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Volumn 55, Issue 3, 1999, Pages 231-250

Abstract Differential Geometry, Differential Algebras of Generalized Functions, and de Rham Cohomology

Author keywords

Abstract differential geometry; de Rham cohomology; Differential algebras

Indexed keywords


EID: 0001160728     PISSN: 01678019     EISSN: None     Source Type: Journal    
DOI: 10.1023/A:1006106718337     Document Type: Article
Times cited : (34)

References (33)
  • 2
    • 0003287020 scopus 로고
    • A Nonlinear Theory of Generalized Functions
    • Springer, New York
    • Biagioni, H. A.: A Nonlinear Theory of Generalized Functions, Lecture Notes in Math. 1421, Springer, New York, 1990.
    • (1990) Lecture Notes in Math. , vol.1421
    • Biagioni, H.A.1
  • 4
    • 0003221810 scopus 로고
    • New Generalized Functions and Multiplication of Distributions
    • North-Holland, Amsterdam
    • Colombeau, J.-F.: New Generalized Functions and Multiplication of Distributions, Math. Stud. 84, North-Holland, Amsterdam, 1984.
    • (1984) Math. Stud. , vol.84
    • Colombeau, J.-F.1
  • 7
    • 0042334441 scopus 로고
    • Algebraic foundations of the theory of differential spaces
    • Heller, M.: Algebraic foundations of the theory of differential spaces, Demonstratio Math. 24 (1991), 349-364.
    • (1991) Demonstratio Math. , vol.24 , pp. 349-364
    • Heller, M.1
  • 8
    • 0009281840 scopus 로고
    • Einstein algebras and general relativity
    • Heller, M.: Einstein algebras and general relativity, Internat. J. Theoret. Phys. 31 (1992), 277-288.
    • (1992) Internat. J. Theoret. Phys. , vol.31 , pp. 277-288
    • Heller, M.1
  • 9
    • 21844519504 scopus 로고
    • Structured spaces and their application to relativistic physics
    • Heller, M. and Sasin, W.: Structured spaces and their application to relativistic physics, J. Math. Phys. 36 (1995), 3644-3662.
    • (1995) J. Math. Phys. , vol.36 , pp. 3644-3662
    • Heller, M.1    Sasin, W.2
  • 12
    • 0002486696 scopus 로고
    • On the categoricity in power of elementary deductive systems and some related problems
    • Loš, J.: On the categoricity in power of elementary deductive systems and some related problems, Colloq. Math. 3 (1954), 58-62.
    • (1954) Colloq. Math. , vol.3 , pp. 58-62
    • Loš, J.1
  • 14
    • 0342793666 scopus 로고
    • On an axiomatic treatment of differential geometry via vector sheaves
    • Mallios, A.: On an axiomatic treatment of differential geometry via vector sheaves, (Intern. Plaza) Math. Japonica 48 (1988), 93-184.
    • (1988) (Intern. Plaza) Math. Japonica , vol.48 , pp. 93-184
    • Mallios, A.1
  • 15
    • 38249001341 scopus 로고
    • The de Rham-Kähler complex of the Gel'fand sheaf of a topological algebra
    • Mallios, A.: The de Rham-Kähler complex of the Gel'fand sheaf of a topological algebra, J. Math. Anal. Appl. 175 (1993), 143-168.
    • (1993) J. Math. Anal. Appl. , vol.175 , pp. 143-168
    • Mallios, A.1
  • 16
    • 0041332741 scopus 로고
    • On an abstract form of Weil's integrality theorem
    • invited paper
    • Mallios, A.: On an abstract form of Weil's integrality theorem, Note Mat. 12 (1992), 167-202 (invited paper).
    • (1992) Note Mat. , vol.12 , pp. 167-202
    • Mallios, A.1
  • 17
    • 25344452378 scopus 로고    scopus 로고
    • On an axiomatic approach to geometric prequantization: A classification scheme à la Kostant-Souriau-Kirillov
    • Mallios, A.: On an axiomatic approach to geometric prequantization: A classification scheme à la Kostant-Souriau-Kirillov, J. Math. Sci. (former J. Soviet Math.) 98-99.
    • J. Math. Sci. (Former J. Soviet Math.) , vol.98-99
    • Mallios, A.1
  • 18
    • 84972515093 scopus 로고
    • The differentiable space structures of Milnor classifying spaces, simplicial complexes, and geometric realizations
    • Mostow, M. A.: The differentiable space structures of Milnor classifying spaces, simplicial complexes, and geometric realizations, J. Differential Geom. 14 (1979), 255-293.
    • (1979) J. Differential Geom. , vol.14 , pp. 255-293
    • Mostow, M.A.1
  • 20
    • 0041332742 scopus 로고
    • Differential calculus founded on an isomorphism
    • Nel, L. D.: Differential calculus founded on an isomorphism, Appl. Categ. Structures 1 (1993), 51-57.
    • (1993) Appl. Categ. Structures , vol.1 , pp. 51-57
    • Nel, L.D.1
  • 21
    • 0002360177 scopus 로고
    • Solution of Continuous Nonlinear PDEs through Order Completion
    • North-Holland, Amsterdam, see also MR 95k:35002
    • Oberguggenberger, M. B. and Rosinger, E. E.: Solution of Continuous Nonlinear PDEs through Order Completion, Norht-Holland Math. Stud. 181, North-Holland, Amsterdam, 1994, see also MR 95k:35002.
    • (1994) Norht-Holland Math. Stud. , vol.181
    • Oberguggenberger, M.B.1    Rosinger, E.E.2
  • 23
    • 0041332746 scopus 로고
    • Embedding of the script D sign′ distributions into pseudotopological algebras
    • Rosinger, E. E.: Embedding of the script D sign′ distributions into pseudotopological algebras, Stud. Cerc. Mat. 18(5) (1966), 687-729.
    • (1966) Stud. Cerc. Mat. , vol.18 , Issue.5 , pp. 687-729
    • Rosinger, E.E.1
  • 24
    • 0042835339 scopus 로고
    • Pseudotopological spaces, the embedding of the script D sign′ distributions into algebras
    • Rosinger, E. E.: Pseudotopological spaces, the embedding of the script D sign′ distributions into algebras, Stud. Cerc. Mat. 20(4) (1968), 553-582.
    • (1968) Stud. Cerc. Mat. , vol.20 , Issue.4 , pp. 553-582
    • Rosinger, E.E.1
  • 25
    • 0007286788 scopus 로고
    • Distributions and Nonlinear Partial Differential Equations
    • Springer, New York
    • Rosinger, E. E.: Distributions and Nonlinear Partial Differential Equations, Lecture Notes in Math. 684, Springer, New York, 1978.
    • (1978) Lecture Notes in Math. , vol.684
    • Rosinger, E.E.1
  • 26
    • 0007280554 scopus 로고
    • Nonlinear Partial Differential Equations, Sequential and Weak Solutions
    • North-Holland, Amsterdam
    • Rosinger, E. E.: Nonlinear Partial Differential Equations, Sequential and Weak Solutions, North-Holland Math. Stud. 44, North-Holland, Amsterdam, 1980.
    • (1980) North-Holland Math. Stud. , vol.44
    • Rosinger, E.E.1
  • 27
    • 85013520859 scopus 로고
    • Generalized Solutions of Nonlinear Partial Differential Equations
    • North-Holland, Amsterdam
    • Rosinger, E. E.: Generalized Solutions of Nonlinear Partial Differential Equations, North-Holland Math. Stud. 146, North-Holland, Amsterdam, 1987.
    • (1987) North-Holland Math. Stud. , vol.146
    • Rosinger, E.E.1
  • 28
    • 0004218556 scopus 로고
    • Nonlinear Partial Differential Equations, An Algebraic View of Generalized Solutions
    • North-Holland, Amsterdam
    • Rosinger, E. E.: Nonlinear Partial Differential Equations, An Algebraic View of Generalized Solutions, North-Holland Math. Stud. 164, North-Holland, Amsterdam, 1990.
    • (1990) North-Holland Math. Stud. , vol.164
    • Rosinger, E.E.1
  • 30
    • 0041332743 scopus 로고    scopus 로고
    • 717 35001, MR 92d:46097
    • Rosinger, E. E.: Parametric Lie group actions on global generalised solutions of nonlinear PDEs, including a solution to Hilbert's fifth problem. See also MR 92d:46098; Zbl. Math. 717 35001, MR 92d:46097; Bull. Amer. Math. Soc. 20(1) (1989), 96-101, MR 89g:35001.
    • Zbl. Math.
  • 31
    • 0042835352 scopus 로고
    • MR 89g:35001
    • Rosinger, E. E.: Parametric Lie group actions on global generalised solutions of nonlinear PDEs, including a solution to Hilbert's fifth problem. See also MR 92d:46098; Zbl. Math. 717 35001, MR 92d:46097; Bull. Amer. Math. Soc. 20(1) (1989), 96-101, MR 89g:35001.
    • (1989) Bull. Amer. Math. Soc. , vol.20 , Issue.1 , pp. 96-101
  • 33
    • 0010784290 scopus 로고
    • Groupes différentiels
    • Differential Geometric Methods in Mathematical Physics, Springer, New York
    • Souriau, J.-M.: Groupes différentiels, in: Differential Geometric Methods in Mathematical Physics, Lecture Notes in Math. 836, Springer, New York, 1980, pp. 91-128.
    • (1980) Lecture Notes in Math. , vol.836 , pp. 91-128
    • Souriau, J.-M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.