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References

  1. Barbu, V.: Nonlinear semigroups and differential equations in Banach spaces, Noordhoff, 1975.

    Google Scholar 

  2. Browder, F.E.: Nonlinear operators and nonlinear equations of evolution in Banach spaces, Vol. 18: 2 of Proc. Symp. Pure Math., Amer. Math. Soc., 1976.

    Google Scholar 

  3. Cloranescu, I.: Geometry of Banach spaces, duality mappings and nonlinear problems, Kluwer Acad. Publ., 1990.

    Google Scholar 

  4. Crandall, M.G., and Liggett, T.: ‘Generation of semigroups of nonlinear transformations in general Banach spaces’, Amer. J. Math. 93 (1971), 265–298.

    MathSciNet  MATH  Google Scholar 

  5. Crandall, M.G., and Pazy, A.: ‘Nonlinear evolution equations in Banach spaces’, Israel J. Math. 11 (1972), 57–94.

    MathSciNet  MATH  Google Scholar 

  6. Deimling, K.: Nonlinear functional analysis, Springer, 1985.

    MATH  Google Scholar 

  7. Kartsatos, A.G.: ‘Recent results involving compact perturbations and compact resolvents of accretive operators in Banach spaces’: Proc. World Congress Nonlinear Analysts, Tampa, Florida (1992), Vol. III, W. de Gruyter, 1995, pp. 2197–2222.

    Google Scholar 

  8. Kato, T.: ‘Nonlinear semigroups and evolution equations’, J. Math. Soc. Japan 19 (1967), 508–520.

    MathSciNet  MATH  Google Scholar 

  9. Ruess, W.: ‘Existence of solutions to partial functional differential equations with delay’, in A.G. Kartsatos (ed.): Theory and Applications of Nonlinear Operators of Accretive and Monotone Type, M. Dekker, 1996, pp. 259–288.

    Google Scholar 

  10. Hampel, F.R., Ronchetti, E.M., Rousseeuw, P.J., and Stahel, W.A.: Robust statistics: The approach based on influence functions, Wiley, 1986.

    MATH  Google Scholar 

  11. Huber, P.J.: ‘Robust estimation of a location parameter’, Ann. Math. Stat. 35 (1964), 73–101.

    MATH  Google Scholar 

  12. Huber, P.J.: Robust statistics, Wiley, 1981.

    MATH  Google Scholar 

  13. Maronna, R.A.: ‘Robust M-estimators of multivariate location and scatter’, Ann. Statist. 4 (1976), 51–67.

    MathSciNet  MATH  Google Scholar 

  14. Rousseeuw, P.J., and Leroy, A.: Robust regression and outlier detection, Wiley, 1987.

    MATH  Google Scholar 

  15. Rousseeuw, P.J., and Yohai, V.J.: ‘Robust regression by means of S-estimators’, in J. Franke, W. Härdle, and R.D. Martin (eds.): Robust and Nonlinear Time Ser. Analysis, Vol. 26 of Lecture Notes Statistics, Springer, 1984, pp. 256–272.

    Google Scholar 

  16. Feynman, R., Leighton, R., and Sands, M.: The Feynman lectures on physics, Vol. 2, Addison-Wesley, 1964.

    Google Scholar 

  17. Landau, L.D., and Lifshits, Ye.M.: Course of theoretical physics: Electrodynamics of continuous media, Vol. VIII, Nauka, 1992, English transi.: Pergamon. (In Russian.)

    Google Scholar 

  18. Landau, L.D., and Lifshits, Ye.M.: Course of theoretical physics: Electrodynamics of continuous media, Vol. VIII, Nauka, 1992, English transi.: Pergamon. (In Russian.)

    Google Scholar 

  19. Boyd, D.W.: ‘Kronecker’s theorem and Lehmer’s problem for polynomials in several variables’, J. Number Th. 13 (1981), 116–121.

    MATH  Google Scholar 

  20. Boyd, D.W.: ‘Two sharp inequalities for the norm of a factor of a polynomial’, Mathematika 39 (1992), 341–349.

    MathSciNet  MATH  Google Scholar 

  21. Boyd, D.W.: ‘Mahler’s measure and special values of L-functions’, Experim. Math. 37 (1998), 37–82.

    Google Scholar 

  22. Deninger, C.: ‘Deligne periods of mixed motives, if-theory and the entropy of certain Zn-actions’, J. Amer. Math. Soc. 10 (1997), 259–281.

    MathSciNet  MATH  Google Scholar 

  23. Dobrowolski, E.: ‘On a question of Lehmer and the numberof irreducible factors of a polynomial’, Acta Arith. 34 (1979), 391–401.

    MathSciNet  MATH  Google Scholar 

  24. Dobrowolski, E.: ‘Mahler’s measure of a polynomial in function of the number of its coefficients’, Canad. Math. Bull. 34 (1991), 186–195.

    MathSciNet  MATH  Google Scholar 

  25. Everest, G., and Ni Fhlathúin Brid: ‘The elliptic Mahler measure’, Math. Proc. Cambridge Philos. Soc. 120, no. 1 (1996), 13–25.

    MathSciNet  MATH  Google Scholar 

  26. Mahler, K.: ‘On some inequalities for polynomials in several variables’, J. London Math. Soc. 37, no. 2 (1962), 341–344.

    MathSciNet  MATH  Google Scholar 

  27. Schmidt, K.: Dynamical systems of algebraic origin, Birkhäuser, 1995.

    MATH  Google Scholar 

  28. Smyth, C.J.: ‘On the product of the conjugates outside the unit circle of an algebraic integer’, Bull. London Math. Soc. 3 (1971), 169–175.

    MathSciNet  MATH  Google Scholar 

  29. Ehrenpreis, L.: ‘Solutions of some problems of division I’, Amer. J. Math. 76 (1954), 883–903.

    MathSciNet  MATH  Google Scholar 

  30. Ehrenpreis, L.: ‘Solutions of some problems of division IF’, Amer. J. Math. 78 (1956), 685–715.

    MathSciNet  MATH  Google Scholar 

  31. Folland, G.B.: Introduction to partial differential equations, Princeton Univ. Press, 1995.

    MATH  Google Scholar 

  32. Hörmander, L.: ‘On the theory of genercd partial differential operators’, Acta Math. 94 (1955), 161–258.

    MathSciNet  MATH  Google Scholar 

  33. Hörmander, L.: The analysis of linear partial differential operators I, Vol. 256 of Grundl. Math. Wissenschaft., Springer, 1983.

    MATH  Google Scholar 

  34. Hörmander, L.: The analysis of linear partial differential operators II, Vol. 257 of Grundl. Math. Wissenschaft., Springer, 1983.

    MATH  Google Scholar 

  35. König, H.: ‘An explicit formula for fundamental solutions of linear partial differential equations with constant coefficients’, Proc. Amer. Math. Soc. 120 (1994), 1315–1318.

    MathSciNet  MATH  Google Scholar 

  36. Malgrange, B.: ‘Existence et approximation des solutions des équations aux dérivées partielles et des équations de convolution’, Ann. Inst. Fourier (Grenoble) 6 (1955/6), 271–355.

    MathSciNet  Google Scholar 

  37. Rosay, J-P.: ‘A very elementary proof of the Malgrange-Ehrenpreis theorem’, Amer. Math. Monthly 98 (1991), 518 – 523.

    MathSciNet  MATH  Google Scholar 

  38. Treves, F.: ‘Thèse d’Hörmander’, Sern. Bourbaki Exp. 130 (1956).

    Google Scholar 

  39. Bracho, J., and Montejano, L.: ‘The combinatorics of coloured triangulations of manifolds’, Geom. Dedicata 22 (1987), 303–328.

    MathSciNet  MATH  Google Scholar 

  40. Cavicchioli, A.: ‘A combinatorial characterization of S 3 × S 1 among closed 4-manifolds, Proc. Amer. Math. Soc. 105 (1989), 1008–1014.

    MathSciNet  MATH  Google Scholar 

  41. Cavicchioli, A.: ‘On the genus of smooth 4-manifolds’, Trans. Amer. Math. Soc. 331 (1992), 203–214.

    MathSciNet  MATH  Google Scholar 

  42. Cavicchioli, A., and Meschiari, M.: ‘On classification of 4-manifolds according to genus’, Cah. Topol. Géom. Diff. Cat. 34 (1993), 37–56.

    MathSciNet  MATH  Google Scholar 

  43. Cavicchioli, A., and Meschiari, M.: ‘A homology theory for colored graphs’, Discrete Math. 137 (1995), 99–136.

    MathSciNet  MATH  Google Scholar 

  44. Cavicchioli, A., Repovs, D., and Skopenkov, A.B.: ‘Open problems on graphs arising from geometric topology’, Topol. Appl. 84 (1998), 207–226.

    MathSciNet  MATH  Google Scholar 

  45. Ferri, M., and Gagliardi, C.: ‘Crystallization moves’, Pacific J. Math. 100 (1982), 85–103.

    MathSciNet  MATH  Google Scholar 

  46. Ferri, M., Gagliardi, C., and Grasselli, L.: ‘A graph-theoretical representation of PL-manifolds: A survey on crystallizations’, Aequat. Math. 31 (1986), 121–141.

    MathSciNet  MATH  Google Scholar 

  47. Pezzana, M.: ‘Sulla struttura topologica delle varietà compatte’, Atti Sem. Mat. Fis. Univ. Modena 23 (1974), 269–277.

    Google Scholar 

  48. Ranicki, A.: High-dimensional knot theory, Springer, 1998.

    Google Scholar 

  49. Amitsur, S.A.: ‘On rings of quotients’: Symposia Math., Vol. VIII, Acad. Press, 1972, pp. 149–164.

    Google Scholar 

  50. Ara, P., and del Rio, A.: ‘A question of Passman on the symmetric ring of quotients’, Israel J. Math. 68 (1989), 348–352.

    MathSciNet  MATH  Google Scholar 

  51. Kharchenko, V.K.: ‘Generalized identities with automorphisms’, Algebra and Logic 14 (1976), 132–148.

    MATH  Google Scholar 

  52. Kharchenko, V.K.: ‘Generalized identities with automorphisms’(Algebra i Logika 14 (1975), 215–237.)

    MathSciNet  MATH  Google Scholar 

  53. Kharchenko, V.K.: ‘Algebras of invariants of free algebras’, Algebra and Logic 17 (1979), 316–321.

    Google Scholar 

  54. Kharchenko, V.K.: ‘Algebras of invariants of free algebras’ (Algebra i Logika 17 (1978), 478–487.)

    MathSciNet  Google Scholar 

  55. Lewin, J.: ‘The symmetric ring of quotients of a 2-fir’, Commun. Algebra 16 (1988), 1727–1732.

    MathSciNet  MATH  Google Scholar 

  56. Martindale Martindale III, W.S.: ‘Prime rings satisfying a generalized polynomial identity’, J. Algebra 12 (1969), 576–584.

    MathSciNet  MATH  Google Scholar 

  57. Martindale III, W.S.: ‘The normal closure of the coproduct of rings over a division ring’, Trans. Amer. Math. Soc. 293 (1986), 303–317.

    MathSciNet  MATH  Google Scholar 

  58. Martindale III, W.S.: ‘The symmetric ring of quotients of the coproduct of rings’, J. Algebra 143 (1991), 295–306.

    MathSciNet  MATH  Google Scholar 

  59. Martindale III, W.S.: and Montgomery, S.: ‘The normal closure of coproducts of domains’, J. Algebra 82 (1983), 1–17.

    MathSciNet  MATH  Google Scholar 

  60. Montgomery, S.: ‘Automorphism groups of rings with no nilpotent elements’, J. Algebra 60 (1979), 238–248.

    MathSciNet  MATH  Google Scholar 

  61. Montgomery, S.: ‘X-inner automorphisms of filtered algebras’, Proc. Amer. Math. Soc. 83 (1981), 263–268.

    MathSciNet  MATH  Google Scholar 

  62. Passman, D.S.: ‘Computing the symmetric ring of quotients’, J. Algebra 105 (1987), 207–235.

    MathSciNet  MATH  Google Scholar 

  63. Rosen, J.D., and Rosen, M.P.: ‘The Martindale ring of quotients of a skew polynomial ring of automorphism type’, Commun. Algebra 21 (1993), 4051–4063.

    MATH  Google Scholar 

  64. Antonelli, P.L. (ed.): Mathematical essays on growth and the emergence of form, Univ. Alberta Press, 1985.

    MATH  Google Scholar 

  65. Antonelli, P.L., and Bradbury, R.: Volterra-Hamilton models in the ecology and evolution of colonial organisms, Ser. Math. Biol, and Medicine. World Sci., 1996.

    MATH  Google Scholar 

  66. Antonelli, P., Bradbury, R., and Lin, X.: ‘On Hutchinson’s competition equations and their homogenization: A higher-order principle of competitive exclusion’, Ecol. Modelling 60 (1992), 309–320.

    Google Scholar 

  67. Antonelli, P.L., Fuller, K.D., and Kazarinoff, N.D.: ‘A study of large amplitude periodic solutions in a model of starfish predation on coral’, IMA J. Math. Appl. in Medicine and Biol. 4 (1987), 207–214.

    MathSciNet  MATH  Google Scholar 

  68. Bradbury, R. (ed.): Acanthaster and the coral reef: A theoretical perspective, Vol. 88 of Lecture Notes Biomath., Springer, 1990.

    Google Scholar 

  69. Breen, P., Caros, T.A., Foster, J.B., and Stewart, E.A.: ‘Changes in subtidal community structure associated with British Columbia sea otter transplants’, Marine Eco. 7 (1982), 13–20.

    Google Scholar 

  70. Bryant, J.T.: ‘The regulation of snowshoe hare feeding behaviour during winter by plant anti-herbivore chemistry’, in K. Myers and CD. McInness (eds.): Proc. World Lago- morph Conf., Guelph Univ. Press, 1979.

    Google Scholar 

  71. Elredge, N.: Time frames, the evolution of punctuated equilibria, Princeton Univ. Press, 1989.

    Google Scholar 

  72. Elton, C.S.: The ecology of invasion by animals and plants, Methuen, 1958.

    Google Scholar 

  73. Endean, R.: Acanthaster planei infestations of reefs of the Great Barrier Reef: Proc. Third Internat. Coral Reef Symp., Vol. 1, 1977, pp. 185–191.

    Google Scholar 

  74. Gause, G.F.: The struggle for existence, Williams and Wilkins, 1934.

    Google Scholar 

  75. Gause, G.F., and Witt, A.A.: ‘Behaviour of mixed populations and the problem of natural selection’, Amer. Nat. 69 (1935), 596–609.

    Google Scholar 

  76. Gilpin, M.E.: ‘Do hares eat lynx?’, Amer. Nat. 107 (1973), 727–730.

    Google Scholar 

  77. Gilpin, M., and Ayala, F.J.: ‘Global models of growth and competition’, Proc. Nat. Acad. Sci. 70 (1973), 3590–3593.

    MATH  Google Scholar 

  78. Harper, J.L.: The population biology of plants, Acad. Press, 1977.

    Google Scholar 

  79. Hassard, B., Kazarinoff, N.D., and Wan, Y.-H.: ‘Theory and applications of Hopf bifurcations’: London Math. Soc.Lecture Notes, Vol. 41, Cambridge Univ. Press, 1981.

    Google Scholar 

  80. Hutchinson, G.E.: An introduction to population biology, Yale Univ. Press, 1978.

    Google Scholar 

  81. Keith, L.B.: Wildlife’s ten-year cycle, Univ. Wisconsin Press, 1963.

    Google Scholar 

  82. Mann, K.: ‘Kelp, sea urchins and predators: a review of strong interactions in rocky subtidal systems of eastern Canada 1970–1980’, Netherl. J. Sea Research 16 (1982), 414–423.

    Google Scholar 

  83. Rhoades, D.F.: ‘Offensive-defensive interactions between herbivores and plants: their relevance in herbivore population dynamics and ecological theory’, Amer. Nat. 125 (1985), 205–223.

    Google Scholar 

  84. Ricklefs, R.E.: Ecology, second ed., Chiron Press, 1979.

    Google Scholar 

  85. Bart, H., Gohberg, I., and Kaashoek, M.A.: Minimal factorization of matrix and operator functions, Birkhäuser, 1979.

    MATH  Google Scholar 

  86. Clancey, K., and Gohberg, I.: Factorization of matrix functions and singular integral operators, Birkhäuser, 1981.

    MATH  Google Scholar 

  87. Gohberg, I., Goldberg, S., and Kaashoek, M.A.: Classes of linear operators, Vol. I—II, Birkhäuser, 1990–1993.

    MATH  Google Scholar 

  88. Malyshev, A.N.: ‘Matrix equations: Factorization of matrix polynomials’, in M. Hazewinkel (ed.): Handbook of Algebra, Vol. I, Elsevier, 1995, pp. 79–116.

    Google Scholar 

  89. Marcus, M., and Minc, H.: A survey of matrix theory and matrix inequalities, Dover, 1992, p. 122ff.

    Google Scholar 

  90. Noble, B., and Daniel, J.W.: Applied linear algebra, Prentice-Hall, 1969, pp. Sect. 9.4–9.5.

    MATH  Google Scholar 

  91. Rodman, L.: ‘Matrix functions’, in M. Hazewinkel (ed.): Handbook of Algebra, Vol. I, Elsevier, 1995, pp. 117–154.

    Google Scholar 

  92. Stoer, J. and Bulirsch, R.: Introduction to numerical analysis, Springer, 1993.

    MATH  Google Scholar 

  93. Strang, G.: Linear algebra and its applications, Harcourt- Brace-Jovanovich, 1976.

    MATH  Google Scholar 

  94. Young, D.M., and Gregory, R.T.: A survey of numerical1 mathematics, Vol. II, Dover, 1988.

    Google Scholar 

  95. Bougerol, P., and Lacroix, J.: Products of random matrices with applications to Schrödinger operators, Birkhäuser, 1985.

    Google Scholar 

  96. Carmeli, M.: Statistical theory and random matrices, M. Dekker, 1983.

    Google Scholar 

  97. Cohen, J.E., Resten, H., and Newman, C.M. (eds.): Random matrices and their applications, Amer. Math. Soc, 1986.

    MATH  Google Scholar 

  98. Gupta, A.K., and Girko, V.L.: Multidimensional statistical analysis and theory of random matrices, VSP, 1996.

    MATH  Google Scholar 

  99. Gupta, A.K., and Varga, T.: Elliptically contoured models in statistics, Kluwer Acad. Publ., 1993.

    MATH  Google Scholar 

  100. Mehta, M.L.: Random matrices, second ed., Acad. Press, 1991.

    MATH  Google Scholar 

  101. Connes, A., and Schwarz, A.: ‘Matrix Vieta theorem revisited’, Lett. Math. Phys. 39, no. 4 (1997), 349–353.

    MathSciNet  MATH  Google Scholar 

  102. Fuchs, D., and Schwarz, A.: ‘Matrix Vieta theorem’, Amer. Math. Soc. Transl. (2) 169 (1995), 15–22.

    MathSciNet  Google Scholar 

  103. Gel’fand, I.M., Krob, D., Lascoux, A., Leclerc, B., Redakh, V.S., and Thibon, J.Y.: ‘Noncomutative symmetric functions’, Adv. Math. 112 (1995), 218–348.

    MathSciNet  Google Scholar 

  104. Gel’fand, I.M., and Redakh, V.S.: ‘A theory of noncom-mutative determinants and characteristic functions of graphs I’, Publ. LACIM (Univ. Quebec) 14, 1–26.

    Google Scholar 

  105. Alperin, J.L.: ‘The main problem of block theory’, in W.R. Scott and F. Gross (eds.): Proc. Conf. Finite Groups (Park City, Utah, 1975), Acad. Press, 1976.

    Google Scholar 

  106. McKay, J.: ‘Irreducible representations of odd degree’, J. Algebra 20 (1972), 416–418.

    MathSciNet  MATH  Google Scholar 

  107. Fock, V.A.: ‘On the representation of an arbitrary function by integrals involving the Legendre function with a complex index’, Dokl. Akad. Nauk SSSR 39, no. 7 (1943), 279–283. (In Russian.)

    Google Scholar 

  108. Lebedev, N.N.: ‘The Parseval theorem for the Mehler-Fock integral transform’, Dokl. Akad. Nauk SSSR 68 (1949), 445–448. (In Russian.)

    MATH  Google Scholar 

  109. Mehler, F.G.: ‘Ueber eine mit den Kugel- und cylinderfunc-tionen verwandte Function und ihre Anwendung in der Theorie der Electricitätsvertheilung’, Math. Ann. 18 (1881), 161–194.

    MathSciNet  Google Scholar 

  110. Oberhettinger, F., and Higgins, T.P.: Tables of Lebedev, Mehler and generalized Mehler transforms, Boeing Sci. Res. Lab., 1961.

    Google Scholar 

  111. Sneddon, I.N.: The use of integral transforms, McGraw-Hill, 1972, p. Chap. 7.

    MATH  Google Scholar 

  112. Yakubovich, S.B.: ‘On the Mehler-Fock integral transform in Lp-spaces’, Extrada Math. 8, no. 2–3 (1993), 162–164.

    MathSciNet  Google Scholar 

  113. Yakubovich, S.B.: Index transforms, World Sci., 1996, p. Chap. 3.

    MATH  Google Scholar 

  114. Schneider, H.: Convex bodies: the Brunn-Minkowski theory, Cambridge Univ. Press, 1993.

    MATH  Google Scholar 

  115. Urbanski, R.: ‘A generalization of the Minkowski-Radström-Hörmander theorem’, Bull Acad. Polon. Sci. Ser. Sci. Math., Astr., Phys. 24 (1976), 709–715.

    MathSciNet  MATH  Google Scholar 

  116. Knobloch, E.: ‘Euler and the history of a problem in probability theory’, Ganita-Bharati 6 (1984), 1–12.

    MathSciNet  MATH  Google Scholar 

  117. Attouch, H.: Variational convergence for functions and operators, Applicable Math. Pitman, 1984.

    MATH  Google Scholar 

  118. Attouch, H., and Azé, D.: ‘Approximation and regularization of arbitrary functions in Hilbert spaces by the Lasry-Lions method’, Ann. Inst. H. Poincaré Anal. Non Lin. 10 (1993), 289–312.

    MATH  Google Scholar 

  119. Cepedello-Boiso, M.: ‘On regularization in superreflexive Banach spaces by infimal convolution formulas’, Studia Math. 129 (1998), 265–284.

    MathSciNet  MATH  Google Scholar 

  120. Crandall, M.G., and Lions, P.-L.: ‘Viscosity solutions of Hamilton-Jacobi equations’, Trans. Amer. Math. Soc. 277 (1983), 1–42.

    MathSciNet  MATH  Google Scholar 

  121. Ekeland, I., and Lasry, J.M.: ‘On the number of periodic trajectories for a Hamiltonian flow on a convex energy surface’, Ann. of Math. 112 (1980), 283–319.

    MathSciNet  MATH  Google Scholar 

  122. Hopf, E.: The partial differential equation u t +uu x = μu xx , Commun. Pure Appl. Math. 3 (1950), 201–230.

    MathSciNet  MATH  Google Scholar 

  123. Hopf, E.: ‘Generalized solutions of non-linear equations of first order’, J. Math. Mech. 14 (1965), 951–973.

    MathSciNet  MATH  Google Scholar 

  124. Lasry, J.-M., and Lions, P.-L.: ‘A remark on regularization in Hilbert spaces’, Israel J. Math. 55 (1986), 257–266.

    MathSciNet  MATH  Google Scholar 

  125. Lax, P.D.: ‘Hyperbolic systems of conservation laws II’, Commun. Pure Appl. Math. 10 (1957), 537–566.

    MathSciNet  MATH  Google Scholar 

  126. Lions, P.-L.: Generalized solutions of Hamilton-Jacobi equations, Vol. 69 of Res. Notes Math., Pitman, 1982.

    MATH  Google Scholar 

  127. Moreau, J-J.: ‘Proximité et dualité dans un espace hilbertien’, Bull. Soc. Math. France 93 (1965), 273–299.

    MathSciNet  MATH  Google Scholar 

  128. Rockafellar, R.T., and Wets, R.J.-B.: Variational analysis, Springer, 1998.

    MATH  Google Scholar 

  129. Strömberg, T.: ‘On regularization in Banach spaces’, Ark. Mat. 34 (1996), 383–406.

    MathSciNet  MATH  Google Scholar 

  130. Strömberg, T.: ‘Hopfs formula gives the unique viscosity solution’, Math. Scand. (submitted).

    Google Scholar 

  131. Athorne, C.: ‘On the characterization of Moutard transformations’, Inverse Problems 9 (1993), 217–232.

    MathSciNet  MATH  Google Scholar 

  132. Athorne, C., and Nimmo, J.J.C.: ‘On the Moutard transformation for integrable partial differential equations’, Inverse Problems 7 (1991), 809–826.

    MathSciNet  MATH  Google Scholar 

  133. Estevez, P.G., and Leble, S.: ‘A wave equation in 2n + 1: Painlevé analysis and solutions’, Inverse Problems 11 (1995), 925–937.

    MathSciNet  MATH  Google Scholar 

  134. Gahzha, E.: ‘On completeness of the Moutard transformations’, solv-int@xyz.lanl.gov 9606001 (1996).

    Google Scholar 

  135. Matveev, V.B., and Salle, M.A.: Darboux transformations and solitons, Springer, 1991.

    MATH  Google Scholar 

  136. Bestvina, M.: ‘Characterizing k-dimensional universal Menger compacta’, Memoirs Amer. Math. Soc. 71, no. 380 (1988), 1–110.

    MathSciNet  Google Scholar 

  137. Borsuk, K.: ‘On movable compacta’, Fund. Math. 66 (1969), 137–146.

    MathSciNet  MATH  Google Scholar 

  138. Borsuk, K.: ‘On the n-movability’, Bull. Acad. Polon. Sci. Ser. Sci. Math. Astr. Phys. 20 (1972), 859–864.

    MathSciNet  MATH  Google Scholar 

  139. Chigogidze, A.Ch.: ‘Theory of nshape’, Uspekhi Mat. Nauk 44, no. 5 (1989), 117–140. (In Russian.)

    MathSciNet  Google Scholar 

  140. Dydak, J.: ‘The Whitehead and the Smale theorems in shape theory’, Dissert. Math. 156 (1979), 1–55.

    MathSciNet  Google Scholar 

  141. Keesling, J.E.: ‘On the Whitehead theorem in shape theory’, Fund. Math. 92 (1976), 247–253.

    MathSciNet  MATH  Google Scholar 

  142. Bell, D., Raiffa, H., and Tversky, A. (eds.): Decision making: Descriptive, normative, and prescriptive interactions, Cambridge Univ. Press, 1988.

    MATH  Google Scholar 

  143. French, S.: Decision theory, an introduction to the mathematics of rationality, Horwood, 1988.

    MATH  Google Scholar 

  144. Keeney, R., and Raiffa, H.: Decisions with multiple objectives: Preferences and value trade-offs, Wiley, 1976.

    Google Scholar 

  145. Lootsma, F.A.: Fuzzy logic for planning and decision making, Kluwer Acad. Publ., 1997.

    MATH  Google Scholar 

  146. Lootsma, F.A.: Multi-criteria decision analysis via ratio and difference judgement, Kluwer Acad. Publ., 1999.

    MATH  Google Scholar 

  147. Roy, B.: Multicriteria methodology for decision aiding, Kluwer Acad. Publ., 1996.

    MATH  Google Scholar 

  148. Saaty, T.L.: The analytic hierarchy process, planning, priority setting, and resource allocation, McGraw-Hill, 1980.

    Google Scholar 

  149. Wlnterfeldt, D. Von, and Edwards, W.: Decision analysis and behavioral research, Cambridge Univ. Press, 1986.

    Google Scholar 

  150. Aizenberg, L., and Yuzhakov, A.P.: Integral representation and residues in multidimensional complex analysis, Amer. Math. Soc, 1983.

    Google Scholar 

  151. Aizenberg, L., Yuzhakov, A.P., and Tsikh, A.K.: ‘Multidimensional residues and applications’: Several complex variables, II, Vol. 8 of Encycl. Math. Sci., Springer, 1994, pp. 1–58.

    Google Scholar 

  152. Bykov, V.I., Kytmanov, A.M., and Lazman, M.Z.: Elimination method in computer algebra of polynomials, Kluwer Acad. Publ., 1997.

    Google Scholar 

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Hazewinkel, M. (2000). M. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics. Encyclopaedia of Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1279-4_13

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  • DOI: https://doi.org/10.1007/978-94-015-1279-4_13

  • Publisher Name: Springer, Dordrecht

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