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References

  1. Avdoshin, S.M., Belov, V.V., and Maslov, V.P.: ‘Mathematical aspects of computing media synthesis’, MIEM Publ. (1984). (In Russian.)

    Google Scholar 

  2. Baccelli, F.L., Cohen, G., Olsder, G.J., and Quadrat, J.-P.: Synchronization and linearity: an algebra for discrete event systems, Wiley, 1992.

    MATH  Google Scholar 

  3. Cohen, G., and Quadrat, J.-P. (eds.): Discrete Event Systems, Vol. 199 of Lecture Notes in Control and Information Science, Springer, 1994.

    Google Scholar 

  4. Dudnikov, P.I., and Samborskiǐ, S.N.: ‘Endomorphisms of semimodules over semirings with an idempotent operation’, Math. USSR-Izv. 38 (1991), 91–105. (Translated from the Russian.)

    Article  MATH  Google Scholar 

  5. Gunawardena, J. (ed.): Idempotency, Publ. I. Newton Institute. Cambridge Univ. Press, in press.

    Google Scholar 

  6. Litvinov, G.L., and Maslov, V.P.: ‘Idempotent mathematics: correspondence principle and applications’, Russian J. Math. Phys. 4, no. 4 (1996). (Translated from the Russian.)

    Google Scholar 

  7. Litvinov, G.L., and Maslov, V.P.: ‘Correspondence principle for idempotent calculus and some computer applications’, in J. Gunawardena (ed.): Idempotency, Publ. I. Newton Institute, Cambridge Univ. Press, in press.

    Google Scholar 

  8. Maslov, V.P.: Méthodes opératorielles, MIR, 1987. (Translated from the Russian.)

    MATH  Google Scholar 

  9. Maslov, V.P.: ‘New superposition principle for optimization problems’, Russian Math. Surveys 42 (1987). (Translated from the Russian.)

    Google Scholar 

  10. Maslov, V.P., and Kolokoltsov, V.N.: Idempotent analysis and its applications in optimal control, Nauka, 1994. (In Russian.)

    Google Scholar 

  11. Maslov, V.P., and Kolokoltsov, V.N.: Idempotent analysis and applications, Kluwer Acad. Publ., 1996. (Translated from the Russian.)

    Google Scholar 

  12. Maslov, V.P., and Samborskiǐ, S.N. (eds.): Idempotent analysis, Amer. Math. Soc., 1992. (Translated from the Russian.)

    MATH  Google Scholar 

  13. Maslov, V.P., and Volosov, K.A. (eds.): Mathematical aspects of computer engineering, MIR, 1988. (In Russian.)

    Google Scholar 

  14. Shubin, M.A.: ‘Algebraic remarks on idempotent semirings and the kernel theorem in spaces of bounded functions’, in V.P. Maslov and S.N. Samborskiǐ (eds.): Idempotent analysis, Amer. Math. Soc., 1992, pp. 151–166. (Translated from the Russian.)

    Google Scholar 

  15. Del Moral, P.: ‘A survey of Maslov optimization theory’, in V.N. Kolokoltsov and V.P. Maslov (eds.): Idempotent analysis and applications, Kluwer Acad. Publ., 1996, p. Appendix. (Translated from the Russian.)

    Google Scholar 

  16. Kolokoltsov, V.N., and Maslov, V.P.: Idempotent analysis and applications, Kluwer Acad. Publ., 1996. (Translated from the Russian.)

    Google Scholar 

  17. Litvinov, G.L., and Maslov, V.P.: ‘Idempotent mathematics: correspondence principle and applications’, Russian J. Math. Phys 4, no. 4 (1996). (Translated from the Russian.)

    Google Scholar 

  18. Litvinov, G.L., and Maslov, V.P.: ‘Correspondence principle for idempotent calculus and some computer applications’, in J. Gunawardena (ed.): Idempotency, Publ. I. Newton Institute, Cambridge Univ. Press, to appear.

    Google Scholar 

  19. Aho, A.V., Hopcropt, J.E., and Ullman, J.D.: The design and analysis of computer algorithms, Addison-Wesley, 1976.

    Google Scholar 

  20. Baccelli, F.L., Cohen, G., Olsder, G.J., and Quadrat, J.-P.: Synchronization and linearity: an algebra for discrete event systems, Wiley, 1992.

    MATH  Google Scholar 

  21. Carre, B.A.: Graphs and networks, Clarendon Press and Oxford Univ. Press, 1979.

    MATH  Google Scholar 

  22. Cuningham-Green, R.A.: Minimax algebra, Vol. 166 of Lecture Notes in Economics and Mathematical Systems, Springer, 1979.

    Book  Google Scholar 

  23. Golan, J.S.: The theory of semirings with applications in mathematics and theoretical computer science, Vol. 54 of Pitman monographs and surveys in pure and applied mathematics, Longman, 1992.

    Google Scholar 

  24. Gondran, M., and Minoux, M.: Graphes et algorithms, Editions Eyrolles, 1979; 1988.

    Google Scholar 

  25. Gunawardena, J. (ed.): Idempotency, Publ. I. Newton Institute. Cambridge Univ. Press, in press.

    Google Scholar 

  26. Kolokoltsov, V.N., and Maslov, V.P.: Idempotent analysis and applications, Kluwer Acad. Publ., 1996. (Translated from the Russian.)

    Google Scholar 

  27. Maslov, V.P., and Samborskiǐ, S.N. (eds.): Idempotent analysis, Amer. Math. Soc., 1992. (Translated from the Russian.)

    MATH  Google Scholar 

  28. Maslov, V.P., and Volosov, K.A. (eds.): Mathematical aspects of computer engineering, MIR, 1988. (In Russian.)

    Google Scholar 

  29. Zimmermann, U.: ‘Linear and combinatorial optimization in ordered algebraic structures’, Ann. Discrete Math. 10 (1981), 1–380.

    Article  Google Scholar 

  30. Kolokoltsov, V.N., and Maslov, V.P.: Idempotent analysis and applications, Kluwer Acad. Publ., 1996. (Translated from the Russian.)

    Google Scholar 

  31. Maslov, V.P.: ‘New superposition principle for optimization problems’, Russian Math. Surveys 42 (1987). (Translated from the Russian.)

    Google Scholar 

  32. Barendregt, H., Bunder, M., and Dekkers, W.: ‘Systems of illative combinatory logic complete for first-order propositional and predicate calculus’, J. Symbolic Logic 58 (1993), 769–888.

    Article  MathSciNet  MATH  Google Scholar 

  33. Bunder, M.W.: ‘Set theory based on combinatory logic’, Ph.D. Thesis RU Groningen (1969).

    Google Scholar 

  34. Bunder, M.W.: ‘A deduction theorem for restricted generality’, Notre Dame J. Formal Logic 14 (1973), 341–346.

    Article  MathSciNet  MATH  Google Scholar 

  35. Bunder, M.W.: ‘Propositional and predicate calculus based on combinatory logic’, Notre Dame J. Formal Logic 15 (1974), 25–32.

    Article  MathSciNet  Google Scholar 

  36. Church, A.: ‘A set of postulates for the foundation of logic’, Ann. of Math. (2) 33 (1932), 346–366.

    Article  MathSciNet  Google Scholar 

  37. Church, A.: ‘A set of postulates for the foundation of logic’, Ann. of Math. (2) 34 (1933), 839–864.

    Article  MathSciNet  MATH  Google Scholar 

  38. Curry, H.B.: ‘Grundlagen der kombinatorischen Logik. Inauguraldissertation’, Amer. J. Math. 52 (1930), 509–536; 789–834.

    Article  MathSciNet  MATH  Google Scholar 

  39. Curry, H.B.: ‘The inconsistency of certain formal logics’, J. Symbolic Logic 7 (1942), 115–117.

    Article  MathSciNet  MATH  Google Scholar 

  40. Curry, H.B.: ‘Some advances in the combinatory theory of quantification’, Proc. Nat. Acad. Sci. USA 28 (1942), 564–569.

    Article  MathSciNet  MATH  Google Scholar 

  41. Curry, H.B., and Feys, R.: Combinatory logic, Vol. 1, North-Holland, 1958.

    MATH  Google Scholar 

  42. Curry, H.B., Hindley, J.R., and Seldin, J.P.: Combinatory logic, Vol. 2, Noroh-Holland, 1972.

    MATH  Google Scholar 

  43. Dekkers, W., Bunder, M., and Barendregt, H.: ‘Completeness of the propositions-as-types interpretation of intuitionistic logic into illative combinatory logic’, available via wil@cs.kun.nl.

    Google Scholar 

  44. Hindley, J.R., and Seldin, J.P.: Introduction to combinators and λ-calculus, Cambridge Univ. Press, 1986.

    Google Scholar 

  45. Kleene, S., and Rosser, J.B.: ‘The inconsistency of certain formal logics’, Ann. of Math. (2) 36 (1935), 630–636.

    Article  MathSciNet  Google Scholar 

  46. Schönfinkel, M.: ‘Über die Bausteine de mathematischen Logik’, Math. Ann. 92 (1924), 305–316.

    Article  MathSciNet  MATH  Google Scholar 

  47. Bundy, A.: ‘Incidence calculus: a mechanism for probabilistic reasoning’, J. Automated Reasoning 1, no. 3 (1985), 263–284, Earlier version in: Proceedings of FGCS-84 and in: Proceedings of the Workshop on Uncertainty and Probability. Also available from Edinburgh as DAI Research Paper No 216.

    Article  MathSciNet  MATH  Google Scholar 

  48. Bundy, A.: ‘Incidence calculus’: Encycl. Artificial Intelligence, 1992, pp. 663–668, Also available from Edinburgh as DAI Research Paper No. 497.

    Google Scholar 

  49. Bukhvalov, A.V.: ‘A criterion for integral representability of linear operators’, Funktsional. Anal. i Prilozhen. 9, no. 1 (1975), 51. (In Russian.)

    Article  Google Scholar 

  50. Kutateladze, S.S. (ed.): Vector lattices and integral operators, Vol. 358 of Mathematics and its Applications, Kluwer Acad. Publ., 1996.

    Google Scholar 

  51. Lozanovsky, G.Ya.: ‘On almost integral operators in KB-spaces’, Vestnik Leningrad Gos. Univ. 7 (1966), 35–44. (In Russian.)

    Google Scholar 

  52. Nakano, H.: ‘Product spaces of semi-ordered linear spaces’, J. Fac. Sci. Hokkaidô Univ. Ser. I 12, no. 3 (1953), 163–210.

    MATH  Google Scholar 

  53. Schep, A.R.: ‘Kernel operators’, Proc. Kon. Nederl. Akad. Wetensch. A 82 (1979), 39–53.

    MathSciNet  Google Scholar 

  54. Neumann, J. von: Charakterisierung des Spektrums eines Integraloperators, Vol. 229 of Actualités Sc. et Industr., Hermann, 1935.

    Google Scholar 

  55. Bronshteǐn, I.N., and Semendyayev, K.A.: Handbook of mathematics, H. Deutsch, 1985. (Translated from the Russian.)

    Google Scholar 

  56. Hertog, D. Den: Interior point approach to linear, quadratic and convex programming, Kluwer Acad. Publ., 1994.

    Book  MATH  Google Scholar 

  57. Fiacco, A.V., and McCormick, G.P.: Nonlinear programming: sequential unconstrained minimization techniques, Vol. 4 of Classics in Applied Math, SIAM, 1990, reprint.

    MATH  Google Scholar 

  58. Frisch, K.R.: ‘The logarithmic potential method for convex programming’, Institute of Economics, Univ. Oslo (1955).

    Google Scholar 

  59. Karmarkar, N.K.: ‘A new polynomial-time algorithm for linear programming’, Combinatorica 4 (1984), 373–395.

    Article  MathSciNet  MATH  Google Scholar 

  60. Lustig, I.J., Marsten, R.E., and Shanno, D.F.: ‘Interior point methods: computational state of the art’, ORSA J. Computing 6 (1994), 1–15.

    Article  MathSciNet  MATH  Google Scholar 

  61. Nesterov, Yu., and Nemirovskiǐ, A.S.: Interior point polynomial algorithms in convex programming, Vol. 13 of Studies in Applied Mathematics, SIAM, 1994. (Translated from the Russian.)

    Book  Google Scholar 

  62. Terlaky, T. (ed.): Interior point view of mathematical programming, Kluwer Acad. Publ., 1996.

    Google Scholar 

  63. Bandt, C.: ‘Self similar sets I. Topological Markov chains and mixed self-similar sets’, Math. Nachr. 142 (1989), 107–123.

    Article  MathSciNet  MATH  Google Scholar 

  64. Barnsley, M.F., and Demko, D.: ‘Iterated function systems and the global construction of fractals’, Proc. Royal Soc. London A 399 (1985), 243–275.

    Article  MathSciNet  MATH  Google Scholar 

  65. Barnsley, M.F., Elton, J.H., and Hardin, D.P.: ‘Recurrent iterated function systems’, Constr. Approx. 5 (1989), 3–31.

    Article  MathSciNet  MATH  Google Scholar 

  66. Elton, J.: ‘An ergodic theorem for iterated maps’, Ergodic Th. & Dynamical Systems 7 (1987), 481–488.

    MathSciNet  MATH  Google Scholar 

  67. Forte, B., and Vrscay, E.R.: ‘Solving the inverse problem for measures using iterated function systems: a new approach’, Adv. Appl. Prob. 27 (1995), 800–820.

    Article  MathSciNet  MATH  Google Scholar 

  68. Geronimo, J.S., Hardin, D.P., and Massopust, P.R.: ‘Fractal functions and wavelet expansions based on several scaling functions’, J. Approx. Th. 78 (1994), 373–401.

    Article  MathSciNet  MATH  Google Scholar 

  69. Hutchinson, J.E.: ‘Fractals and self-similarity’, Indiana Univ. Math. J. 30 (1981), 713–747.

    Article  MathSciNet  MATH  Google Scholar 

  70. Williams, R.F.: ‘Composition of contractions’, Bol. Soc. Brasil. Mat. 2 (1971), 55–59.

    Article  MathSciNet  MATH  Google Scholar 

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Hazewinkel, M. (1997). I. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics. Encyclopaedia of Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1288-6_9

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