University, 1989, 74 - 94 (Russian).
  18. Levin, A. B. Dimension Polynomials of Difference Modules with m-adic Topology. Collection of Papers "Topological Algebra". Kishinev, Moldavia, 1988, p. 40 (Russian).
  19. Levin, A. B. Difference-Differential Dimension Polynomials and the Strength of a System of Difference-Differential Equations. Collection of Papers of XIX National Conference on Algebra. Lvov, Ukraine, 1987. Part I, p. 157 (Russian).
  20. Levin, A. B.; Mikhalev, A. V. Differential Dimension Polynomial and the Strength of a System of Differential Equations. Collection of Papers "Computable Invariants in the Theory of Algebraic Systems". Novosibirsk, Russia, 1987, 58 - 66 (Russian).
  21. Levin, A. B. Some Methods of Teaching Mathematics in a Freshman Class. Collection of Papers of the National Russian Conference on Mathematics Education, Stavropol, Russia, 1985, p. 16 (Russian).
  22. Levin, A. B. Characteristic Polynomials of Difference-Differential Modules. Collection of Papers of XVIII National Conference on Algebra, Kishinev, Moldavia, 1985. Part I, p. 307 (Russian).
  23. Levin, A. B. Inversive Difference Modules and the Problems of Solvability of Systems of Linear Difference Equations. Moscow State University, VINITI, no. 335-85 (1985), 1 - 20 (Russian).
  24. Levin, A. B. Characteristic Polynomials of D-Modules and of Finitely Generated D-Field Extensions. Moscow State University, VINITI, no. 334-85 (1985), 1 - 23 (Russian).
  25. Levin, A. B. Characteristic Polynomials of Difference Modules and Difference Field Extensions. Summary of the Dissertation for Ph. D. Degree. Kishinev, Moldavia, 1984, 1 - 21 (Russian).
  26. Levin, A. B. Type and Dimension of Finitely Generated Difference Algebras. Collection of Papers of XVII National Conference on Algebra, Minsk, Byelorussia, 1983. Part II, 126 - 127 (Russian).
  27. Levin, A. B. Applications of the Theory of Difference Modules to the Study of Systems of Difference Equations. Collection of Papers "Some Problems of Mathematics and Mechanics", Moscow State University, 1983, 15 - 16 (Russian).
  28. Levin, A. B. Type and Dimension of Inversive Difference Vector Spaces and Difference Algebras. Moscow State University, VINITI, no. 1606-82 (1982), 1 - 36 (Russian).
  29. Levin, A. B. Type and Dimension of Inversive Difference Vector Spaces. Collection of Papers of V National Symposium on the Theory of Rings, Algebras, and Modules, Novosibirsk, Russia, 1987, p. 87 (Russian).
  30. Levin, A. B. Characteristic Polynomials of Difference Modules and of Difference Field Extensions. Vestnik of Moscow University, Ser. 1, 1982, no. 4. p. 78 (Russian).
  31. Levin, A. B. Difference Local Algebras. Collection of Papers of XVI National Conference on Algebra, Leningrad, Russia, 1981, Part 1, 92 - 93 (Russian).
  32. Levin, A. B. Method of Automatic Control of Welding with the Heating. USSR Patient no.743814 (1980).
  33. Levin, A. B. Functor EXT in the Category of Inversive Difference Modules. Collection of Papers of IV National Symposium on the Theory of Rings, Algebras, and Modules, Kishinev, Moldavia, 1980, p. 67 (Russian).
  34. Levin, A. B. Characteristic Polynomials of Difference Modules and Some Properties of Difference Dimension. Moscow State University, VINITI, no. 2175-80 (1980), 1 - 42 (Russian).
  35. Levin, A. B. Characteristic Polynomials of Inversive Difference Modules and Some Properties of Inversive Difference Dimension. Uspekhi Math. Nauk, 35 (1980), no. 1, 201 - 202 (Russian). English translation: Russian Mathematical Surveys, 35, no. 1, 217 - 218. Doi: https://doi.org/10.1070/RM1980v035n01ABEH001588
  1. Levin, A. B.; Lipkin, A. S.; Vigdorchik, S. I. Comprehensive Flow Inspection of Solid Phase Joints and Automatization of Holographic Testing. Collection of papers "Scientific Foundations of Automatization of Industrial Processes", MVTU (Moscow, Russia), 1979, 55 - 57 (Russian).
  2. Karakozov, E. S.; Levin, A. B.; Lipkin, A. S. Some Problems of Holographic Flow Inspection. Aviation Materials, VIAM (Moscow, Russia), no. 6 (1979), 200 - 204 (Russian).
  3. Levin, A. B.; Lipkin, A. S. Theoretically-experimental Study of Roughness of Surface by the Holographic Methods. Collection of papers "Holographic Methods of Processing of Information", MIREA (Moscow, Russia), 1978, 137 - 143 (Russian).
  4. Levin, A. B. Characteristic Polynomials of Filtered Difference Modules and Difference Field Extensions. Uspekhi Math. Nauk, Vol. 33 (1978), no. 3, 177 - 178 (Russian). English translation: Russian Mathematical Surveys, 33, no. 3, 165 - 166. Doi: https://doi.org/10.1070/RM1978v033n03ABEH002480