LIST OF PUBLICATIONS

  1. The representability of algebroidal functions by superpositions
  of analytic functions and of algebroidal functions of one variable. 
  "Functional Analysis and its applications",  v.4, N2, 74-79, 1970;
  translation in Funct. Anal. Appl. 4 (1970), no. 2, 152-156.
 
  2. Superpositions of holomorphic functions with radicals."Uspehi Matem.
  Nauk", v.26, N2, 213-214, 1971 (Russian Math. Surveys).

  3. The representability of functions in quadratures, "Uspehi Matem.
  Nauk", v.26, N4, 251-252, 1971 (Russian Math. Surveys).

  4. Riemann surfaces of functions, representable in quadratures,
  Reports of VI All-Union Topological Conference, Tbilisi, 1972.

  5. The representability of function by quadratures, PhD, Moscow, 1-76,
  1973.

  6. (with Yu. Ilyashenko) Galois theory of systems  of  Fuchs-type
  differential equations with small coefficients, Preprint IPM N117, 1974.

  7. (with  D. Bernstein  and  A. Kushnirenko)  Newton  Polyhedra, "Uspehi
  Matem. Nauk", v.31, N3, 201-202, 1976 (Russian Math. Surveys).

  8. (with D. Bernstein and A. Kushnirenko) Mixed volumes of Newton
  Polyhedra, Milnor's numbers  and  numbers  of  solutions  of algebraic
  equations, "Uspehi Matem. Nauk", v.31, N3, 196, 1976 (Russian Math.
  Surveys).

  9. Newton polyhedra, and toroidal varieties, "Functional Analysis and its
  applications", v.11, N4, 56-64, 1977, translation in Funct. Anal. Appl.
  11 (1977), no.4, 289-296 (1978).

  10. Newton  Polyhedra  and  the genus  of  complete  intersections,
  "Functional Analysis and its applications", v.12, N1, 51-61, 1978;
  translation in Funct. Anal. Appl.  12 (1978), no. 1, 38-46 (1978).

  11. Newton Polyhedra  and  the Euler-Jacoby  formula "Uspehi Matem.
  Nauk", v.33, N6, 237-238, 1978; translation in Russian Math. Surveys 33
  (1978), no. 6, 237-238.

  12. (with L. Kantorovich) The principle of differential optimization
  in application to a one-product dynamic model of the economy  "Siberian
  Math. J.", v.19, N5, 1053-1064, 1978; translation in Siberian Math. J.,
  v.19, no.5, 744-752 (1979).

  13. Explicit solutions in the one-sectorial model of economics
  with continuously distributed fonds, "Sbornik Trudov VNIISI", N9,
  235-240, 1978.

  14. Exponential growth in the one-sectorial model of economics with
  continuously distributed fonds, "Sbornik Trudov VNIISI", N9, 25-36, 1978.

  15. (with L. Kantorovich) Analysis of dynamics of economic parameters in
  the models  with continuously distributed fonds, "Sbornik Trudov VNIISI",
  N9, 5-25, 1978.

  16. Index of a polynomial vector field, "Functional Analysis and its
  applications", v.13, N1, 49-58, 1979; translation in Funct. Anal. Appl.
  13 (1979), no.1, 38-45 (1979).

  17. The explicity of Petrovsky-Olejnik unequalities, "Uspehi Matem.
  Nauk", v.34, N3, 223, 1979 (Russian Math. Surveys).

  18. Geometry of convex polyhedra and algebraic geometry, "Uspehi Matem.
  Nauk", v.34, N4, 160-161, 1979 (Russian Math. Surveys).

  19. (with G.S. Khovanskii) Transformation of the nomograms
  consisting of aligned points and with parallel index into nomograms of C
  of equidistant points. "Doclady AN SSSR", v.248, N3, 535-538, 1979;
  translation in Soviet Math. Dokl. v. 20 (1979)   no. 5, 1041-1048.

  20. On a class of systems of transcendental equations, "Doclady AN SSSR",
  v.255, N4, 804-807, 1980; translation in Soviet   Math. Dokl. v. 22,
  (1980) no. 3, 762-765.

  21. (with O. Gelfond) Real Liouville functions. "Functional Analysis and
  its applications", v.14, N2, 52-53, 1980; translation in Funct. Anal.
  Appl. 14 (1980), no. 2, 122-123 (1980).

  22.  Rectification of circles. "Siberian Mathematical Journal",
  v.21, N4, 221-226, 1980; translation in Siberian Math. J. v.21 (1981),
  no.4, 649-652.

  23. On numbers of solutions of real equations, "Uspehi Matem. Nauk",
  v.35, N5, 213, 1980 (Russian Math. Surveys).
 
  24. Straighting of parallel curves. "Doclady AN SSSR", v. 250,
  N1, 1074-1076, 1980; translation in Soviet Math. Dokl. v. 21 (1980), no.
  1, 284-286.
 
  25. Theorema de Bezout pour les fonctions de Liouville, Preprint IHES,
  81/85, 1-31, 1981.

  26. Sur les racines complexes de systemes d'equations algebraiques
  avant un petit nombre de monomes, C.R.Acad. Sc. Paris, v.292, 937-940,
  1981.

  27. (with G.S. Khovanskii) Representation of classical canonical
  nomographic forms with oriented transporant and circular nomograms.
  "Trudy Seminara po nomografii", 50-52, 1981.

  28. Newton Polyhedra and the index of a vector field, "Uspehi Matem.
  Nauk", v.36, N4, 234, 1981 (Russian Math. Surveys).

  29. (with L. Korkina) Golden rule for the two-sectorial models of
  economic growth, "Trudy Seminara Slozhnykh System", 11-18, 1981.
 
  30. Local multiplicity of a holomorphic map, in the book "Singularities
  of differential maps" by V.Arnold et al, 66-89, 1981.
 
  31. On estimation of real solutions number, "Uspehi Matem. Nauk", v.37,
  N1, 165, 1982 (Russian Math. Surveys).

  32. (with G.S. Khovanskii) Transformation of nomograms from aligned 
  points and with a parallel index into nomograms from equidistant points,
  and investigation of their adaptability. "Nomograficheskii Sbornik",
  v.14, 56-77, 1982.
 
  33. (with   G.S.  Khovanskii)  Methods of nomographing some relations,
  based on the use of two-parameter families of lines, circles and ellipses.
  "Nomograficheskii Sbornik", v.14, 70-105, 1982.
 
  34. (with L. Korkina) Principle of differential optimization and
  economic model, "Trudy VNIISI", N8, 3-10, 1982.

  35. Newton Polyhedra (resolutions of singularities), Current problems in 
  mathematics, Vol. 22, 207-239, Itogi Nauki i Tekhniki, Akad. Nauk SSSR,
  Vsesoyuz. Inst. Nauchn. i Tekhn. Inform., Moscow, 1983.
 
  36. (with L. Kantorovich and L. Korkina) Asymptotic optimization in
  two-sectorial economics, "Siberian Math. J.", v.24, N5, 71-75, 1983;
  translation in Siberian Math. J. v. 24 (1983), no.5, 704-708   (1984).

  37. (with  L.  Kantorovich  and  L.  Korkina)  Optimization  in
  continuous and discrete models of two-sectorial economics, "Trudy
  VNIISI", N9, 14-20, 1983.
 
  38. (with V. Arnold, A. Varchenko, A. Givental) Singularities of
  functions, wave fronts, caustics, and multidimensional integrals,
  Translated   from the Russian. Soviet Sci. Rev. Sect. C: Math. Phys.
  Rev., 4, Mathematical   physics reviews, Vol. 4, 1-92, Harwood Academic
  Publ., Chur, 1984.

  39. Fewnomials and Pfaff manifolds, Proceedings of the International 
  Congress of Mathematicians, Vol.1, 2 (Warsaw, 1983), 549-564, PWN,
  Warsaw, 1984.

  40. Cycles of dynamic systems on a plane and Roll theorem, "Sibirian
  Mathematical Journal", v.25, N3, 198-203, 1984; translation in Siberian
  Math. J. v.25 (1984), no.3, 502-506 (1985).

  41. Real analytic manifolds with the property of finiteness, and complex
  abelian integrals, "Functional Analysis and its applications", v.18, N2,
  40-50, 1984; translation in Funct. Anal. Appl. 18 (1984), no.2, 119-127
  (1984).

  42. Mixed volumes, "Uspehi Matem. Nauk", v.39, N5, 227-228, 1984 (Russian
  Math. Surveys).

  43. On analoques of Alexandrov-Fenchel inequalities for hyperbolic forms,
  "Doclady AN SSSR", v. 276, N6, 1332-1334, 1984; translation in Soviet
  Math. Dokl. v.29(1984), no.3.


  44. (with A. Varchenko) On asymptotic behavior of integrals on vanishing
  cycles, "Doclady AN SSSR", v.283, N3, 521-525, 1985; translation in
  Soviet Math. Dokl. v. 32(1985), no. 1, 122-127.

  45. (with  L. Korkina) Two-sectorial economics with different
  amortization coefficient in different sectors, All-Union Conference on
  Systems Studies, 135-137, 1985.

  46. (with L. Kantorovich and L. Korkina) Comparing of different models of
  economic growth, "Trudy VNIISI", 3-12, 1985.

  47. Linear programming and geometry of convex polyhedra, "Trudi VNIISI",
  73-80, 1985.

  48. Linear programming and generalization of Nikulin's theorem,
  "Trudi VNIISI", 81-86, 1985.
 
  49. Hyperplane sections of polyhedra, toric  varieties and discrete
  groups in Lobachevsky space, "Functional Analysis and   its
  applications", v.20, N1, 50-61, 1986; translation in Funct.   Anal. Appl.
  20 (1986), no. 1, 41-50 (1986).

  50. Newton polyhedra and an algorithm for calculating Hodge-Deligne
  numbers, "Izvestia AN  SSSR", Ser. Mathematica, v.50, N5, 925-945, 1986;
  translation in Math. USSR - Izv.
 
  51. Comparing of different kinds of estimations for differend small
  dimensional economical models, "Trudy VNIISI", 10-23, 1987.

  52. Algebra and mixed volumes "A Series of geometry (Y.D.Burago
  and V.A.Zalgaller, eds)", Springer-Verlag, Berlin and New York. V.285,
  182-207, 1988.

  53. Newton Polyhedra and fewnomials, Russian Doctoral thesis, Moscow,
  1-332, 1988.

  54. Newton Polyhedra (algebra and geometry), Proceedings of XIII 
  All-Union School on the Operator Theory in Functional Spaces,
  Kujbishev, 202-221, 1989; translation in Amer. Math. Soc. Transl.
  (2) v. 153, 1992, 183-199.
 
  55. (with  G.S.Khovanskii) Investigation of methods for the
  representation of the equation $(f\sb {34}-f\sb {12})/(g\sb {34}-g\sb
  {12}) =(f\sb {56}-f\sb {12})/(g\sb {56}-g\sb {12})$ by nomograms with a
  directed transparent carrying a curvilinear index.  Nomography
  collection, No.16, 63-81, 194, Akad. Nauk SSSR, Vychisl. Tsentr, Moscow,
  1990.

  56. (with Yu.Ilyashenko) Galois groups, Stocks operators and theorem of
  Ramise, "Functional Analysis and its applications", v.24, N4; 31-42,
  1990; translation in Funct. Anal. Appl. 24 (1990), no.4, 286-296 (1991).

  57. "Fewnomials" - AMS translated monographs, USA, V.88, viii+139,
  1991.
 
  58. (with A.Pukhlikov) Finitely additive measures of virtual polytopes,
  "Algebra and Analysis", v.4, N2, 161-185, 1992; translation in 
  St.Petersburg Math. J. 4(1993), no.2, 337-356.
 
  59. (with  A.Pukhlikov) A Riemann-Roch theorem for integrals and sums of
  quasipolynomials over virtual polytopes, "Algebra and   Analysis", v.4,
  N4, 188-216, 1992; translation in St. Petersburg Math. J. 4 (1993), no.4,
  789-812.

  60. Newton polyhedron, Hilbert polynomial and the number of points in
  sums of finite sets, "Functional Analysis  and  its   Applications",
  V.26, N4, 57-63, 1992; translation in Functional Anal.   Appl. 26 (1992),
  no.4, 276-281 (1993).

  61. (with J.-M.Kantor) Integral points in integral polyhedra, Preprint
  IHES, France, 1992.

  62. (with J.-M.Kantor) Une application du Theoreme de Riemann-Roch
  combinatoire au polynome d'Ehrhart des polytopes entier de R, C. R. Acad.
  Sci. Paris. Ser.I, V.317, 501-507, 1993.

  63. (with A.Pukhlikov) Integral transforms based on Euler characteristic
  and their application, "Integr.transform and   special function", V.1,
  N.1, 30-36, 1993.

  64. Topological obstructions for representability of functions by
  quadratures, "Journal of dynamical and control systems", V.1, N.1,
  99-132, 1995.

  65. Sums of finite sets, orbits of comutative semigroups and Hilbert
  function, "Funkts. analiz", V.29, N.2, 36-50, 1995; translation in Funct.
  Anal. Appl. 29(1995), no.2, 102-112
 
  66. (with S.Zdravkovska) Branched covers of $S^2$ and braid groups,
  "Jornal of Knot Theoty and its Ramifications", V.5, N.1, 55-75, 1996.
 
  67. (with O.Gelfond) Newton polyhedra and Grothendieck  residues
  "Doklady RAN", V.3, N.350, 298-300, 1996; translation in Doklady
  Mathematics v.54, no.2, 1996, 700-702.
 
  68. (with S. Yakovenko) Generaized Rolle theorem in $R^n$ and $C$,
  "Journal of dynamical and control systems", V.2, N.1, 103-123, 1996.
 
  69. Integration in finite terms (Liouville theory, differential
  Galois theory, topological obstructions) (to appear).
  http://www.math.toronto.edu/askold/askoldpap.html
 
  70. (with G.S.Khovanskii, E.G.Kozlova) On some questions of theoretical
  and applied nomography, "Computer Center of the Russian   Academy of
  Sciences" Computer Center RAN, 96 pp., 1996.

  71. Fewnomials, "PHASIS Publishing House", Moscow, xii+217 pp., 1997.

  72.  Newton polytopes, curves on toric surfaces, and inversion of 
  Weil's theorem, "Uspekhi matematicheskikh nauk",  V.52, N.6(318), 
  113-142, 1997; translation in Russian Math. Surveys 52 (1997), no. 6,
  1251-1279. 
 
  73. Consistent partitions of polytopes and polynomial measures, Topics in
  Singularity Theory: V.I. Arnold's 60th Anniversary Collection,   Amer.
  Math. Soc. Transl., Ser. 2, Vol. 180, Amer. Math. Soc., Providence, RI,
  1997, 157-166.

  74. Topics in Singularity Theory: V.I. Arnold's 60th Anniversary
  Collection, Amer. Math. Soc. Transl., Ser.2, Vol.180, Amer. Math. Soc.,
  Providence, RI, 1997, Editor.
 
  75. On a lemma of Kontsevich, "Funkts. analiz", V.31, N.4, 89-91,
  1997; translation in Funct. Anal. Appl. 31 (1997), no.4, 296-298 (1998)
 
  76. (with others) Vladimir Igorevich  Arnol'd (on the occasion of his
  sixtieth birthday). "Uspekhi mat. nauk", V.52, N5(317), 1997, 235-255;
  translation in Russian Math. Surveys 52 (1997), no.5, 1117-1139.
 
  77. Boundary indexes of 1-forms with homogeneous polynomial coefficients,
  "Algebra and Analysis", V.10, N.3, 1998, 33 pp; translation in St.
  Petersburg Math. J. 10 (1999), no.3, 553-575.

  78. (with A. Gabrielov)  Multiplicity of a Noetherian Intersection,
  Geometry of  Differential Equations, Amer. Math. Soc. Transl., Ser. 2,
  Vol.186, Amer. Math. Soc., Providence, RI, 1998, 119-130.
 
  79. Geometry of  Differential Equations, Amer. Math. Soc. Transl., 
  Ser.2, Vol.186, Amer. Math. Soc., Providence, RI, 1998, Editor.
 
  80. Newton polyhedrons, a new formula for mixed volume, product of roots
  of a system of equations, The Arnoldfest, Proceedings of a Conference in
  Honour of V.I. Arnold for his Sixtieth Birthday, Fields Institute
  Communicatins, Vol. 24, Amer. Math. Soc., Providence, RI, 1999, 325-364.
  
  81. The Arnoldfest, Proceedings of a Conference in Honour of V.I.Arnold
  for his Sixtieth Birthday, Fields Institute Communicatins, Vol.24,
  Amer. Math. Soc., Providence, RI, 1999, Editor.

  82.Introduction to Toric Varieties by W. Fulton. Editor of Russian
  Translation, Publishing House PHASIS, Moscow (to appear).
  http://www.math.toronto.edu/askold/askoldpap.html
 
  83. Geometry of polyhedra and algebraic geometry, in Russion
  Translation "Introduction to Toric Varieties" writen by W. Fulton,
  Publishing House PHASIS, Moscow (to appear). 
  
  84. Families of plane sections of quadrics and classical geometries,   
  "Funkts. analiz", V.34, N.3, 2000, 91-95.
 
  85. Geometrical generalizations of a problem about transformation of the
  nomograms consisting of aligned points into nomograms consisting of
  equidistant points, Nomography collection, N.17, RAN, Vychisl. Tsentr,
  2000, 73-88.

  86. On the continuability of multivalued analytic functions  to an
  analytic subset, "Funkts. analiz", V. 35, N.1, 62-73,  2001; translation
  in Funct. Anal. Appl. 35(2001), no.1, 51-59 (2001).

  87.  Three lectures on Newtov polyhedra, "Singularity Theory and its
  Applications",  proceeding of workshops, 28-31 May, 2001, RIMS, Kyoto
  (to appear).

  88. (with O. Gelfond)  Toric geometry and Grothendieck  residues,
  "Moscow Mathematical Jornal" (to appear).

           In preparation

  89. Toric geometry, multidimensional antiderivative and Purshin's
  symbols.

  90. Topological variant of  Galois theory, monograph.

  91. (with D.Novikov) On Arnold's problem about projective hypersurfaces
  with non degenerate second form.

  92. (with V.Timorin) Euler ordered sets and Hodge-Deligne numbers.

  93. (with O. Gelfond) Newton polyhedra and explicit summation formulas.

  94. Geometry of formulas.

  95. Systems of algebraic equations with common Newton polyhedra, December
  14, 2000   IUM general seminar "Globus".

  96. (with G. Petrov) On a linear bound of the numbers of zeros   of
  abelian integrals.