publications

Pu Publications of L.N. Vaserstein

Updated Jun 30, 2023

Abstract journals: MR = Math. Reviews by Amer.Math.Soc. Z = Zbl = zbMath . R Zh= Ref. Zhurn. Mat. (Russian abstract journal).

Other spellings for the last name: Vasershtein, Wasserstein, Waserstein, Vasserstein, Vaseršteǐn, Vassershtejn, Vasershtejn, Васерштейн, Вассерштейн.

this web[age URL: https://personal.science.psu.edu/lxv1/publications.html

1. Subgroups of finite index of spinor groups of rank ≥ 2,
Mat. Sbornik 75:2 (1968), 178-184 = Math. USSR Sbornik 4, pp.161-166.
MR 37#1475. Z247.20050. RZh 1968.11A324. 1.25.67.

2. The congruence subgroup problem for unitary groups of rank ≥ 2,
Mat.Sbornuk 76:3 (1968), 362-367 = Math.USSR Sbornik 5 , pp. 351-355.
MR 37#5301. Z256.20063. RZh 1969.4A359. 7.17.67.

3. On groups satisfying the property T,
Funk.An. 2:2 (1968), p.86,
MR 37#4200. Z232.20087. RZh 1968.12A333. 12.24.67.

4. Stabilization in algebraic K-theory and the congruence subgroup problem for classical groups,
Dissertation, 28 pages, Moscow State University, 1968.
Defended April 11, 1969.

5. Stabilization in algebraic K-theory and the congruence subgroup problem
for classical groups, Abstract of Dissertation, Moscow State University Press, Moscow 1969,
7 pages. 12.04.68.

6. On stabilization in algebraic K-theory,
Funct. Anal. 3:2 (1969), 85-86 = Funct.Anal.Appl. 3 , 153-154.
MR 42#1910. Z208 p.44. RZh 1969.10A215. 10.25.68.

7. On the congruence subgroup problem for classical groups,
Funk.Anal. 3:3 (1969), 88-89 = Funct,. Anal.Appl. 3, 244-246.
MR 41#1894. Z279.20037. RZh 1969.12A512. 11.12.68.

8. K1-theory and the congruence subgroup problem,
Mat.Zametki 5:2 (1969), 233-244 = Math. Notes 5, 141-148.
MR0246941 (40 #210) MR 42 p.1823. Z177.04301. Z195.32202. RZh 1969.7A320. 12.23.67.

9. On stabilization for general linear groups over a ring,
Mat. Sbornik 79:3 (1969), 405-424 = Math. USSR Sbornik 8, 383-400.
MR 42#1911. Z238.20057. RZh 1969.12A487. 12.12.68. Cited by 160

10. Markov processes on countable space products describing large systems of   automata,
Probl.Pered.Inform. 5:3 (1969), 64-72 = Probl. Inform.Transm. 5:3, 47-52.
MR0314115 (47 #2667) Z273.60054. RZh 1970.2V388.    2.24.69.
Cited in 33 publications in Math Reviews including 51 #7055    | 50 #1326 | 48 #7324   | , Cited by 281 by Google Scholar
Cited by 255 Related articles Google Scholar

Wasserstein distance or metric: | 866 references in MR with Wasserstein anywhere (excluding one with Wasserstein-Robbins); 17 with Vasershtein.
1131 results from Web of Science with Wasserstein in topic; 6 with Vasershtein.

11. (with A.Leontovich) On invariant measures of Markov operators
describing a homogeneous random medium,
Probl.Per.Inform. 6:1 (1970), 71-80 = Probl. Inform. Transm. 6:1, 61-69.
Z306.60043. MR0530400 (58 #26621) RZh 1970.10V49. 3.27.69.

12. Stabilization for unitary and orthogonal groups over a ring with involution,
Mat.Sbornik 81:3 (1970), 328-351 = Math. USSR Sbornik 10, 307-326.
MR 42#4617. Z253.20066. RZh 1970.7A365. 1.29.69.

13. (with A.Mikhalev) On normal subgroups of orthogonal groups over rings
with involution,
Algebra i Log. 9:6 (1970), 629-632 = Algebra & Logic, pp.375-377.
MR 44#2844. Z239.20059. RZh 1971.9A337. 4.21.70.

14. The stable range of rings and the dimension of topological spaces,
Funk.Anal. 5:2 (1971), 17-27 = Funct.An.Appl. 5, 102-110.
MR 44#1701. Z239.16028. RZh 1971.12A482. 4.16.70.

cited in 99 publications in Math Reviews

15. On even unimodular lattices, App. to "Torelli's theory for algebraic
surfaces of type K3" by I.I. Piatetski-Shapiro and I.R.Shafarevich,
Izv. Akad.Nauk, ser.mat. 35 (1971), 530-572, pp. 561-564.
MR 44 #1666 . Z253.14006. cited in 110 publications in Math. Reviews

16. (with Z.V.Tsuypenko, V.I.Chmil, E.B.Sherman) An experiment of posing and
solution of a non-linear many-extremal problem in development and
allocation of industrial production,
Electrotechnical Industry, General, 388 (1971) (in Russian).

17 (with Sherman) A many-extremal problem of development and allocation
with concave objective function,
Abstracts of Talks, The First Conference on Optimal Planning and Control
in Economy, Central Econom.-Mat. Instit. Moscow, 1971.

18. (with A.N.Parshin) Translation of "Basic Number Theory" by A.Weil,
"Mir", Moscow, 1972, 408 pages,
MR 50#4525. Zbl 0238.12001

19. On the group SL2 over Dedekind rings of arithmetic type,
Mat.Sbornik 89:2 (1972), 312-322 = Math. USSR Sbornik 18, 321-332 (1973).
MR 55#8253. Z359.2002 7. RZh 1973.2A369. 12.13.71. Cited by 141

20. (with Gemintern, Sherman) Methods of solution of problems in
development and allocation of manufactoring (in Russian),
"INFORMELECTRO", Moscow, 1972, 44 pages. 7.01.71.

21. (with Sherman) An algorithm for approximate solution of a
multi-extremal problem of development and allocation of manufactoring,
Electrotechn. Industry, General (1972) 14, pp.11-13 (in Russian).

22. Structure of the classical arithmetic groups of rank > 1,
Mat.Sbornik 91:3 (1973), 445-470 = Math. USSR Sbornik 20, 465-492 (1974).
MR 50#2357. Z277.14018, Z291.14016. RZh 1973. 12A382. 5.27.71.

23. (with Rudnev, Sherman) Parametric models of optimization of advanced
sectoral planning, Electrotechnology 11 (1975), 57-60 (in Russian).

24. Foundations of algebraic K-theory,
Uspekhi Mat.Nauk 28:2 (1973), 231-232.
Z264.16016. RZh 1973.10A324.

25. Foundations of algebraic K-theory, Abstract of Address to Moscow Math.
Soc., Uspekhi Mat.Nauk 28:4 (1973), p.203.

26. Stabilization for classical groups over rings,
Mat.Sbornik 93:2 (1974), 268-295 = Math. USSR Sbornik 22, 271-303.
MR 49#2974. Z287.18015, Z305.18007. RZh 1974.9A454. 6.01.71.

27. (with A.A. Suslin) Serre's problem on projective modules over
polynomial rings and algebraic K-theory,
Funk. An. 8:2 (1974), 65-66 = Funct.Anal.Appl. 8, 148-150.
MR 50#303. Z293.13007. RZh 1974.10A336. Sem.Bourbaki No. 448. 11.28.73.

28. (with Chmil, Sherman) A multi-extremal problem for growth and
allocation of production with a concave objective function,
in Math. Methods in Economical Research , "Nauka", Moscow, 1974, pp.138-143.
MR 53#15379. 2.08.72.

29. (with co-authors) Methodology of elaboration of optimal plans for
development, specialization, and placing of manufactoring in electric
industry,
"INFORMELECTRO", Moscow, 1974, 116 pages. 12.12.73.

30 (with co-authors) Problems of advanced planning in electric industry,
"INFORMELECTRO", Moscow, 1974, 96 pages. 6.18.74.

31. (with A.A. Suslin) Serre's problem on projective modules over polynomial
rings, Abstract of Address to Moscow Math. Soc.,
Uspekhi Mat.Nauk 30:5 (1975), p.193.

32. On stabilization for the Milnor functor K2,
Uspekhi Mat.Nauk 30:1 (1975), p.224.
MR 53#8198. Z326.18009. RZh 1976.9A326.

33. (with Sherman) On formation of variants in discrete problems of optimal
sectoral planning, Economics and Mat. Met. 11:4 (1975), 669-680.

34. (with A.A. Suslin) Serre's problem on projective modules over
polynomial rings and algebraic K-theory,
Izv.Akad.Nauk, ser.mat. 40:5 (1976), 993-1054 = Math.USSR Izv. 10:5, 937-1001.
MR 56#5560. Z338.13015, Z379.13009. RZh 1972.2A459. 4.4.75. Cited by 130

35. Foundations of algebraic K-theory,
Uspekhi Mat.Nauk 31:4 (1976), 87-149 = Russian Math. Surveys 31:4, 89-156.
MR 55#458. Z356.18015, Z359.18015. RZh 1977.1A374. 2.26.75.

36. (with Pavlova) An optimization experiment in advanced planning of
manufactoring, development, specialization, and placing in electroceramics industry,
Electr. Industr. General 5 (444) (1976), 19-21.

37. (with Rudnev, Sherman) Parametric models of development and placing of
manufactoring, Economics and Mat. Met. 13:5 (1977), 1008-1021.

38. (with Sherman) Problems of formation of variants for development and
specialization of industrial plants in optimal sectoral planning,
"INFORMELECTRO", Moscow, 1977, 76 pages.

39. (with Rudnev, Sherman) Parametric models of optimization in advanced
sectoral planning,
"INFORMELECTRO", Moscow, 1978.

40. On systems of particles with finite-range and/or repulsive interactions,
Commun.Math.Physics 69 (1979), 31-56.
Physics Abstracts 83 (1980) #37. Physics Briefs 2 (1980), 17535.

In particular, a conjecture posed by van der Waals in his Nobel lecture on Dec. 12, 1910 is proved.

41. On the normal subgroups of GLn over a ring,
in Springer Lecture Notes in Math. #854, 1981 (Algebraic K-theory), pp.454-465.
MR 83c 20058. Z464.20030. Cited by 137

42. On full subgroups in the sense of O'Meara,
J. Algebra 75 (1982), 437-444.
MR 83c 20051. Z488.20035. RZh 1982.11A312. 4.10.81.

43. Book review of "Recurrence in ergodic theory and combinatorial number
theory"
by H.Furstenberg and "Rudiments of Ramsey theory" by R.L. Graham,
Bull. London Math.Soc. 14 (1982), 458-460.

44. Classical groups over rings,
Abstracts of papers presented to A.M.S. 3:2 (1982), p.164.

45. (with B.Magurn, R.Oliver) Units in Whitehead groups of finite groups,
Prep.Ser. Aarhus Univ. 27 (1982), 56 pp.
Z482.18005. RZh 1982.11A314.

46. On K1-theory of topological spaces,
Abstracts of papers presented to A.M.S. 4:7 (November 1983), 524-525.

47. (with B.Magurn, R.Oliver) Units in Whitehead groups of finite groups,
J. Algebra 84:2 (1983), 324-360.
Z517.16011. MR 85a:18015. RZh 1984.3A488. 2.15.82, 9.29.82.

48. (with R.K. Dennis, B. Magurn) Generalized Euclidean group rings,
J.Reine Ang. Math. 351 (1984), 113-128.
MR 85f:16012. Z527.16007. RZh 1985.1A484.

49. (with C.Matthews, B.Weisfeiler) Congruence properties of
Zariski -dense subgroups, I,
Proc.London Math.Soc. 48:3 (1984), 514-532.
MR 85d:20040. Z551.20029. RZh 1984.12A449. 5.9.83, 9.20.83.

50. (with R.Herman) The stable range of C*-algebras,
Invent. Mathem. 77:3 (1984), 553-555.
MR 86a:46074. Z559.46025. RZh 1985.6B821.

51. Bass's first stable range condition,
J.Pure Appl.Algebra 34:2-3 (1984), 319-330.
MR 86c:18009. Z547.16017. RZh 1985.8A442. Cited by 128

52. Classical groups over rings,
Canad.Math.Soc.Confer.Proc. v.4 (1984), 131-140.
MR 86d: 20056. Z577.2003 3.

53. On normal subgroups of the general linear groups over Banach algebras
and von Neumann regular rings,
Abstracts of A.M.S. 6:2 (1985), p.185.

54. Computation of K1 via Mennicke symbols,
Abstracts of A.M.S. 6:2 (1985), p.185.

55. On arithmetic subgroups of simple algebraic groups,
Linear Algebra Appl. 72 (Dec.1985), 93-96.
MR 87b:22023. Z594.20038. RZh.1986.8A459.

56. On full subgroups of Chevalley groups,
Tôhoku Mathem.J. 37:4 (1985), 423-454.
MR 87b:20058. Z598.20051. RZh.1986.8A457.

57. Quadratic forms over rings of continuous functions,
Abstracts of Conf. on "Surgery and L-theory" ,
Oberwolfach, March 17-23, 1985, p.11.

58. On catching a moving particle by narrow strips,
Geometr. Dedicata 20:2 (1986), 143-146.
MR 87g:52020. Z586.51017. RZh.1986.9A646.

59. Normal subgroups of the general linear groups over von Neumann regular rings,
Proc. Amer. Math. Soc. 96:2 (1986), 209-214.
MR 87g:16020. Z594.16007. RZh.1986.10A207.

60. On normal subgroups of Chevalley groups over commutative rings,
Tôhoku Mathem.J. 38:2 (1986), 219-230.
MR 87k:20081. Z578.20036.

61. Vector bundles and projective modules,
Trans. Amer. Math. Soc. 294:2 (1986), 749-755.
MR 87c:18010. Z592.55012. RZh. 1986.11A.652.

62. Operations on orbits of unimodular vectors,
J. of Algebra 100:2 (1986), 456-461.
MR 87j:13018. Z592.20053. RZh. 1986.11A.481.

63. On K1-theory of topological spaces,
in Amer. Math. Soc. Cont. Math. 55 (1986), 729-740
MR 87m:18025. Z594.18013.

64. (with R.Swan) On absolute stable range of rings of continuous functions,
in Amer. Math .Soc. Cont. Math. 55 (1986), 689-692.
MR 88f:18017. Z592.18006.

65. (with R.Herman) K1 of compact operators is zero,
in Geometric Methods in Operator Algebras,
Proc. of US-Japan Sem.(Kyoto, July 1983), Pitman,1986, p.237-241.
MR 88f:46135. Z641.46046.

66. (with J.Anderson) Commutators in ideals of trace class operators,
Ind. Univ. Math. J. 35:2 (1986), 345-372.
MR 87f:47025. Z602.47032.

67. Normal subgroups of the general linear groups over Banach algebras,
J. Pure Appl. Algebra 41:1 (1986), 99-112.
MR 88a:18023. Z589.20030.

68. (with T.Bridges) The local evaluation of the derivative of a determinant,
J. of Comput. Physics 65:1 (July 1986), 107-119.
MR 87h:65074. Z593.65028. RZh. 1986.12B1578.

69. Every integral matrix is the sum of three squares,
Linear and Mult. Algebra 20(1986), 1-4.
MR 88e:15009. Z603.10050.

70. (with W.Thurston) On K1-theory of the Euclidean space,
Topology and Appl. 23:2 (July 1986), 145-148.
MR 87m:18023. Z611.18007.

71. The subnormal structure of general linear groups,
Math. Proc. Cambridge Phil. Soc. 99:3 (1986), 425-431.
MR 87k:20080. Z601.20046. RZh.1986.9A172.

72. An answer to the question of M. Newman on matrix completion,
Proc. Amer. Math. Soc. 97:2 (1986), 189-196.
MR 88e:18012. Z601.15011. RZh.1986.12A441.

73. Computation of K1 via Mennicke symbols,
Commun.in Algebra 15:3 (1987), 611-656.
MR 88m:18019. Z614.16018.

74. On the sum of powers of matrices,
Linear and Mult. Algebra 21:3 (1987), 261-270.
MR 89a:15016. Z637.10041.

75. Waring's problem for algebras over fields,
J. Number Theory 26:3 (July 1987), 286-298.
MR 89e:11059. Z624.10049.

76. Waring's problem for commutative rings,
J. Number Theory 26:3 (July 1987), 299-307.
MR 89e:11060.

77. (with B.A. Magurn) Prestabilization for K1 of Banach algebras,
Linear Algebra 95 (Oct.1987), 69-96.
MR 89c:16034. Z629.20021. RZh. 1988.5A360.

78. Normal and subnormal structure of classical groups over rings,
Abstract of talk at conference in Bejijng, May 1987. 6 pages.

79. (with R.K. Dennis) On a question of M. Newman on the number of
commutators,
J. Algebra 118:1 (1988), 150-161.
MR 89k:20062. Z649.20048.

80. Every integer is a sum or difference of 28 integral eighth powers,
J. Number Theory 28:1 (1988), 66-68.
MR 89f:11139. Z634.10042. R.Zh. 1989 7A122.

81. Structure of gauge groups, Abstract in "Algebraic K-theory" ,
Oberwolfach, June 5-11, 1988, p.5.

82. Subnormal structure of the general linear groups over Banach algebras,
J. Pure Appl. Alg. 52 (1988), 187-195.
MR 89i:18008. Z653.20050.

83. Normal subgroups of classical groups over Banach algebras,
Comm.Math. Helv. 63:1 (1988), 103-107.
MR 89f:46105. Z708.46047. R.Zh.1988.8A411.

84. Normal subgroups of orthogonal groups over commutative rings,
Amer. J. Math. 110:5 (1988), 955-973.
MR 89i:20071. Z654.20052.

85. Reduction of a matrix depending on parameters to a diagonal form by
addition operations,
Proc. Amer. Math. Soc. 103:3 (1988), 741-746.
MR 89h:18015. Z657.55005.

86. (with B. A. Magurn and W. van der Kallen) Absolute stable rank and Witt
cancellation for noncommutative rings,
Inv. Math. 91:3 (1988), 525-542.
MR 88m:18017. Z639.16015.

87. On the best choice of a damping sequence in iterative optimization methods,
Publ. Matem. Univ. Aut. Barcelona 32 (1988), 275-287.
MR 90d:90077. Z657.90100.

88. (with G.Dafni) Matrix zeros of quadratic polynomials.
J.Number Theory 30 (1988), 27-50.
MR 89j:13008. Z657.13005.

89. Normal subgroups of gauge groups,
in Classical groups and related topics,
Amer. Math. Soc. Cont.Math., 82 (1989), 199-220
MR 89m:22001. Z679.22013.

90. Linear algebra and algebraic K-theory,
in Classical groups and related topics,
Amer. Math. Soc. Cont.Math., 82 (1989), 191-198.
MR 89k:18025. Z669.15001.

91. Non-commutative number theory,
in Algebraic K-theory and algebraic number theory,
Amer. Math. Soc. Cont. Math. 83 (1989), 445-449.
MR0991989 MR 90d:11033. Z666.10032.

92. Normal subgroups of classical groups over rings and gauge groups,
in Algebraic K-theory and algebraic number theory,
Amer. Math. Soc. Cont. Math. 83 (1989), 451-459.
MR 90e:20041. Z676.20025.

93. Normal subgroups of symplectic groups over rings,
K-theory 2 (1989), 647-673.
MR 90f:20064. Z669.20040.

94. (with R.K. Dennis) Commutators in linear groups,
K-theory 2 (1989), 761-767 .
MR 90h:20045. Z676.20024.

95. (with P.Menal) On subgroups of GL2 over non-commutative local rings
which are normalized by elementary matrices,
Math. Ann. 285:2 (1989), 221-231.
MR 90k:20085. Z662.20039.

96. On normal subgroups of GL2 over rings with many units,
Composito Mathematica 74 (1990), 157-164.
MR 91j:19004. Z697.20040.

97. The subnormal structure of general linear groups over rings,
Math. Proc. Cambridge Phil. Soc. 108:2 (Sept. 1990), 219-230.
MR 92d:20064. Z711.20030 .

98. (with P.Menal) On the structure of GL2 over stable range one rings,
J. P. A. Algebra 64:2 (June 1990), 149-162.
MR 92a:20058. Z702.20037.

99. (with E.Wheland) Factorization of invertible matrices over rings of
stable rank one,
J. Australian Math. Soc. A48 (1990), 455-460.
MR 91d:15028. Z705.15004.

100. (with E.Wheland) Commutators and companion matrices over rings of
stable rank 1,
Linear Algebra 142 (1990), 263-277.
MR 92a:19002. Z713.15003.

101. I. I. Piatetski-Shapiro, my advisor and friend,
in Israel Proc. Math. Conf. vol. 2 (1990), p. 1-4.
MR 93g:01089b. Z0699.01028.

102. (with Grunewald and Mennicke) On symplectic groups over polynomial rings,
Math. Zeitschrift 206:1 (1991), 35-56.
MR 92a:19001. Z725.20038.

103. On sums of cubes in polynomial rings,
Mathem. of Computation 56 (1991) , 349-357.

MR 91e:11106. Z711.1101 3.

104. (with P.Menal) On subgroups of GL2 over Banach algebras and von
Neumann regular rings which are normalized by elementary matrices,
J. Algebra 138:1 (1991), 99-120.
MR 92h:16009. Z724.20034.

105. (with C. Byrne) An improved algorithm for finding saddlepoints of
two-person zero-sum games, Game Theory, 20:2 (1991), 149-159.
MR 93b:90113. Z754.90067.

106. Unstable K1-theory of topological spaces is nilpotent,
in Algebraic K-theory, Commutative Algebra, and Algebraic Geometry,
Amer. Math. Soc. Cont. Math. 126 (1992), 193-196.
MR 93c:19002. Z762.19002.

107. Ramsey's theorem and the Waring's problem for algebras over fields,
pp. 435-442 in Proceedings of workshop "The Arithmetic of Function Fields,"
1991,Ohio State University, Walter de Gruyter Verlag, 1992.
MR 94a:11155. Z817.12002.

108. (with G. Payne) Sums of three cubes,
pp. 443-454 in Proceedings of workshop "The Arithmetic of Function Fields" 1991, Ohio State University, Walter de Gruyter Verlag, 1992.
MR 93k:11090. Z799.11039.

109. (with F.A. Arlinghaus) Work of Pere Menal on normal subgroups,
Publ. Matem. Univ. Aut. Barcelona 36 (1992), 389-400.
MR 94k:20085. Z790.20064.

110. (with E.Wheland) Products of conjugacy classes of two by two matrices,
Abstracts of "Algebraic K-theory" conference in Oberwolfach,
June 27-July 3, 1993, page 22.

111. (with Yu. Lyubich) Isometric embeddings between classical Banach
spaces, cubature formulas, and spherical designs,
Geom. Dedicata 47:3 (Sept. 1993), 327-362.
MR 94j:46017. Z785.52002.

112. (with F. Grunewald and J.Mennicke) On the groups SL2(Z[x]) and SL2(k[x, y]),
Isr. J. Math., 86:1-3 (1994), 157-194.
MR 95h:20061. Z805.20042.

113. (with W. Conn) On sums of three integral cubes,
in Proceedings of Radamacher Conference, Penn State Univ. 1992, AMS Cont. Math. 166 (1994), 285-294.
MR 95g:11128. Z808.11075.

PSU Report No. PM 131 March 1992 10 pages. scanned to

http://www.math.psu.edu/vstein/113P.pdf

114. (with F.A. Arlinghaus and H. You) Normal subgroups of classical groups
over von Neumann regular rings,
Journal of Algebra 169:3 (1994), 863-873.
MR 95k:20082. Z819.20052.

115. (with F.A. Arlinghaus and H. You) Products of involutary matrices
over stable range one rings,
Linear Algebra 229:1 (1995), 37-48.
MR 96f:15015. Z836.15006.

116. (with E.Wheland) Products of conjugacy classes of two by two matrices,
Linear Algebra 230 (1995), 165-188.
MR 96j:20061. Z840.20040.

117. (with F.A. Arlinghaus and H. You) Commutators in psueudo-orthogonal groups
J. Austral. Math .Soc. Sr.A 59:3 (1995), 353-362.
MR 96c.20094. Z847.20042.

118. (with H. You ) Normal subgroups of classical groups over rings,
J.P. Appl. Algebra 105:1 (1995), 93-106.
MR 96k:20096. Z843.20037.

119. (with coauthors) Solving quadratic equations over polynomial rings of characteristic two,
Publ. Math. Barcelona 41:1 (1998), 131-142.
MR 99e:13030. Z915.13017.

120. (with E. Wheland) Rigid relations in SL(2),
Linear Algebra Appl. 28:1-3 (1998), 25-31.
MR 99f:20076. Z944.20028.

121. On recollections of Yu.Suhov, in the book `R.L.Dobrushin, To 70th Birthday,'
Editorial URSS, Moscow 1999 (in Russian), pp.64-65.
(AMS Translations--Series 2, Advances in the Mathematical Sciences Volume: 198 , 2000.) [http://www.iitp.ru/ru/about/432.htm in Russian]
Z0954.01014.

122. (with E. Wheland) Two-dimensional representations of the free group in
two generators over an arbitrary field,
Linear Algebra, 307 (2000), 145-150.
MR 2001c:20013. Z1007.20021.

123. Quantum (abc)-theorems,
J. Number Theory 81:2 (2000), 351-368.
MR 2001d:11039. Z990.11015.

124. (with R. Gar-El) On the Diophantine equation a³+b³+c³+d³ = 0,
J. Number Theory, 94:2 (June 2002), 219-223.
dvi | ps | pdf | MR 2003d:11039 . Z1031.11015.

125. (with E.R.Wheland), Vanishing polynomial sums,
Comm. Algebra, 31:2 (2003), 751 - 772.
dvi | ps | pdf | TeX | MR1968922 . Z1073.12001.

126. Introduction to Linear Programming, Prentice Hall, 2003.

Publication Date: November 17, 2002 | ISBN-10: 0130359173 | ISBN-13: 978-0130359179 |
title page: ps | pdf || copyright page: ps | pdf || contents&preface: ps | pdf || student's manual: ps | pdf |
Chinese translation by Mechanical Industry Publishing House, ISBN: 7111173295 .

127. (with L. Gallardo and E. Wheland) Berlekamp's discriminant and cubic equations in characteristic two,
JP Journal of Algebra, Number Theory and Appl., 2:3 (2003), 169-178.
Z1061.11070 . MR1999157.

128. On the Whitehead determinant for semi-local rings, Journal of Algebra 283:2 (2005), 690-699.
ps | pdf . Z1059.19002 . MR2111217.

129. (with U. Onn and A.Prasad) A note on Bruhat decomposition of GL(n) over local principal ideal rings
Communications in Algebra, 34 (2006), no. 11, 4119--4130.
MR2267575 . Zbl 1112.15020. arXiv GR/0506094 [abs, ps, pdf, other]

130. (with L. Gallardo and O. Rahavandrainy)
Representations of polynomials over finite fields of characteristic two as A²+ A + BC + D³,
Finite Fields and Their Applications., 13 (2007), 648-658.

Zbl 1127.11079 . MR2391463. MR2332492.

131. Linear Programming, Chapter 50 in Handbook of Linear Algebra, Chapman & Hall/CRC Press, 24 pp.
(October, 2006) # ISBN: 1584885106. amazon

MR2279160 (2007j:15001) Zbl 1122.15001

132. (with S. Frisch) Parametrization of Pythagorian triples by a single triple of polynomials, J. P A Alg. 212 (2008), 271-274.
arXiv:0706.0290 [ps, pdf, other] MR2391463 MR2355049 Zbl 05201873

133. (with M. Car, L. H. Gallardo, O. Rahavandrainy) About the period of Bell numbers modulo a prime, Bull Korean Math. Soc., 45:1 (2008), 143-155.
MR2391463 . Zbl 1195.11034

134. Polynomial parametrization for the solutions of Diophantine equations and
arithmetic groups , Annals of Math. 171:2 (March of 2010), 979–1009. abstract

MR2630059. Zbl 05712747

135. (with L. Gallardo) The strict Waring problem for polynomial rings,
J. Number Theory 128 (2008), no. 12, 2963--2972.
MR2464848. Zbl 05486357

136. (with Nir Avni, Uri Onn, Amritanshu Prasad) Similarity classes of 3x3 matrices over a local principal ideal ring
Comm. in Algebra 37:8 (2009), 2601--2615.

MR2543507. Zbl 1176.15013

137. (with L.Gallardo) Sums and strict sums of biquadrats in F_q[t], Rocky Mountain Journal. 40: 6 (2010), 1863-1874.

Zbl 05837630. MR2764225

138. (with R. T. Farouki and T. Sakkalis ) Non-existence of rational arc length parameterizations for curves in ℝⁿ,
Journal of Computational and Applied Mathematics 228:1 (2009), 494-497.

MR2514307. Zbl 1166.53002

139. (with S. Frisch and T. Sakkalis) Polynomial parametrization of Pythagorean tuples., Int. J. Number Theory.Vol. 6 (6) (2010), 1261-1272.
Zbl 05802994. MR2726581

140. Book review: Additive Combinatorics by T.Tao and V.H.Yu, SIAM Review 92:1 (March 2010), p.215-216.

MR2650678

141. The stable rank of pullbacks, J. of Algebra. Volume 410, 15 July 2014, Pages 239–243

MR3201051 Zbl 06335822

142. (with S.Frisch) Polynomial parametrization of Pythagorean quadruples, quintuples and sextuples,

Journal of Pure and Applied Algebra 216 (2012) 184–191.

MR2826432 (2012k:11035). Zbl 1273.11053

143. Linear Programming, Chapter 68 in Handbook of Linear Algebra, Chapman & Hall/CRC Press, 24 pp. Second Edition 2013

Publication Date: November 26, 2013 | ISBN-10: 1466507284 | ISBN-13: 978-1466507289 | Edition: 2

144. (with L. Gallardo) CONSTANTS AS SUMS OF POLYNOMIAL CUBES IN CHARACTERISTIC 2

Journal of Combinatorics and Number Theory 5:1 (2013) , 1-9.

Zbl 06242291 MR3113617

145. (with L. Gallardo) Polynomial parametrization of the integer matrices with given determinant

Journal of Pure and Applied Algebra . 218,:2 (2014,), 321 - 322.

Zbl 1273.11053 MR3120632

--------------------------

preprints

Reduction of Linear Programming to Linear Approximation, 3 pp,
arXiv:math/0602339 [ps, pdf, other] 15 Feb 2006.

Matrix Games, Linear Programming, and Linear Approximation, 5 pp.
arXiv:cs/0609056 [ps, pdf, other] abstract 12 Sep 2006.

(with Nir Avni, Uri Onn, Amritanshu Prasad) Similarity classes of 3x3 matrices over a local principal ideal ring

arXiv:0708.1608 [ps, pdf, other] 13 pp. Submitted on 12 Aug 2007. published [136]

Linear Approximation, Matrix Games, and Linear Programming, 35 pp.

Bounded reduction of invertible matrices over polynomial rings by addition operations, 12 pp.

----------------------

http://ecommons.cornell.edu/handle/1813/15167
Interview conducted in August of 1980 by Dynkin.

Five talks at Gelfand seminar in 1972 (2/14, 3/6, 3/13, 10/13, 10/19), notes by A. Kirillov. L.N. Vasserstein. http://www.mccme.ru/gelfand/notes/by-author-000158.html#begin

A problem in Quant

Задачник <Кванта> по математике pdf

http://www.problems.ru/view_by_source_new.php?parent=162603&start=20

-----------Translations -----------

Besides the book translation [18] above from English to Russian, I translated many articles, including

MR0244257 (39 #5574) Bass, H.; Milnor, J.; Serre, J.-P. Solution of the congruence subgroup problem for ${\rm SL}_{n}\,(n\geq 3)$ and ${\rm Sp}_{2n}\,(n\geq 2)$. Inst. Hautes Études Sci. Publ. Math. No. 33 1967 59--137. 14.50 (20.00)

(translated from the English by L. N. Vaseršteĭn) Matematika 15:1 1971 (pp. 44–60) MR0429414 (55 #2431)

MR0272790 (42 #7671) Serre, Jean-Pierre Le problème des groupes de congruence pour SL2. (French) Ann. of Math. (2) 92 1970 489–527. 14.50.

(translated from the French by L. N. Vaseršteĭn) Matematika 15:6 1971 (pp. 12–45) MR0339966 (49 #4723)

and 24 translations from Russian to English, see loca link.

----- Reviews (more than 1160) ------

242 reviews (of [apers published since 1977) in Math Reviews by L.Vaserstein since 1982.
781 reviews (of papers published since 1977) in Zentralblatt Mat.(mow zbMath) by L.Vaserstein; including 330 publications since 2010;

here are additional 99 scanned reviews (local link) of papers published in 1974-1982.

Numerous reviews in Ref. Zh. Mat. by Vaserstein;

partial list of 62 articles local link.

------ Citations and Impact -----

My name in title.

There are

20,105 titles with my name

in three html files at my website. 13MB, 13MB, and 12MB:

6,961 titles appeared till 2018

6,796 titles appeared in 2019-2020,

6,348 titles since 2021.

These 3 files contain most of

1288 titles at arXiv, 640 titles at zbMATH ,

106 books, 256 theses/dissertations, 445 patents,

485 videos, and 686 ƒmr reviews from Math Reviews.

By comparison, arXiv has

604 titles with Archimedes OR archimedean

and

163 titles with Pythagoras OR pythagorean.

Most of titles and more can be found at Google Scholar or WorldCat. They include

500 titles from Math Reviews (with my name spelled as Vaserstein, Wasserstein.

Vasershtein, Vasserstein , or Vasseršteĭn),

470 titles from ZbMath (with my name spelled as Vaserstein | Wasserstein),

875 titles from arXiv (with my name spelled as Vaserstein, Wasserstein, or WGAN.

2204 papers in arXiv with my name in abstract my page

2,154+ reviews in Math Reviews with Wasserstein (1378),Vaserstein (618), Vasserstein (5), Vasershtein (17), or Vassershtein (1) anywhere.

2.5K reviews in Zentralblattt Math. with Wasserstein (1505 excluding 1 by Wasserstein-Robbins, and 1 by Wasserstein, Ronald ), Vaserstein (992), Vasserstein (6),

Vasershtein (27), or WGAN (2) anywhere.
2K preprints with Wasserstein anywhere in arXiv.org

23 preprints with Vaserstein anywhere in arXiv.org

2 preprints with Vasershtein anywhere in arXiv.org

106 papers with WGAN in arXiv
756 + 28+5+6 results from Web of Science with Wasserstein, (excluding history), Vaserstein, Vasserstein, or Vasershtein in topic

2150 books (local link, mostly from google books) mentioning my name including books on differential equations, statistics, computing, computer vision, machine learning, networks, probability, sociology, physics, optimization, data analysis, actuarial theory, health science, life sciences, quantum field theory.

My name in encyclopedia, 133 including 62 wiki articles

number of citations (local link)

88 newspapers articles mentioning WGAN = Wasserstein GAN

from google news

Google search results

August 11, 2020

Wasserstein AI 813K

Wasserstein brain 1M

Wasserstein learning 1450K Wasserstein & distance 789K

wasserstein duality 151K wasserstein geometry 231K

wasserstein IE 362K Wasserstein teaching 110K Wasserstein dynamics 396K

Wasserstein loss 354K improving wasserstein 387K

Wasserstein clustering 136K wasserstein algebra 74K

Wasserstein GAN 354K

Vaserstein metric 13K vaserstein symbol 31K

Mallows-Wasserstein 37K

google, google scholar

"Wasserstein autoencoder" 7K "Wasserstein autoencoders" 4K

"Wasserstein ball" 5K Wasserstein balls" 25K

"Wasserstein barycenter" 8K,641 "Wasserstein barycenters" 10K, 733

"Wasserstein based" 3K, 416 "Wasserstein-based" 4K, 416

"Wasserstein contraction" 3K, 182
"Wasserstein convergence" 1K, 117

"Wasserstein diffusion" 2K ,84

"Wasserstein discrepancy" 1K, 123

"Wasserstein distance" 162K, 1540 "Wasserstein distances" 34K, 3370

"Wasserstein distance matlab" 4K

"Wasserstein divergence" 2K, 114

"Wasserstein dynamics" 1K , 19

"Wasserstein-Fisher" 1K, 58 "Wasserstein Fisher" 1K,58

"Wasserstein flow" 1K, 30

"Wasserstein GAN" 63K, 6850 "Wasserstein GANs" 38K, 4510

"Wasserstein generative adversarial network" 15K, 494

"Wasserstein generative adversarial networks" 19K , 1

"Wasserstein geodesics" 3K,240

"Wasserstein geometry" 1K, 301

"Wasserstein gradient" 15K, 903

"Wasserstein learning" 3K, 193

"Vaserstein linear" 1K, 3

"Wasserstein loss" 9K 877

"Wasserstein metric" 47K,6090 "Wasserstein metrics" 7K , 1080

"Wasserstein pseudodistance" 3K, 109 "Wasserstein pseudodistances" 1K, 43

"Wasserstein pseudometric" 5K, 15 "Wasserstein pseudometrics" 4K, 32

"Wasserstein space" 26K, 2310 "Wasserstein spaces" 9K , 7790

"Wasserstein statistics" 340K,248

"Wasserstein training" 2K, 117

"Wasserstein type" 2K, 285 "Wasserstein -type" 3K, 285

"wgan divergent" 20K

"wgan-gp" 32K 2K

"wgan-e" 1K 53

"Vaserstein metric" 44K, 48

"Vasershtein distance" 1K 69

Dennis-Vaserstein 23K Swan-Vaserstein 5K

Vaserstein-Suslin 3K Bass-Vaserstein 5K

Serre-Vaserstein 10K Gromov-vaserstein 2K

"conditional Wasserstein" 12K. 2K

"deep Wasserstein" 5K 35

"discrete Wasserstein" 3K, 132

"dual Wasserstein" 1K , 38

"entropic Wasserstein" 2K G 66 GS

"euclidean Wasserstein" 1K 105

"estimation of Wasserstein" 24K,132

"estimating Wasserstein" 443, 28

"generalized Wasserstein" 2K 166

"improved Wasserstein" 1`M 58K

"improved Wasserstein GAN" 1K

"learning Wasserstein" 1K

"learning with Wasserstein" 6K

"lp Wasserstein" 3K "l1 Wasserstein" 1K "l2 Wasserstein" 13K

"quantum Wasserstein" 2K

"relaxed Wasserstein" 1K 89

"robust Wasserstein" 3K 165

"sliced Wasserstein" 17K 687

"training with Wasserstein" 1K "training Wasserstein" 1K

“using Wasserstein” 21K 588

"weighted Wasserstein" 2K 271

"Bures-Wasserstein" 1K "Bures-Wasserstein's" 31K

"Gromov-Wasserstein" 6K "Gromov-Wasserstein's" 19K

"Gromov Wasserstein" 8K

"Kantorovich-Wasserstein" 7K

"Rubinstein-Wasserstein" 1K

"Wasserstein -Fisher" 1K 63

------ my talks——

talks partial list (local link)@vstein15, check out the notifications you have on Twitter

—Ph.D. papers, Vaserstein advisor—

LIMIT THEOREMS FOR INFINITE URN MODELS IN PROBABILITY THEORY (PARTICLES, CENTRAL LIMIT, CELLS)

by DUTKO, MICHAEL

The Pennsylvania State University, 1984

An urn model is defined as follows: n balls are thrown at an infinite array of urns, where each ball has probability p(,k) > 0 of independently hitting the...

Ann. Probab. 17, No.3, 1255-1263 (1989).

EXTRACTION OF MTH ROOTS IN MATRIX RINGS OVER FIELDS (LINEAR ALGEBRA)

by OTERO, DANIEL EDUARDO

The Pennsylvania State University, 1987

Linear Algebra Appl. 128, 1-26 (1990).

Involutions in classical groups and related topics

by Arlinghaus, Francis Anthony

The Pennsylvania State University, 1993

New modeling principles for games and a social dilemma example

by Byrne, Christopher C

The Pennsylvania State University, 1995

Particle systems and generalized billiards