Bibliography
1972
Vinogradov, A. M.: The logic algebra for the theory of linear differential operators, Dokl. Akad. Nauk SSSR 205(5) (1972), 1025–1028 (in Russian); English transl. in Soviet Math. Dokl. 13(4) (1972), 1058–1062.
1974
Krasil'shchik, I. S.: Hamiltonian formalism in canonical rings, The 8th Voronezh Winter Mathematical School, Voronezh State University Publ., Voronezh, 1974 (in Russian).
Vinogradov, M. M.: De Rham cohomology of fields P(z 1,..., z n ) and residue theory, The 8th Voronezh Winter Mathematical School, Voronezh State University Publ., Voronezh, 1974, pp. 18–19 (in Russian).
1975
Vinogradov, A. M. and Krasil'shchik, I. S.: What is the Hamiltonian formalism?, Uspekhi Mat. Nauk 30(1) (1975), 173–198 (in Russian); English transl. in Russian Math. Surveys 30(1) (1975), 177–202; Also in: London Math. Soc. Lecture Notes Series 60, Cambridge Univ. Press, London, 1981, pp. 241–266.
1977
Vinogradov, A. M.: On the algebro-geometric foundations of Lagrangian field theory, Dokl. Akad. Nauk SSSR 236(2) (1977), 284–287 (in Russian); English transl. in Soviet Math. Dokl. 18(5) (1977), 1200–1204.
Vinogradov, A. M., Krasil'shchik, I. S., and Lychagin, V. V.: Application of Nonlinear Differential Equations in Civil Aviation, Moskov. Inst. Inz. Grazdan. Aviacii, Moscow, 1977, p. 123 (in Russian).
1978
Vinogradov, A. M.: A spectral system associated with a non-linear differential equation and the algebro-geometric foundations of Lagrangian field theory with constraints, Dokl. Akad. Nauk SSSR 238(5) (1978), 1028–1031 (in Russian); English transl. in Soviet Math. Dokl. 19(1) (1978), 144–148.
Vinogradov, M. M.: On de Rham and Spencer algebraic cohomology of smooth manifolds, Dokl. Akad. Nauk SSSR 242(5) (1978) 989–992 (in Russian); English transl. in Soviet Math. Dokl. 19(5) (1978), 1220–1224.
1979
Vinogradov, A. M.: Some homological systems associated with differential calculus over commutative algebras, Uspekhi Mat. Nauk 34(6) (1979), 145–150 (in Russian); English transl. in Russian Math. Surveys 34(6) (1979), 250–255.
1980
Bocharov, A. V.: Spencer cohomology of affine algebraic varieties, Dokl. Akad. Nauk SSSR 252(6) (1980), 1296–1299 (in Russian); English transl. in Soviet Math. Dokl. 21(1–6) (1980), 912–916.
Krasil'shchik, I. S.: Hamiltonian cohomologies of canonical algebras, Dokl. Akad. Nauk SSSR 251(6) (1980) (in Russian); English transl. in Soviet Math. Dokl. 21 (1980), 625–629.
Vinogradov, M. M.: Residue theory on commutative algebras, Uspekhi Mat. Nauk 35(2) (1980), 203–204.
1981
Bocharov, A. V.: Spencer cohomologies of an algebraic curve with coefficients in the normalization, Dokl. Akad. Nauk SSSR 261(5) (1981), 1036–1240 (in Russian); English transl. in Soviet Math. Dokl. 24(3) (1981), 629–633.
Vinogradov, A. M.: Category of nonlinear differential equations, XV Voronezh winter mathematical school, Voronezh Gos. Univ. Publ., VINITI, No 5691, 1981, pp. 9–10 (in Russian).
Vinogradov, M. M.: Extensions of fields and extensions of linear differential operators, Mat. Zametki 30(2) (1981), 237–248 (in Russian).
1982
Vinogradov, A. M.: Category of nonlinear differential equations, Equations on Manifolds, Novoe Global. Anal., Voronezh. Gos. Univ., Voronezh, 1982, pp. 26–51 (in Russian).
1983
Vinogradov, A. M.: Category of nonlinear differential equations, Addendum in J.-F. Pommaret, Systems of Partial Differential Equations and Lie Pseudogroups, Translated from the English by A. V. Bocharov, M. M. Vinogradov and I. S. Krasil'shchik. Translation edited and with a preface by A. M. Vinogradov, Mir, Moscow, 1983, pp. 379–391 (in Russian).
1984
Vinogradov, A. M.: Category of partial differential equations, Lecture Notes in Math., 1108, Springer-Verlag, Berlin, 1984, pp. 77–102.
Vinogradov, A. M.: The C-spectral sequence, Lagrangian formalism, and conservation laws. I. The linear theory, J. Math. Anal. Appl. 100(1) (1984), 1–40.
Vinogradov, A. M.: The C-spectral sequence, Lagrangian formalism, and conservation laws. II. The nonlinear theory, J. Math. Anal. Appl. 100(1) (1984), 41–129.
Vinogradov, A. M.: The category of differential equations and its significance for physics, in: D. Krupka (ed.), Proc. Conf. Diff. Geom. Appl. (Brno, 1984) J. E. Purkyně Univ., Brno, Czechoslovakia, 1984, pp. 289–301.
1986
Astashov, A. M. and Vinogradov, A. M.: On the structure of Hamiltonian operators in field theory, J. Geom. Phys. 3(2) (1986), 263–287.
Krasil'shchik, I. S.: Poincaré delta-lemma, Proc. Seminar on Algebra and Geometry of Differential Equations, VINITI, No 858/86B, Moscow, 1986, pp. 147–152 (in Russian).
Krasil'shchik, I. S., Lychagin, V. V. and Vinogradov, A. M.: Geometry of Jet Spaces and Nonlinear Differential Equations, Adv. Stud. Contemp. Math. 1, Gordon and Breach, New York, London, 1986.
Vinogradov, A. M., Krasil'shchik, I. S. and Lychagin, V. V.: Introduction to the Geometry of Nonlinear Differential Equations, Nauka, Moscow, 1986 (in Russian).
Vinogradov, M. M.: Residues without duality, Proc. Seminar on Algebra and Geometry of Differential Equations, VINITI, No 858/86B, Moscow, 1986, pp. 183–201 (in Russian).
1988
Krasil'shchik, I. S.: Schouten brackets and canonical algebras, Global Anal. and Math. Physics, Voronezh State University, Voronezh, 1987, pp. 73–94 (in Russian); English transl. in Lecture Notes in Math. 1334, Springer-Verlag, Berlin, 1988, pp. 79–110.
1989
Vinogradov, M. M.: Principal functors of differential calculus in graded algebras, Uspekhi Mat. Nauk 44(3) (1989), 161–152 (in Russian); English transl. in Russian Math. Surveys 44(3) (1989), 220–221.
1990
Vinogradov, A. M.: A common generalization of the Schouten and Nijenhuis brackets, cohomology, and superdifferential operators, Mat. Zametki 47(6) (1990), 138–140 (in Russian); English transl. in Math. Notes 47 (1990).
1991
Krasil'shchik, I. S.: Supercanonical algebras and Schouten brackets, Mat. Zametki 49(1) (1991), 70–76 (in Russian); English transl. in Math. Notes 49 (1991).
Modugno, M. and Vinogradov, A. M.: Some variations on the notion of connection, Dip. Mat. Appl. G. Sansone, Univ. Stud. Firenze, 13 (1991); Also in: Ann. Mat. Pyra ed Appli. 167 (1994), 33–71.
Vinogradov, M. M.: On general algebraic theory of linear differential operators, Dokl. Akad. Nauk SSSR 317(2) (1991), 275–279 (in Russian); English transl. in Soviet Math. Dokl. 43(2) (1991), 355–359.
1992
Cabras, A. and Vinogradov, A. M.: Extension of the Poisson bracket to differential forms and multi-vector fields, J. Geom. Phys 9(1) (1992), 75–100.
Krasil'shchik, I. S.: Differential operators of constant growth and Jacobi structures of infinite order, Publ. IRMA (Univ. of Lille) 30(11) (1992), 1–21.
Krasil'shchik, I. S.: Some new cohomological invariants for nonlinear differential equations, Differential Geom. Appl. 2(4) (1992), 307–350.
Krasil'shchik, I. S. and Kersten, P. H. M.: Deformations and recursion operators for evolution equations, Memorandum Twente University 1104, Enschede, 1992; Also in: A. Pràstaro, Th. M. Rassias (eds.), Geometry in Partial Differential Equations, World Scientific, Singapore, 1995, pp. 114–154.
1993
Krasil'shchik, I. S.: An algebraic model for characteristics of differential equations, Preprint of the Erwin Schrödinger Internat. Inst. for Mathematical Physics 48, Vienna, 1993.
Krasil'shchik, I. S. and Kersten, P. H. M.: Graded Frölicher-Nijenhuis brackets and the theory of recursion operators for super differential equations, Memorandum Twente University 1147, Enschede, 1993; Also in: V. V. Lychagin (ed.), The Interplay between Differential Geometry and Differential Equations, Adv. Math. Sci. 24, Amer. Math. Soc., Providence, 1995, pp. 91–130.
1994
Vinogradov, M. M.: Coconnections and integral forms, Doklady Ross. Akad. Nauk 338(3) (1994), 295–297 (in Russian); English transl. in Russian Acad. Sci. Math. Dokl. 50(3) (1995), 229–233.
1995
Krasil'shchik, I. S.: Hamiltonian formalism and supersymmetry for nonlinear differential equations, Preprint of the Erwin Schrödinger Internat. Inst. for Mathematical Physics 257, Vienna, 1995.
Krasil'shchik, I. S. and Kersten, P. H. M.: Graded differential equations and their deformations: a computational theory for recursion operators, Acta Appl. Math. 41 (1995), 167–191; Also in: P. H. M. Kersten, I. S. Krasil'shchik (eds), Geometric and Algebraic Structures in Differential Equations, Kluwer Acad. Publ., Dordrecht, Boston, London, 1995, pp. 114–154.
Verbovetsky, A. M.: On quantized algebra of Wess-Zumino differential operators at roots of unity, Preprint SISSA 66/95/FM, Trieste, 1995.
Verbovetsky, A. M.: Differential operators over quantum spaces, Preprint SISSA 66/95/FM, Trieste, 1995.
1996
Krasil'shchik, I. S.: Poisson structures on nonlinear evolution equations, Memorandum Twente University, 1320, Enschede, 1996.
Krasil'shchik, I. S.: A supersymmetry approach to Poisson structures over differential equations, in I. Koláě (ed.), Proc. Conf. Diff. Geom. Appl., Brno, Aug. 28–Sept. 1, 1995, J. E. Purkyně Univ., Brno, 1996, pp. 381–392.
Verbovetsky, A. M.: Lagrangian formalism over graded algebras, J. Geom. Phys. 18(3) (1996), 195–214.
Rights and permissions
About this article
Cite this article
Foreword. Acta Applicandae Mathematicae 49, 229–234 (1997). https://doi.org/10.1023/A:1017143604709
Issue Date:
DOI: https://doi.org/10.1023/A:1017143604709