Dr. ALEXANDER LEVIN
Department of Mathematics
The Catholic University of America
Washington,  D. C.  20064
Tel:  (202) 319-5221 (Office),  (301) 770-3057 (Home)
E-mail:  levin@cua.edu

LIST OF PUBLICATIONS

1.  Multivariable Difference Dimension Polynomials, 26 pp.  To appear in the Journal of Mathematical Sciences (Kluwer Academic Publishers). Download ps-version.
2.  Difference Algebra (monograph). To be published in the Kluwer Acdemic Publishers.
3.  Difference Algebra. To be published in the Handbook of Algebra (ELSVIER, Amsterdam, The Netherlands), Vol. 4 (2003- 2004).
4.  Graceful Numbers (Jointly with K. Bhutani.).  International Journal of  Mathematics and Mathematical Sciences,
Vol. 29 (2002),  no. 8,  495 – 499.
5.  On the Set of Hilbert Polynomials.  Bulletin of  the Australian Mathematical Society, Vol. 64 (2001), 291 – 305.
6.  Multivariable Dimension Polynomials and New Invariants of Differential Field Extensions. International Journal of Mathematics and Mathematical Sciences, Vol. 27 (2001),  no. 4,  201 – 214. (Download PS-Version)
7.  Reduced Gröbner Bases, Free Difference-Differential Modules and Difference-Differential Dimension Polynomials. Journal of Symbolic Computation, Vol. 30  (2000), 357 - 382.
8.  Characteristic Polynomials of Finitely Generated Modules over Weyl Algebras.  Bulletin of  the Australian Mathematical Society, Vol. 61 (2000), no. 3,  387 - 403.
9.  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.
10.  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.
11.  Computation of Hilbert Polynomials in Two Variables. Journal of Symbolic Computation, Vol. 28 (1999),
681 - 709.
12.  The Problem of Sawing a Chain. (Jointly with K. Bhutani.) Journal of  Recreational Mathematics, Vol. 31, no.1 (2002-2003), 32 – 35.
13.  Differential and Difference Dimension Polynomials. (Jointly with M. Kondrateva, A. Mikhalev, and E. Pankratev.)
436 pp. Kluwer Academic Publishers. Dordrecht/Boston/London, 1999.
14.  Type and Dimension of Finitely Generated G-algebras.  (Jointly with A. Mikhalev.)  Contemporary Mathematics, Vol. 184 (1995), 275 - 280.
15.  Computation of Dimension Polynomials.  (Jointly with M. Kondrateva, A. Mikhalev, and E. Pankratev). International Journal of Algebra and Computations, Vol.3, no. 2 (1992), 117 - 137.
16.  Dimension Polynomials of Filtered Differential G-modules and Extensions of  Differential G-fields.  (Jointly with A. Mikhalev.) Contemporary Mathematics,  Vol.131 (1992), Part 2, 469 - 489.
17.  Mathematical Foundations of Automatic Control. Higher School Press,  104 pp.  Moscow, 1992. (In Russian).
18.  Dimension Polynomials of Difference-Differential Modules and of Difference-Differential Field Extensions. (Jointly with A. Mikhalev.) Abelian Groups and Modules, no. 10 (1991), 56-82. (In Russsian.)
19.  Type and Dimension of Finitely Generated G-algebras. (Jointly with A. Mikhalev.) Collection of Papers of the International Conference on Algebra  in the Memory of A. Shirshov. Barnaul, Russia, 1991, p. 70.  (In Russian.)
20.  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. (In Russian.)
21.   Type and Dimension of Finitely Generated Vector G-spaces. (Jointly with A. Mikhalev.) Vestnik of Moscow University, Ser. I, 1991, no. 4, 72 - 74. (In Russian.) English translation: Moscow University Mathematics Bulletin,  Vol. 46, no. 4,
51 - 52.
22.  Differential Calculus. Functions of One Variable. (Jointly with V. Safray). MMI Press, 32 pp. Moscow, Russia, 1991.
(In Russian.)
23.  Net Functions and Difference Equations.  (Jointly with V. Safray). MMI Press, 32 pp. Moscow, Russia, 1990.
(In Russian.)
24.  Characteristic Polynomials of Filtered Modules over Twisted Group Rings.  (Jointly with A. Mikhalev). Collection of  Papers of VI National Symposium on  the Theory of Rings, Algebras, and Modules. Lvov, Ukraine, 1990, p. 80.
(In Russian.)
25.  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. (In Russian.)
26.  The Use of Multilevel Problems in Precalculus and Calculus.  Collection of Papers of the International Conference on Mathematics Education. Tula,  Russia, 1989, 11 - 12. (In Russian.)
27.  Dimension Polynomials of Differential Modules.  (Jointly with A. Mikhalev.)  Abelian Groups and Modules, no. 9 (1989), 51 - 67. (In Russian.)
28.  Extremal Problems. (Jointly with A. Zibulnikov and V. Nikiforovsky.) MMI Press, 32 pp. Moscow, Russia, 1989.
(In Russian.)
29.  Fourier Series and Fourier Transform. (Jointly with  V. Safray.) MMI Press, 32 pp. Moscow, Russia, 1989.  (In Russian.)
30.  Solving of the Fundamental Problem of Linear Programming with the  Computer ISKRA. (Jointly with L. Pokrovsky.) MMI Press, 32 pp. Moscow, Russia, 1988. (In Russian.)
31.  Dimension Polynomials of Filtered G-modules. ). Moscow State University  and VINITI  (Moscow, Russia),
no. 6849-B88 (1988), 1 - 27. (In Russian.)
32.  Difference-Differential Dimension Polynomials.  (Jointly with A. Mikhalev.) Moscow State University and VINITI (Moscow, Russia),  no. 6848-B88 (1988), 1 - 64.  (In Russian.)
33.  Dimension Polynomials of Filtered G-modules and of Finitely Generated G-field Extensions.(Jointly  with A. Mikhalev.) Collection of Papers on Algebra. Moscow State University, 1989, 74 - 94. (In Russian.)
34.  Dimension Polynomials of Difference Modules with m-adic Topology. Collection of Papers "Topological Algebra". Kishinev, Moldavia, 1988, p. 40. (In Russian.)
35.  Theory of Functions of One Complex Variable and Laplace Transform. (Jointly with V. Nikiforovsky). MMI Press, 32 pp. Moscow, Russia, 1987.  (In Russian.)
36.  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. (In Russian.)
37.  Differential Dimension Polynomial and the Strength of a System of  Differential Equations. (Jointly with Mikhalev.) Collection of Papers "Computable Invariants in the Theory of Algebraic Systems". Novosibirsk, Russia, 1987, 58 - 66.
(In Russian.)
38.  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. (In Russian.)
39.  Characteristic Polynomials of Difference-Differential Modules.  Collection of Papers of XVIII National Conference on Algebra, Kishinev, Moldavia, 1985. Part I, p. 307. (In Russian.)
40.  Inversive Difference Modules and the Problems of Solvability of Systems of Linear Difference Equations. Moscow State University and VINITI (Moscow, Russia), no. 335-85 (1985), 1 - 20. (In Russian.)
41.  Characteristic Polynomials of D-Modules and of Finitely Generated D-Field Extensions. Moscow State University and VINITI (Moscow, Russia),  no. 334-85 (1985), 1 - 23. (In Russian.)
42.  Elementary Functions and their Graphs.  (Jointly with A. Zulkov.)  MMI Press, 32 pp. Moscow, Russia, 1985.
(In Russian.)
43.   Simplex Method in Linear Programming.  (Jointly with V. Dudin and L. Pokrovsky.)  MMI Press, 32 pp. Moscow, Russia, 1985. (In Russian.)
44.  Mathematical Programming. Geometric Method. (Jointly with V. Dudin.)  MMI Press, 32 pp. Moscow, Russia, 1984.
(In Russian.)
45.  Limits of Sequences and Functions. (Jointly with V. Safray.)  MMI Press, 32 pp. Moscow, Russia, 1984. (In Russian.)
46.  Characteristic Polynomials of Difference Modules and Difference Field Extensions. Summary of the Dissertation for
Ph. D. Degree. Kishinev, Moldavia, 1984, 1 - 21. (In Russian.)
47.  Type and Dimension of Finitely Generated Difference Algebras.  Collection of Papers of  XVII National Conference on Algebra, Minsk, Byelorussia, 1983. Part II, 126 - 127. (In Russian.)
48.  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. (In Russian.)
49.  Type and Dimension of Inversive Difference Vector Spaces and Difference Algebras. Moscow State University and VINITI (Moscow, Russia), no. 1606-82 (1982), 1 - 36. (In Russian.)
50.  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. (In Russian.)
51.  Characteristic Polynomials of Difference Modules and of Difference Field Extensions. Vestnik of Moscow University, Ser. 1, 1982, no. 4. p. 78. (In Russian.)
52.  Difference Local Algebras.  Collection of Papers of XVI National Conference on Algebra, Leningrad, Russia, 1981, Part 1, 92 - 93. (In Russian.)
53.  Method of Automatic Control of Welding with the Heating. USSR Patient  no.743814 (1980).
54.  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. (In Russian.)
55.  Characteristic Polynomials of Difference Modules and Some Properties of Difference Dimension. Moscow State University and VINITI (Moscow, Russia), no. 2175-80 (1980),    1 - 42. (In Russian.)
56.  Characteristic Polynomials of Inversive Difference Modules and Some Properties of Inversive Difference Dimension.  Uspekhi Math. Nauk, Vol. 35 (1980),  no. 1, 201 - 202. (In Russian.)   English translation: Russian Mathematical Surveys, Vol. 35, no. 1, 217 - 218.
57.  Comprehensive Flow Inspection of Solid Phase Joints and Automatization of Holographic Testing. (Jointly with A. Lipkin and S. Vigdorchik.) Collection of papers "Scientific Foundations of Automatization of Industrial Processes", MVTU (Moscow, Russia), 1979, 55 - 57. (In Russian.)
58.  Fourier Series.  Moscow Metallurgical Institute (MMI) Press, 22 pp. Moscow, Russia, 1980. (In Russian.)
59.  Some Problems of Holographic Flow Inspection. (Jointly with A. Lipkin and  E. Karakozow.) Aviation Materials, VIAM (Moscow, Russia), no. 6  (1979), 200 -  204. (In Russian.)
60.  Theoretically-experimental Study of Roughness of Surface by the Holographic Methods. (Jointly with Lipkin.)  Collection of papers "Holographic Methods of Processing of Information", MIREA (Moscow, Russia), 1978, 137 - 143.
(In Russian.)
61.  Characteristic Polynomials of Filtered Difference Modules and Difference Field Extensions.Uspekhi Math. Nauk, Vol. 33 (1978), no. 3, 177 - 178. (In Russian.)  English translation: Russian Mathematical Surveys, Vol. 33, no. 3, 165 - 166.