Skip to main content

Part of the book series: Encyclopaedia of Mathematics ((ENMA))

  • 1075 Accesses

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Daboussi, H., and Indlekofer, K.-H.: ‘Two elementary proofs of Halász’s theorem’, Math. Z. 209 (1992), 43–52.

    MathSciNet  MATH  Google Scholar 

  2. Erdös, P.: ‘Some unsolved problems’, Michigan Math. J. 4 (1957), 291–300.

    MathSciNet  Google Scholar 

  3. Halasz, G.: ‘Über die Mittelwerte multiplikativer zahlentheoretischer Funktionen’, Acta Math. Acad. Sci. Hung. 19 (1968), 365–403.

    MathSciNet  MATH  Google Scholar 

  4. Halasz, G.: ‘On the distribution of additive and the mean values of multiplicative arithmetic functions’, Studia Sci. Math. Hung. 6 (1971), 211–233.

    MathSciNet  Google Scholar 

  5. Halasz, G.: ‘Remarks to my paper ”On the distribution of additive and the mean values of multiplicative arithmetic functions”’, Acta Math. Acad. Sci. Hung. 23 (1972), 425–432.

    MathSciNet  MATH  Google Scholar 

  6. Indlekofer, K.-H.: ‘Remark on a theorem of G. Halász’, Archiv Math. 36 (1981), 145–151.

    MathSciNet  MATH  Google Scholar 

  7. Parson, A., and Tull, J.: ‘Asymptotic behavior of multiplicative functions’, J. Number Th. 10 (1978), 395–420.

    MathSciNet  MATH  Google Scholar 

  8. Tuljaganova, M.I.: ‘A generalization of a theorem of Halász’, Izv. Akad. Nauk UzSSR 4 (1978), 35–40; 95. (In Russian.)

    MathSciNet  Google Scholar 

  9. Wirsing, E.: ‘Das asymptotische Verhalten von Summen über multiplikative Funktionen, II’, Acta Math. Acad. Sci. Hung. 18 (1967), 414–467.

    MathSciNet  Google Scholar 

  10. Bondy, J. A.: ‘Pancyclic graphs: recent results’: Infinite and Finite Sets 1, Vol. 10 of Colloq. Math. Soc. J anos Bolyai, North-Holland, 1975, pp. 181–187.

    MathSciNet  Google Scholar 

  11. Bondy, J.A., and Lovász, L.: ‘Length of cycles in Halin graphs’, J. Graph Th. 8 (1985), 397–410.

    Google Scholar 

  12. Borie, R.B., Parker, R.G., and Tovey, C.A.: ‘Automatic generation of linear-time algorithms from predicate calculus descriptions of problems on recursively constructed graph families’, Algorithmica 7 (1992), 555–581.

    MathSciNet  MATH  Google Scholar 

  13. Halin, R.: ‘Studies on minimally n-connected graphs’, in D.J.A. Welsh (ed.): Combinatorial Mathematics and Its Applications, Acad. Press, 1971, pp. 129–136.

    Google Scholar 

  14. Horton, S.B., Parker, R.G., and Borie, R.B.: ‘On some results pertaining to Halin graphs’, Congressus Numerantium 93 (1992), 65–87.

    MathSciNet  Google Scholar 

  15. Lovász, L., and Plummer, M.D.: ‘On a family of planar bicritical graphs’, Proc. London Math. Soc. 30 (1975), 160–175.

    MathSciNet  MATH  Google Scholar 

  16. Hall, M.: ‘A basis for free Lie rings and higher commutators in free groups’, Proc. Amer. Math. Soc. 1 (1950), 57–581.

    Google Scholar 

  17. Macdonald, I.G.: Symmetric functions and Hall polynomials, second ed., Clarendon Press, 1995.

    MATH  Google Scholar 

  18. Reutenauer, C.: Free Lie algebras, Vol. 7 of London Math. Soc. Monographs New Series, Oxford Univ. Press, 1993.

    Google Scholar 

  19. Bourbaki, N.: Groupes et algèbres de Lie, Vol. II. Algebres de Lie libres, Hermann, 1972.

    MATH  Google Scholar 

  20. Melançon, G.: ‘Combinatorics of Hall trees and Hall words’, J. Combin. Th. 59A, no. 2 (1992), 285–308.

    Google Scholar 

  21. Reutenauer, C.: Free Lie algebras, Vol. 7 of London Math. Soc. Monographs New Series, Oxford Univ. Press, 1993.

    Google Scholar 

  22. Viennot, X.: Algèbres de Lie libres et monoides libres, Vol. 691 of Lecture Notes in Mathematics, Springer, 1978.

    Google Scholar 

  23. Melançon, G.: ‘Combinatorics of Hall trees and Hall words’, J. Combin. Th. 59A, no. 2 (1992), 285–308.

    Google Scholar 

  24. Viennot, X.: Algebres de Lie libres et monoides libres, Vol. 691 of Lecture Notes in Mathematics, Springer, 1978.

    Google Scholar 

  25. Björner, A.: ‘Topological methods’, in R. Graham, M. Grötschel, and L. Lovász (eds.): Handbook of Combinatorics, North-Holland, 1995.

    Google Scholar 

  26. Fadell, E., and Husseini, S.: ‘An ideal-valued cohomological index theory with applications to Borsuk-Ulam and Bourgin-Yang theorems’, Ergod. Th. & Dynam. Sys. 8 (1988), 73–85.

    MathSciNet  Google Scholar 

  27. Ramos, E.: ‘Equipartitions of mass distributions, by hyper-planes’, Discr. and Comp. Geometry.

    Google Scholar 

  28. Steinlein, H.: ‘Borsuk’s antipodal theorem and its generalizations, and applications: a survey’: Topological Methods in Nonlinear Analysis, Vol. 95 of Sérn. Math. Sup., Presses Univ. Montréal, 1985, pp. 166–235.

    Google Scholar 

  29. Živaljevič, R.T.: ‘Topological methods’, in J.E. Goodman and J. O’rourke (eds.): CRC Handbook of Discrete and Combinatorial Geometry.

    Google Scholar 

  30. Živaljevič, R.T.: User’s guide to equivariant methods in combinatorics, Inst. Math. Belgrade, 1996.

    Google Scholar 

  31. Elliott, P.D.T.A.: Probabilistic number theory, Vol. I–II, Springer, 1979–1980.

    MATH  Google Scholar 

  32. Erdös, P.: ‘On the distribution function of additive functions’, Ann. of Math. 47 (1946), 1–20.

    MathSciNet  MATH  Google Scholar 

  33. Galambos, J.: ‘The sequences of prime divisors of integers’, Acta Arith. 31 (1976), 213–218.

    MathSciNet  MATH  Google Scholar 

  34. Hall, R.R., and Tenenbaum, G.: Divisors, Vol. 90 of Tracts in Math., Cambridge Univ. Press, 1988.

    Google Scholar 

  35. Hardy, G.H., and Ramanujan, S.: ‘The normal number of prime factors of a number n, Quart. J. Math. 48 (1917), 76–92.

    MATH  Google Scholar 

  36. Tenenbaum, G.: Introduction to analytic and probabilistic number theory, Cambridge Univ. Press, 1995.

    Google Scholar 

  37. Coifman, R.R., and Weiss, G.: ‘Extensions of Hardy spaces and their use in analysis’, Bull. Amer. Math. Soc. 83 (1977), 569–645.

    MathSciNet  MATH  Google Scholar 

  38. Fefferman, C., and Stein, E.M.: H p spaces of several variables’, Acta Math. 129 (1972), 137–193.

    MathSciNet  MATH  Google Scholar 

  39. Folland, G.B., and Stein, E.M.: Hardy spaces on homogeneous groups, Princeton Univ. Press, 1982.

    MATH  Google Scholar 

  40. Stein, E.M.: Harmonic analysis, Princeton Univ. Press, 1993.

    MATH  Google Scholar 

  41. Brown, T.H., and Chattarji, S.: ‘Hebbian synaptic plasticity: Evolution of the contemporary concept’, in E. Domany, J.L. van Hemmen, and K. Schulten (eds.): Models of neural networks, Vol. II, Springer, 1994, pp. 287–314.

    Google Scholar 

  42. Gerstner, W., Ritz, R., and Hemmen, J.L. van: ‘Why spikes? Hebbian learning and retrieval of time-resolved excitation patterns’, Biol. Cybern. 69 (1993), 503–515,

    MATH  Google Scholar 

  43. See also: W. Gerstner and R. Kempter and J.L. van Hemmen and H. Wagner: A neuronal learning rule for sub-millisecond temporal coding, Nature 383 (1996), 76–78.

    Google Scholar 

  44. Hebb, D.O.: The organization of behavior-A neurophysiological theory, Wiley, 1949.

    Google Scholar 

  45. Herz, A.V.M., Sulzer, B., Kühn, R., and Hemmen, J.L. Van: ‘The Hebb rule: Storing static and dynamic objects in an associative neural network’, Europhys. Lett. 7 (1988), 663–669. (Biol. Cybem. 60 (1989), 457–467.)

    Google Scholar 

  46. Hopfield, J.J.: ‘Neural networks and physical systems with emergent collective computational abilities’, Proc. Nat. Acad. Sci. USA 79 (1982), 2554–2558.

    MathSciNet  Google Scholar 

  47. Palm, G.: Neural assemblies: An alternative approach to artificial intelligence, Springer, 1982.

    Google Scholar 

  48. Sejnowski, T.J.: ‘Statistical constraints on synaptic plasticity’, J. Theor. Biol 69 (1977), 385–389.

    Google Scholar 

  49. Hemmen, J.L. van, Gerstner, W., Herz, A.V.M., Kühn, R., and Vaas, M.: ‘Encoding and decoding of patterns which are correlated in space and time’, in G. Dorffner (ed.): Konnektionismus in artificial Intelligence und Kognitions-forschung, Springer, 1990, pp. 153–162.

    Google Scholar 

  50. Duffus, D., Sands, B., and Woodrow, R.: ‘On the chromatic number of the product of graphs’, J. Graph Th. 9 (1985), 487–495.

    MathSciNet  MATH  Google Scholar 

  51. Duffus, D., and Sauer, N.W.: ‘Lattices arising in catego-rial investigations of Hedetniemi’s conjecture’, Discrete Math. 153 (1996).

    Google Scholar 

  52. El-Zahar, M.H., and Sauer, N.W.: ‘The chromatic number of the product of two 4-chromatic graphs is 4’, Combinatorica 5, no. 2 (1985), 121–126.

    MathSciNet  MATH  Google Scholar 

  53. Haggkvist, R., Hell, P., Miller, D.J., and Lara, V.N.: ‘On multiplicative graphs and the product conjecture’, Combinatorica 8, no. 1 (1988), 63–74.

    MathSciNet  Google Scholar 

  54. Hajnal, A.: ‘The chromatic number of the product of two dichromatic graphs can be countable’, Combinatorica 5 (1985), 137–140.

    MathSciNet  MATH  Google Scholar 

  55. Hedetniemi, S.: ‘Homomorphisms of graphs and automata’, Univ. Michigan Technical Report 03105–44-T (1966).

    Google Scholar 

  56. Hell, P., Zhou, H., and Zhu, X.: ‘Homomorphisms to oriented cycles’, Combinatorica.

    Google Scholar 

  57. Lovász, L.: ‘Operations with structures’, Acta Math. Acad. Sci. Hung. (1967), 321–328.

    Google Scholar 

  58. Miller, D.J.: ‘The categorical product of graphs’, Canad. J. Math. 20 (1968), 1511–1521.

    MathSciNet  MATH  Google Scholar 

  59. Nowakowski, R.J., and Rall, D.: ‘Associative graph products and their independence, domination and coloring numbers’, J. Graph Th. (??).

    Google Scholar 

  60. Poljak, S.: ‘Coloring digraphs by iterated antichains’, Comment. Math. Univ. Carolin. 32, no. 2 (1991), 209–212.

    MathSciNet  MATH  Google Scholar 

  61. Poljak, S., and Rödl, V.: ‘On the arc-chromatic number of a digraph’, JCT B 31 (1981), 190–198.

    MATH  Google Scholar 

  62. Sabidussi, G.: ‘Graph multiplication’, Math. Z. 72 (1960), 446–457.

    MathSciNet  MATH  Google Scholar 

  63. Sauer, N.W., and Zhu, X.: ‘An approach to Hedetniemi’s conjecture’, J. Graph Th. 16, no. 5 (1992), 423–436.

    MathSciNet  MATH  Google Scholar 

  64. Sauer, N.W., and Zhu, X.: ‘Multiplicative posets’, Order 8 (1992), 349–358.

    MathSciNet  MATH  Google Scholar 

  65. Fujii, J.I., Fujii, M., Furuta, T., and Nakamoto, R.: ‘Norm inequalities related to Mcintosh type inequality’, Ni-honkai Math. J. 3 (1992), 67–72.

    MathSciNet  MATH  Google Scholar 

  66. Fujii, J.I., Fujii, M., Furuta, T., and Nakamoto, R.: ‘Norm inequalities equivalent to Heinz inequality’, Proc. Amer. Math. Soc. 118 (1993), 827–830.

    MathSciNet  MATH  Google Scholar 

  67. Heinz, E.: ‘Beiträge zur Störungstheorie der Spektralzerlegung’, Math. Ann. 123 (1951), 415–438.

    MathSciNet  MATH  Google Scholar 

  68. McIntosh, A.: ‘Heinz inequalities and perturbation of spectral families’, Macquarie Math. Reports (1979), unpublished.

    Google Scholar 

  69. Fujii, M., Izumino, S., and Nakamoto, R.: ‘Classes of operators determined by the Heinz-Kato-Furuta inequality and the Hölder-MacCarthy inequality’, Nihonkai Math. J. 5 (1994), 61–67.

    MathSciNet  MATH  Google Scholar 

  70. Furuta, T.: ‘An extension of the Heinz-Kato theorem’, Proc. AMS 120 (1994), 785–787.

    MathSciNet  MATH  Google Scholar 

  71. Fujii, M., and Furuta, T.: ‘Löwner-Heinz, Cordes and Heinz-Kato inequalities’, Math. Japon. 38 (1993), 73–78.

    MathSciNet  MATH  Google Scholar 

  72. Furuta, T.: ‘Norm inequalities equivalent to Löwner-Heinz theorem’, Rev. Math. Phys. 1 (1989), 135–137.

    MathSciNet  MATH  Google Scholar 

  73. Heinz, E.: ‘Beiträge zur Störungstheorie der Spektralzerlegung’, Math. Ann. 123 (1951), 415–438.

    MathSciNet  MATH  Google Scholar 

  74. Kato, T.: ‘Notes on some inequalities for linear operators’, Math. Ann. 125 (1952), 208–212.

    MathSciNet  MATH  Google Scholar 

  75. Henkin, L.: ‘The completeness of the first-order functional calculus’, J. Symb. Logic 14 (1949), 159–166.

    MathSciNet  MATH  Google Scholar 

  76. Keisler, H.J.: ‘A survey of ultraproducts, logic’, in Y. Bar-Hillel (ed.): Logic, Methodology and Philosophy of Science, North-Holland, 1965, pp. 112–126.

    Google Scholar 

  77. Weaver, G.: Henkin-Keisler models, Kluwer Acad. Publ., 1997.

    MATH  Google Scholar 

  78. Kuhlmann, F.-V.: Valuation theory of fields, abelian groups and modules, Algebra, Logic and Applications. Gordon & Breach, forthcoming.

    Google Scholar 

  79. Pop, F.: ‘On Grothendieck’s conjecture of birational anabelian geometry’, Ann. of Math. 138 (1994), 145–182.

    Google Scholar 

  80. Prestel, A., and Ziegler, M.: ‘Model theoretic methods in the theory of topological fields’, J. Reine Angew. Math. 299/300 (1978), 318–341.

    MathSciNet  Google Scholar 

  81. Ribenboim, P.: ‘Equivalent forms of Hensel’s lemma’, Expo. Math. 3 (1985), 3–24.

    MathSciNet  MATH  Google Scholar 

  82. Warner, S.: Topological fields, Vol. 157 of Mathematics Studies, North-Holland, 1989.

    Google Scholar 

  83. Ax, J.: ‘A metamathematical approach to some problems in number theory, Appendix’: Vol. 20 of Proc. Symp. Pure Math., Amer. Math. Soc., 1971, pp. 161–190.

    MathSciNet  Google Scholar 

  84. Ribenboim, P.: Théorie des valuations, Presses Univ. Montréal, 1964.

    Google Scholar 

  85. Schep, A.R.: ‘Compactness properties of Carleman and Hille-Tamarkin operators’, Canad. J. Math. 37 (1985), 921–933.

    MathSciNet  MATH  Google Scholar 

  86. Zaanen, A.C.: Riesz spaces, Vol. II, North-Holland, 1983.

    MATH  Google Scholar 

  87. Choquet, G.: ‘Convergences’, Ann. Univ. Grenoble 23 (1948), 55–112.

    MathSciNet  Google Scholar 

  88. Hausdorff, F.: Grundzüge der Mengenlehre, Leipzig, 1914.

    MATH  Google Scholar 

  89. Kuratowski, K.: Topology, Acad. Press & PWN, 1966–1968.

    Google Scholar 

  90. Matheron, G.: Random sets and integral geometry, Wiley, 1975.

    MATH  Google Scholar 

  91. Michael, E.: ‘Topologies on spaces of subsets’, Trans. Amer. Math. Soc. 71 (1951), 152–183.

    MathSciNet  MATH  Google Scholar 

  92. Polkowski, L.: ‘Mathematical morphology of rough sets’, Bull. Polish Acad. Math. 41 (1993), 241–273.

    MathSciNet  MATH  Google Scholar 

  93. Serra, J.: Image analysis and mathematical morphology, Acad. Press, 1982.

    MATH  Google Scholar 

  94. Skowron, A., and Polkowski, L.: ‘Analytical morphology’, Fundam. Inform. 26–27 (1996), 255–271.

    MathSciNet  Google Scholar 

  95. Vietoris, L.: ‘Stetige Mengen’, Monatsh. Math, und Phys. 31 (1921), 173–204.

    MathSciNet  MATH  Google Scholar 

  96. Hodgkin, A.L., and Huxley, A. F.: ‘A quantitative description of membrane current and its application to conduction and excitation in nerve’, J. Physiology 117 (1952), 500–544.

    Google Scholar 

  97. Rinzel, J.: ‘Electrical excitability of cells, theory and experiment: review of the Hodgkin-Huxley foundation and an update’, Bull. Math. Biology 52 (1990), 5–23.

    Google Scholar 

  98. Denker, M.: Asymptotic distribution theory in nonparametric statistics, Advanced Lectures in Mathematics. F. Vieweg, 1985.

    MATH  Google Scholar 

  99. Hoeffding, W.: ‘A class of statistics with asymptotically normal distribution’, Ann. Math. Stat. 19 (1948), 293–325.

    MathSciNet  MATH  Google Scholar 

  100. Lee, A.J.: U-statistics. Theory and practice, Vol. 110 of Statistics textbooks and monographs, M. Dekker, 1990.

    Google Scholar 

  101. Lehmann, E.L.: ‘Consistency and unbiasedness of certain nonparametric tests’, Ann. Math. Stat. 22 (1951), 165–179.

    MathSciNet  MATH  Google Scholar 

  102. Ahlswede, R., and Daykin, D.E.: ‘An inequality for the weights of two families, their unions and intersections’, Z. Wahrsch. verw. Gebiete 43 (1978), 183–185.

    MathSciNet  MATH  Google Scholar 

  103. Fishburn, P.C.: ‘Correlation in partially ordered sets’, Discrete Appl. Math. 39 (1992), 173–191.

    MathSciNet  MATH  Google Scholar 

  104. Fortuin, C.M., Kasteleyn, P.N., and Ginibre, J.: ‘Correlation inequalities for some partially ordered sets’, Comm. Math. Phys. 22 (1971), 89–103.

    MathSciNet  MATH  Google Scholar 

  105. Holley, R.: ‘Remarks on the FKG inequalities’, Comm. Math. Phys. 36 (1974), 227–231.

    MathSciNet  Google Scholar 

  106. Andronov, A.A., Leontovich, E.A., Gordon, I.I., and Maier, A.G.: Theory of bifurcations of dynamical systems on a plane, Israel Program of Scientific Translations, 1971. (Translated from the Russian.)

    Google Scholar 

  107. Arnol’d, V.I., Afraimovich, V.S., Il’yashenko, Yu.S., and Shil’nikov, L.P.: ‘Bifurcation theory’, Dynamical Systems V, in V.I. Arnol’d (ed.), Encycl. Math. Sci. Springer, 1994. (Translated from the Russian.)

    Google Scholar 

  108. Gavrilov, N.K., and Shilnikov, L.P.: ‘On threedimensional systems close to systems with a structurally unstable homoclinic curve: I’, Mat. USSR-Sb. 17 (1972), 467–485. (In Russian.)

    Google Scholar 

  109. Gavrilov, N.K., and Shilnikov, L.P.: ‘On threedimensional systems close to systems with a structurally unstable homoclinic curve: II’, Mat. USSR-Sb. 19 (1973), 139–156. (In Russian.)

    Google Scholar 

  110. Kuznetsov, Yu.A.: Elements of applied bifurcation theory, Springer, 1995.

    MATH  Google Scholar 

  111. Moser, J.: Stable and random motions in dynamical systems, Princeton Univ. Press, 1973.

    MATH  Google Scholar 

  112. Neimark, Yu.I.: ‘On motions close to a bi-asymptotic motion’, Dokl. AKad. Nauk SSSR 142 (1967), 1021–1024. (In Russian.)

    MathSciNet  Google Scholar 

  113. Nitecki, Z.: Differentiable dynamics, MIT, 1971.

    MATH  Google Scholar 

  114. Shil’nikov, L.P.: ‘On the generation of a periodic motion from a trajectory which leaves and re-enters a saddle-saddle state of equilibrium’, Soviet Math. Dokl. 7 (1966), 1155–1158. (Translated from the Russian.)

    MATH  Google Scholar 

  115. Shil’nikov, L.P.: ‘On a Poincaré-Birkhoff problem’, Mat. USSR Sb. 3 (1967), 353–371. (In Russian.)

    Google Scholar 

  116. Shil’nikov, L.P.: ‘On the generation of periodic motion from trajectories doubly asymptotic to an equilibrium state of saddle type’, Mat. USSR-Sb. 6 (1968), 427–437. (In Russian.)

    Google Scholar 

  117. Shil’nikov, L.P.: ‘On a new type of bifurcation of multidimensional dynamical systems’, Soviet Math. Dokl. 10 (1969), 1368–1371. (Translated from the Russian.)

    MATH  Google Scholar 

  118. Shil’nikov, L.P.: ‘A contribution to the problem of the structure of an extended neighborhood of a rough equilibrium state of saddle-focus type’, Mat. USSR-Sb. 10 (1970), 91–102. (In Russian.)

    MATH  Google Scholar 

  119. Smale, S.: ‘Differentiable dynamical systems’, Bull. Amer. Math. Soc. 73 (1967), 747–817.

    MathSciNet  MATH  Google Scholar 

  120. Wiggins, S.: Global bifurcations and chaos, Springer, 1988.

    MATH  Google Scholar 

  121. Wiggins, S.: Introduction to applied non-linear dynamical systems and chaos, Springer, 1990.

    Google Scholar 

  122. Hopf, E.: Ergodentheorie, Springer, 1937.

    Google Scholar 

  123. Hopf, E.: ‘Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krummung’, Ber. Verh. Sachs. Akad. Wiss. Leipzig 91 (1939), 261–304.

    MathSciNet  Google Scholar 

  124. Hopf, E.: ‘Ergodic theory and the geodesic flow on surfaces of constant negative curvature’, Bull. Amer. Math. Soc. 77 (1971), 863–877.

    MathSciNet  MATH  Google Scholar 

  125. Kaimanovich, V.A.: ‘Ergodicity of harmonic invariant measures for the geodesic flow on hyperbolic spaces’, J. Reine Angew. Math. 455 (1994), 57–103.

    MathSciNet  MATH  Google Scholar 

  126. Krengel, U.: ‘Darstellungsätze für Strömungen und Halbströmungen I’, Math. Ann. 176 (1968), 181–190.

    MathSciNet  MATH  Google Scholar 

  127. Krengel, U.: ‘Darstellungsätze für Strömungen und Halbströmungen II’, Math. Ann. 182 (1969), 1–39.

    MathSciNet  MATH  Google Scholar 

  128. Krengel, U.: Ergodic theorems, de Gruyter, 1985.

    MATH  Google Scholar 

  129. Andronov, A.A., Leontovich, E.A., Gordon, LI., and Maier, A.G.: Theory of bifurcations of dynamical systems on a plane, Israel Program of Scientific Translations, 1971. (Translated from the Russian.)

    Google Scholar 

  130. Arnol’d, V.I.: Geometrical methods in the theory of ordinary differential equations, Vol. 250 of Grundlehren der mathematischen Wissenschaften, Springer, 1983. (Translated from the Russian.)

    Google Scholar 

  131. Guckenheimer, J., and Holmes, Ph.: Nonlinear oscillations, dynamical systems and bifurcations of vector fields, Springer, 1983.

    Google Scholar 

  132. Iooss, G.: Bifurcations of maps and applications, North-Holland, 1979.

    Google Scholar 

  133. Kelley, A.: ‘The stable, center stable, center, center unstable and unstable manifolds’, J. Differential Equations 3 (1967), 546–570.

    MathSciNet  MATH  Google Scholar 

  134. Kuznetsov, Yu.A.: Elements of applied bifurcation theory, Springer, 1995.

    MATH  Google Scholar 

  135. Marsden, J., and McCracken, M.: Hopf bifurcation and its applications, Springer, 1976.

    MATH  Google Scholar 

  136. Whitley, D.C.: ‘Discrete dynamical systems in dimensions one and two’, Bull. London Math. Soc. 15 (1983), 177–217.

    MathSciNet  MATH  Google Scholar 

  137. Boyer, C.P.: ‘Conformai duality and compact complex surfaces’, Math. Ann. 274 (1986), 517–526.

    MathSciNet  MATH  Google Scholar 

  138. Dragomir, S., and Ornea, L.: Locally conformai Kähler geometry, Birkhäuser, 1997.

    Google Scholar 

  139. Gauduchon, P.: ‘Structures de Weyl-Einstein, espaces de twisteurs et variétés de type S 1 × S3’, J. Reine Angew. Math. 455 (1995), 1–50.

    MathSciNet  Google Scholar 

  140. Ornea, L., and Piccinni, P.: ‘Locally conformai Kähler structures in quaternionic geometry’, Trans. Amer. Math. Soc. 349 (1997), 641–655.

    MathSciNet  MATH  Google Scholar 

  141. Pontecorvo, M.: ‘Uniformization of conformally flat Hermitian surfaces’, Diff. Geom. Appl. 3 (1992), 295–305.

    MathSciNet  Google Scholar 

  142. Vaisman, I.: ‘Generalized Hopf manifolds’, Geom. Dedicata 13 (1982), 231–255.

    MathSciNet  MATH  Google Scholar 

  143. Vaisman, I., and Reischer, C.: ‘Local similarity manifolds’, Ann. Mat. Pura Appl. 35 (1983), 279–292.

    MathSciNet  Google Scholar 

  144. Greither, C.: ‘Extensions of finite group schemes, and Hopf Galois theory over a complete discrete valuation ring’, Math. Zeit. 210 (1992), 37–67.

    MathSciNet  MATH  Google Scholar 

  145. Larson, R.G.: ‘Hopf algebra orders determined by group valuations’, J. Algebra 38 (1976).

    Google Scholar 

  146. Tate, J., and Oort, F.: ‘Group schemes of prime order’, Ann. Sci. Ecol. Norm. Super. (4) 3 (1970).

    Google Scholar 

  147. Underwood, R.G.: ‘R-Hopf algebra orders in KC p 2’, J. Algebra 169 (1994).

    Google Scholar 

  148. Underwood, R.G.: ‘The valuative condition and R-Hopf algebra orders in KC p 3’, Amer. J. Math. (4) 118 (1996), 701–743.

    MathSciNet  MATH  Google Scholar 

  149. Childs, L.: ‘Taming wild extensions with Hopf algebras’, Trans. Amer. Math. Soc. 304 (1987).

    Google Scholar 

  150. Greither, C.: ‘Extensions of finite group schemes, and Hopf Galois theory over a complete discrete valuation ring’, Math. Zeit. 210 (1992), 37–67.

    MathSciNet  MATH  Google Scholar 

  151. Sekiguchi, T., and Suwa, N.: ‘Théories de Kummer-Artin-Schreier-Witt’, C.R. Acad. Sci. Ser. I 319 (1994), 1–21.

    MathSciNet  Google Scholar 

  152. Underwood, R.G.: ‘The group of Galois extensions in KC p 2’ , Trans. Amer. Math. Soc. 349 (1997), 1503–1514.

    MathSciNet  MATH  Google Scholar 

  153. Eccles, P.J., Turner, P.R., and Wilson, W.S.: ‘On the Hopf ring for the sphere’, Math. Zeitschrift (to appear).

    Google Scholar 

  154. Hopkins, M.J., and Hunton, J.R.: ‘The structure of spaces representing a Landweber exact cohomology theory’, Topology (to appear).

    Google Scholar 

  155. Hunton, J.R., and Ray, N.: ‘A rational approach to Hopf rings’, J. Pure and Applied Algebra (to appear).

    Google Scholar 

  156. Kashiwabara, T.: ‘Hopf rings and unstable operations’, J. Pure and Applied Algebra 194 (1994), 183–193.

    MathSciNet  Google Scholar 

  157. Kashiwabara, T., Strickland, N.P., and Turner, P.R.: ‘Morava K-theory Hopf ring for BP’, in C. Broto et al. (eds.): Algebraic Topology: New Trends in Localization and Periodicity, Vol. 139 of Progress in Mathematics, Birkhauser, 1996, pp. 209–222.

    Google Scholar 

  158. Kramer, R.: ‘The periodic Hopf ring of connective Morava K-theory’, PhD thesis, Johns Hopkins Univ. (1990).

    Google Scholar 

  159. Li, Y.: ‘On the Hopf ring for the sphere’, PhD thesis, Johns Hopkins Univ. (1996).

    Google Scholar 

  160. Ravenel, D.C., and Wilson, W.S.: ‘The Hopf ring for complex cobordism’, J. Pure and Applied Algebra 9 (1977), 241–280.

    MathSciNet  MATH  Google Scholar 

  161. Ravenel, D.C., and Wilson, W.S.: ‘The Morava K-theories of Eilenberg-Mac Lane spaces and the Conner-Floyd conjecture’, Amer. J. Math. 102 (1980), 691–748.

    MathSciNet  MATH  Google Scholar 

  162. Ravenel, D.C., and Wilson, W.S.: ‘The Hopf ring for P(n)’ Canadian J. Math. (to appear).

    Google Scholar 

  163. Strickland, N.: ‘Bott periodicity and Hopf rings’, PhD thesis, Univ. Manchester (1992).

    Google Scholar 

  164. Turner, P.R.: ‘Dickson coinvariants and the homology of H * QS 0,, Math. Zeitschrift (to appear).

    Google Scholar 

  165. Wilson, W.S.: Brown-Peters on homology: an introduction and sampler, Vol. 48 of CBMS, Amer. Math. Soc., 1982.

    Google Scholar 

  166. Wilson, W.S.: ‘The Hopf ring for Morava K-theory’, Publ. RIMS Kyoto Univ. 20 (1984), 1025–1036.

    MATH  Google Scholar 

  167. Ahlfors, L.V., and Sario, L.: Riemann surfaces, Princeton Univ. Press, 1960.

    MATH  Google Scholar 

  168. Hopf, E.: ‘Statistik der geodätischen Linien in Mannigfaltigkeiten negativer Krummung’, Ber. Verh. Sachs. Akad. Wiss. Leipzig 91 (1939), 261–304.

    MathSciNet  Google Scholar 

  169. Hopf, E.: ‘Ergodic theory and the geodesic flow on surfaces of constant negative curvature’, Bull. Amer. Math. Soc. 77 (1971), 863–877.

    MathSciNet  MATH  Google Scholar 

  170. Kaimanovich, V.A.: ‘Ergodicity of harmonic invariant measures for the geodesic flow on hyperbolic spaces’, J. Reine Angew. Math. 455 (1994), 57–103.

    MathSciNet  MATH  Google Scholar 

  171. Lyons, T., and Sullivan, D.: ‘Function theory, random paths and covering spaces’, J. Diff. Geom. 19 (1984), 299–323.

    MathSciNet  MATH  Google Scholar 

  172. Nicholls, P.J.: Ergodic theory of discrete groups, Cambridge Univ. Press, 1989.

    MATH  Google Scholar 

  173. Sullivan, D.: ‘The density at infinity of a discrete group of hyperbolic motions’, IHES Publ. Math. 50 (1979), 171–202.

    MATH  Google Scholar 

  174. Sullivan, D.: ‘On the ergodic theory at infinity of an arbitrary discrete group of hyperbolic motions’, Ann. Math. Studies 97 (1980), 465–496.

    Google Scholar 

  175. Tsuji, M.: Potential theory in modern function theory, Maruzen, 1959.

    MATH  Google Scholar 

  176. Yue, C.B.: ‘The ergodic theory of discrete isometry groups on manifolds of variable negative curvature’, Trans. Amer. Math. Soc. 348 (1996), 4965–5005.

    MathSciNet  MATH  Google Scholar 

  177. Ballard, D.H.: ‘Generalizing the Hough transform to detect arbitrary shapes’, Pattern Recognition 13 (1981), 111–122.

    MATH  Google Scholar 

  178. Bässmann, H., and Besslich, PH.W.: Konturorientierte Verfahren in der digitalen Bildverarbeitung, Springer, 1989.

    MATH  Google Scholar 

  179. Rosenfeld, A., and Kak, A.C.: Digital picture processing, Vol. 2, Acad. Press, 1982.

    Google Scholar 

  180. Anderson, B.A., Schellenberg, P.J., and Stinson, D.R.: ‘The existence of Howell designs of even side’, J. Combin. Th. A 36 (1984), 23–55.

    MathSciNet  MATH  Google Scholar 

  181. Dinitz, J.H.: ‘Howell designs’, in C.J. Colbourn and J.H. Dinitz (eds.): CRC Handbook of Combinatorial Designs, CRC Press, 1996, pp. 381–385.

    Google Scholar 

  182. Dinitz, J.H., and Stinson, D.R.: ‘Room squares and related designs’, in J.H. Dinitz and D.R. Stinson (eds.): Contemporary Design Theory: A Collection of Surveys, Wiley, 1992, pp. 137–204.

    Google Scholar 

  183. Lamken, E.R., and Vanstone, S.A.: ‘The existence of skew Howell designs of side 2n and order 2n + 2’, J. Combin. Th. A 54 (1990), 20–40.

    MathSciNet  MATH  Google Scholar 

  184. Stinson, D.R.: ‘The existence of Howell designs of odd side’, J. Combin. Th. A 32 (1982), 53–65.

    MathSciNet  MATH  Google Scholar 

  185. Gallager, R.: ‘Variations on a theme by Huffman’, IEEE Trans. Inform. Theory IT-24 (1978), 668–674.

    MathSciNet  MATH  Google Scholar 

  186. Huffman, D.A.: ‘A method for the construction of minimum redundancy codes’, Proc. I.R.E. 40 (1952), 1098–1101.

    Google Scholar 

  187. Lelewer, D.A., and Hirschberg, D.S.: ‘Data compression’, ACM Comput. Surv. 19 (1987), 261–296.

    MATH  Google Scholar 

  188. Longo, G., and Galasso, G.: ‘An application of informational divergence to Huffman codes’, IEEE Trans. Inform. Theory IT-28 (1982), 36–43.

    Google Scholar 

  189. Berezin, A.A., Phys. Status. Solidi (b) 50 (1972), 71.

    Google Scholar 

  190. Berezin, A.A., Phys. Rev. B 33 (1986), 2122.

    Google Scholar 

  191. Hulthen, L., Ark. Mat. Astron. Fys 28A (1942), 5,

    MathSciNet  Google Scholar 

  192. Hulthen, L., Ark. Mat. Astron. Fys: 29B, 1.

    Google Scholar 

  193. Hulthen, L., and Sugawara, M., in S. Flugge (ed.): Handbuch der Physik, Springer, 1957.

    Google Scholar 

  194. Lai, C.S., and Lin, W.C., Phys. Lett. A 78 (1980), 335.

    Google Scholar 

  195. Lam, C.S., and Varshni, Y.P., Phys. Rev. A 4 (1971), 1875.

    Google Scholar 

  196. Patil, S.H., J. Phys. A 17 (1984), 575.

    Google Scholar 

  197. Popov, V.S., and Wienbe rg, V.M., Phys. Lett. A 107 (1985), 371.

    Google Scholar 

  198. Pyykko, P., and Jokisaari, J., Chem. Phys. 10 (1975), 293.

    Google Scholar 

  199. Roy, B., and Roychoudhury, R., J. Phys. A 20 (1987), 3051.

    Google Scholar 

  200. Roy, B., and Roychoudhury, R., J. Phys. A 23 (1990), 5095.

    MathSciNet  MATH  Google Scholar 

  201. Tietz, T., J. Chem. Phys. 35 (1961), 1917.

    Google Scholar 

  202. Baragar, A.: ‘Asymptotic growth of Markoff-Hurwitz numbers’, Compositio Math. 94 (1994), 1–18.

    MathSciNet  MATH  Google Scholar 

  203. Baragar, A.: ‘Integral solutions of Markoff-Hurwitz equations’, J. Number Th. 49, no. 1 (1994), 27–44.

    MathSciNet  MATH  Google Scholar 

  204. Herzberg, N.P.: ‘On a problem of Hurwitz’, Pacific J. Math. 50 (1974), 485–493.

    MathSciNet  MATH  Google Scholar 

  205. Hurwitz, A.: ‘Über eine Aufgabe der unbestimmten Analysis’, Archiv. Math. Phys. 3 (1907), 185–196,

    Google Scholar 

  206. Hurwitz, A.: Mathematisch Werke, Vol. 2, Chapt. LXX (1933 and 1962), 410–421.

    Google Scholar 

  207. Markoff, A.A.: ‘Sur les formes binaires indéfinies’, Math. Ann. 17 (1880), 379–399.

    MathSciNet  MATH  Google Scholar 

  208. Mordell, L.J.: ‘On the integer solutions of the equation x 2 + y 2 + z 2 + 2xyz = n’, J. London Math. Soc. 28 (1953), 500–510.

    MathSciNet  MATH  Google Scholar 

  209. Rosenberger, G.: ‘Über die Diophantische Gleichung ax 2 + by 2 + cz 2 = dxyz’, J. Reine Angew. Math. 305 (1979), 122–125.

    MathSciNet  MATH  Google Scholar 

  210. Wang, L.: ‘Rational points and canonical heights on K3-surfaces in P 1 × P 1 × P 1’, Contemporary Math. 186 (1995), 273–289.

    Google Scholar 

  211. Zagier, D.: ‘On the number of Markoff numbers below a given bound’, Math. Comp. 39 (1982), 709–723.

    MathSciNet  MATH  Google Scholar 

  212. Dickson, L.E.: ‘On quaternions and their generalization and the history of the eight square theorem’, Ann. of Math. 20 (1919), 155.

    Google Scholar 

  213. Fock, V.: ‘Zur Theorie des Wasserstoffatoms’, Z. Phys. 98 (1935), 145.

    MATH  Google Scholar 

  214. Hopf, H.: ‘Über die Abbildungen der dreidimensionalen Sphäre auf die Kugelfläche’, Math. Ann. 104 (1931), 637.

    MathSciNet  Google Scholar 

  215. Hurwitz, A.: ‘Über die Komposition der quadratischen Formen von beliebig vielen Variablen’, Nachrichten K. Gesellschaft Wissenschaft. Göttingen (1898), 309.

    Google Scholar 

  216. Kibler, M., and Labastie, P.: ‘Transformations generalizing the Levi-Civita, Kustaanheimo-Stiefel and Fock transformations’, in Y. Saint-Aubin and L. Vinet (eds.): Group Theoretical Methods in Physics, World Sci., 1989.

    Google Scholar 

  217. Kibler, M., and Winternitz, P.: ‘Lie algebras under constraints and non-bijective transformations’, J. Phys. A: Math. Gen. 21 (1988), 1787.

    MathSciNet  MATH  Google Scholar 

  218. Kustaanheimo, P., and Stiefel, E.: ‘Perturbation theory of Kepler motion based on spinor regularization’, J. Reine Angew. Math. 218 (1965), 204.

    MathSciNet  MATH  Google Scholar 

  219. Lambert, D., and Kibler, M.: ‘An algebraic and geometric approach to non-bijective quadratic transformations’, J. Phys. A: Math. Gen. 21 (1988), 307.

    MathSciNet  MATH  Google Scholar 

  220. Levi-Civita, T.: ‘Sur la régularisation du problème des trois corps’, Acta Math. 42 (1918), 99.

    MathSciNet  Google Scholar 

  221. Polubarinov, I.V.: On the application of Hopf fiber bundles in quantum theory, Report E2–84–607. JINR: Dubna (Russia), 1984.

    Google Scholar 

  222. Wene, G.P.: ‘A construction relating Clifford algebras and Cayley-Dickson algebras’, J. Math. Phys. 25 (1984), 2351.

    Google Scholar 

  223. Hale, J.: Theory of functional differential equations, second ed., Springer, 1977.

    MATH  Google Scholar 

  224. Hutchinson, G.: ‘Circular causal systems in ecology’, Ann. N.Y. Acad. Sci. 50 (1948–1950), 221–246.

    Google Scholar 

  225. Kolesov, A.Yu., and Kolesov, Yu.S.: ‘Relaxation oscillation in mathematical models of ecology’, Proc. Steklov Inst. Math. 199, no. 1 (1995). (Translated from the Russian.)

    Google Scholar 

  226. Coornaert, M., Delzant, T., and Papadopoulos, A.: Géométrie et théorie des groupes: les groupes hyperboliques de Gromov, Vol. 1441 of Lecture Notes in Mathematics, Springer, 1991.

    Google Scholar 

  227. Epstein, D.B.A., Cannon, J.W.W., Holt, D.F., Levy, S.V.F., Paterson, M.S., and Thurston, W.P.: Word processing in groups, Bartlett and Jones, 1992.

    MATH  Google Scholar 

  228. Ghys, E., and Harpe, P. de la (eds.): Sur les groupes hyperboliques d’après Mikhael Gromov, Vol. 83 of Progress in Maths., Birkhäuser, 1990.

    Google Scholar 

  229. Gromov, M.: ‘Hyperbolic groups’, in S.M. Gersten (ed.): Essays in Group Theory, Vol. 8 of MSRI Publ., Springer, 1987, pp. 75–263.

    Google Scholar 

  230. Bakry, D.: ‘L’hypercontractivité et son utilisation en théorie des semi-groups’, in P. Bernard (ed.): Lectures on Probability Theory, Vol. 1581 of Lecture Notes in Mathematics, Springer, 1994, pp. 1–114.

    Google Scholar 

  231. Beckner, W.: ‘Inequalities in Fourier analysis’, Ann. of Math. 102 (1975), 159–182.

    MathSciNet  MATH  Google Scholar 

  232. Bonami, A.: ‘Études des coefficients de Fourier des fonctions de L 2(G)’, Ann. Inst. Fourier 20, no. 2 (1970), 335–402.

    MathSciNet  MATH  Google Scholar 

  233. Davies, E.B.: Heat kernels and spectral theory, Cambridge Univ. Press, 1989.

    MATH  Google Scholar 

  234. Deuschel, J. D., and Stroock, D. W.: Large deviations, Vol. 137 of Pure Appl. Math., Acad. Press, 1989.

    Google Scholar 

  235. Diaconis, P., and Saloff-Coste, L.: ‘Logarithmic Sobolev inequalities for finite Markov chains’, Ann. Appl. Prob. (1996).

    Google Scholar 

  236. Gross, L.: ‘Logarithmic Sobolev inequalities’, Amer. J. of Math. 97 (1975), 1061–1083.

    Google Scholar 

  237. Gross, L.: ‘Logarithmic Sobolev inequalities and contractivity properties of semigroups’, in G. Dell’antonio and U. Mosco (eds.): Dirichlet Forms, Vol. 1563 of Lecture Notes in Mathematics, Springer, 1993, pp. 54–88.

    Google Scholar 

  238. Nelson, E.: ‘A quartic interaction in two dimensions’, in R. Goodman and I.E. Segal (eds.): Mathematical Theory of Elementary Particles, MIT Press, 1966, pp. 69–73.

    Google Scholar 

  239. Stroock, D.: ‘Logarithmic Sobolev inequalities for Gibbs states’, in G. Dell’Antonio and U. Mosco (eds.): Dirichlet Forms, Vol. 1563 of Lecture Notes in Mathematics, Springer, 1993, pp. 194–228.

    Google Scholar 

  240. Berezanskiǐ, Yu.: ‘Hypercomplex systems with a discrete basis’, Dokl. Akad. Nauk SSSR (N.S.) 81 (1954), 825–828. (In Russian.)

    Google Scholar 

  241. Bloom, W.R., and Heyer, H.: Harmonic analysis of probability measures on hypergroups, Vol. 20 of Studies in Mathematics, W. de Gruyter, 1995.

    Google Scholar 

  242. Chilana, A., and Ross, K.: ‘Spectral synthesis in hyper-groups’, Pacific J. Math. 76 (1978), 313–328.

    MathSciNet  MATH  Google Scholar 

  243. Delsarte, J.: ‘Hypergroupes et opérateurs de permutation et de transmutation’: La théorie des équations aux dérivées partielles (Nancy, 9–15 avril 1956), Vol. 71 of Colloque CNRS, CNRS, 1956, pp. 29–45.

    Google Scholar 

  244. Dixmier, J.: ‘Opérateurs de rang fini dans les représentation unitaires’, IHES Publ. Math. (1960), 305–317.

    Google Scholar 

  245. Floris, P.: ‘On quantum groups, hypergroups and q-special functions’, Ph.D. Thesis RU Leiden (1995).

    Google Scholar 

  246. Gebuhrer, M.O.: ‘Analyse harmonique sur les espaces de Gel’fand-Levitan et applications à la théorie des semigroupes de convolution’, Thœse de doctorat d’etat Univ. Louis Pasteur, Strasbourg (1989).

    Google Scholar 

  247. Gebuhrer, M.O.: ‘Remarks on amenability of discrete hypergroups’, in M.A. Picardello (ed.): Harmonic Analysis and Discrete Potential Theory, Plenum, 1992, pp. 479–482.

    Google Scholar 

  248. Gebuhrer, M.O.: About the fine structure of compact commutative hypergroups, Preprint. IRMA, Strasbourg, 1996.

    Google Scholar 

  249. Gebuhrer, M.O.: ‘The Haar measure on a locally compact hypergroup’, in Pr. Komrakov and Pr. Litvinov (eds.): Proc. Conf. Differential Geometry on Homogeneous Spaces and Harmonic Analysis on Lie Groups (Moscow, 1994), Kluwer Acad. Publ., 1996.

    Google Scholar 

  250. Gebuhrer, M.O., and Kumar, A.: ‘The Wiener property for a class of discrete hypergroups’, Math. Z. 202 (1989), 271–274.

    MathSciNet  MATH  Google Scholar 

  251. Gebuhrer, M.O., and Schwartz, A.L.: ‘Sidon sets and Riesz sets on the disk algebra’, Colloq. Math. (1996).

    Google Scholar 

  252. Jewett, R.I.: ‘Spaces with an abstract convolution of measures’, Adv. in Math. 18 (1975), 1–101.

    MathSciNet  MATH  Google Scholar 

  253. Levitan, B., and Povzner, A.: ‘Differential equations of the Sturm-Liouville type on the semi-axis and Plancherel’s theorem’, Dokl. Akad. Nauk SSSR (N.S.) 52 (1946), 479–482. (In Russian.)

    Google Scholar 

  254. Spector, R.: ‘Mesures invariantes sur les hypergroupes’, Trans. Amer. Math. Soc. 239 (1978), 147–165.

    MathSciNet  MATH  Google Scholar 

  255. Vrem, R.: ‘Lacunarity on compact hypergroups’, Math. Z. 164 (1968), 13–104.

    MathSciNet  Google Scholar 

  256. Vrem, R.: ‘Harmonic analysis on compact hypergroups’, Pacif. J. Math. 85 (1979), 239–251.

    MathSciNet  Google Scholar 

  257. Woess, W., and Kaimanovitch, V.: Construction of discrete non-unimodular hypergroups, No. 9 in Preprint Quaderno. Univ. Milano, 1995.

    Google Scholar 

  258. Krasnosel’skiǐ, M.A., and Pokrovskiǐ, A.V.: Systems with hysteresis, Springer, 1989. (Translated from the Russian.)

    Google Scholar 

  259. Mayergoyz, I.D.: Mathematical models of hysteresis, Springer, 1991.

    MATH  Google Scholar 

  260. Visintin, A.: Differential models of hysteresis, Vol. 111 of Applied Math. Sci., Springer, 1994.

    Google Scholar 

  261. Krasnosel’skiǐ, M.A., and Pokrovskiǐ, A.V.: Systems with hysteresis, Springer, 1989. (Translated from the Russian.)

    Google Scholar 

Download references

Authors

Editor information

M. Hazewinkel

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Kluwer Academic Publishers

About this chapter

Cite this chapter

Hazewinkel, M. (1997). H. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics. Encyclopaedia of Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1288-6_8

Download citation

  • DOI: https://doi.org/10.1007/978-94-015-1288-6_8

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4896-7

  • Online ISBN: 978-94-015-1288-6

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics