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References
Arima, A., Horie, H., and Tanabe, Y.: ‘Generalized Racah coefficient and its application’, Prog. Theor. Phys. (Kyoto) 11 (1954), 143–154.
Bargmann, V.: ‘On the representations of the rotation group’, Rev. Mod. Phys. 345 (1962), 829–845.
Biedenharn, L.C.: ‘An identity satisfied by Racah coefficients’, J. Math. Phys. 31 (1953), 287–293.
Biedenharn, L.C., Blatt, J.M., and Rose, M.E.: ‘Some properties of the Racah and associated coefficients’, Rev. Mod. Phys. 24 (1952), 249–257.
Biedenharn, L.C., Chen, W.Y.C., Lohe, M.A., and Louck, J.D.: ‘The role of 3n — j coefficients in SU (3)’, in T. Lulek, W. Florek, and S. Walcerz (eds.): Proc. 3rd SSCPM, World Scientific, 1995, pp. 150–182.
Biedenharn, L.C., and Louck, J.D.: Angular momentum in quantum physics, Vol. 8 of Encyclopaedia of Math. Sci., Cambridge Univ. Press, 1981.
Biedenharn, L.C., and Louck, J.D.: The Racah-Wigner algebra in quantum theory, Vol. 9 of Encyclopaedia of Math. Sci., Cambridge Univ. Press, 1981.
Danos, M.
Edmonds, A.R.: Angular momentum in quantum mechanics, Princeton Univ. Press, 1957.
Elliot, J.P.: ‘Theoretical studies in nuclear spectroscopy. V: The matrix elements of non-central forces with an application to the 2p-shell’, Proc. Roy. Soc. A 218 (1953), 345–370.
Fano, U., and Racah, G.: Irreducible tensorial sets, Acad. Press, 1959.
Jahn, H.A., and Hope, J.: ‘Symmetry properties of the Wigner 9j symbol’, Phys. Rev. 93 (1954), 318–321.
Yutsis, A.P. and Bandzaitis, A.A.: Angular momentum theory in quantum mechanics, Molslas: Vilnius, 1977. (In Russian.)
Yutsis, A.P. Levinson, I.B., and Vanagas, V.V.: Mathematical apparatus of the theory of angular momentum, Gordon and Breach, 1964. (Translated from the Russian.)
Judd, B.R., and Lister, G.M.S.: ‘A class of generalized 9j coefficients for Sp(2n)’, J. Phys. A: Math. Gen. 20 (1986), 3159–3169.
Louck, J.D.: ‘Unitary symmetry, combinatorics and generating functions’, J. Discrete Math.
Racah, G.: ‘Theory of complex spectra. II’, Phys. Rev. 62 (1942), 438–462.
Racah, G.: ‘Theory of complex spectra. III’, Phys. Rev. 63 (1943), 367–382.
Regge, T.: ‘Symmetry properties of Clebsch-Gordan coefficients’, Nuovo Cim. 10 (1958), 544–545.
Regge, T.: ‘Symmetry properties of Racah’s coefficients’, Nuovo Cim. 11 (1959), 116–117.
Rose, M.E.: Elementary theory of angular momentum, Wiley, 1957.
Schwinger, J.: ‘On angular momentum’, in L.C. Bidenharn and H. van Dam (eds.): Quantum Theory of Angular Momentum, Acad. Press, 1965, pp. 229–279.
Sharp, W.T.: Racah algebra and the contraction of groups, Thesis Princeton Univ. Press, 1960.
Varshalovich, D.A., Moskalev, A.N., and KhersonskiÄ, V.K.: Quantum theory of angular momentum, Nauka, 1975. (In Russian.)
Wigner, E.P.: ‘On the matrices which reduce the Kronecker products of representation of S.R. groups’, in L.C. Biedenharn and H. van Dam (eds.): Quantum Theory of Angular Momentum, Acad. Press, 1965, pp. 87–133.
Wu, A.C.T.: ‘Structure of the Wigner 9j coefficients in the Bargmann approach’, J. Math. Phys. 13 (1972), 84–90.
Endler, O.: Valuation theory, Springer, 1972.
Serre, J.P.: Corps locaux, Hermann, 1962.
Albers, D.J.: ‘A nice genius’, Math Horizons November (1996), 18–23.
Graham, R.L., Rothschild, B.L., and Spencer, J.H.: Ramsey theory, Wiley, 1990.
Graham, R.L., and Spencer, J.H.: ‘Ramsey theory’, Scien tific Amer. July (1990), 112–117.
McKay, B.D., and Radziszowski, S.P.: ‘The first classical Ramsey number for hypergraphs is computed’: Proc. 2nd ACM-SIAM Symp. on Discrete Algebra (San Francisco, 1991), SIAM, 1991, pp. 304–308.
Spencer, J.: Paul Erdös: The art of counting, MIT, 1973.
Spencer, J.: ‘Ramsey theory and Ramsey theoreticians’, J. Graph Th. 7 (1983), 15–23.
West, D.B.: Introduction to graph theory, Prentice-Hall, 1996.
Winn, J.A.: Asymptotic bounds for classical Ramsey numbers, Polygonal, 1988.
Bellman, R., and Pennington, R.: ‘Effects of surface tension and viscosity on Taylor instability’, Quart. Appl. Math. 12 (1954), 151–162.
Cole, R.L., and Tankin, R.S.: ‘Experimental study of Taylor instability’, Phys. Fluids 16 (1973), 1810–1815.
Duff, R.E., Harlow, F.H., and Hirt, C.W.: ‘Effect of diffusion on interface instability between gases’, Phys. Fluids 5 (1962), 417–425.
Emmons, H.W., Chang, C.T., and Watson, B.C.: ‘Taylor instability of finite surface waves’, J. Fluid Mech. 7 (1960), 177–193.
Kull, H.: ‘Theory of the Rayleigh-Taylor instability’, Phys. Rep. 206 (1991), 197–325.
Lewis, D.J.: ‘The instability of liquid surfaces when accelerated in a direction perpendicular to their planes’, Proc. Roy. Soc. A. 202 (1950), 81–96.
Lord Rayleigh: ‘Investigation of the character of the equilibrium of an incompressible heavy fluid of variable density’: Scientific Papers, Vol. II, Cambridge Univ. Press, 1900, pp. 200–207.
Ratafia, M.: ‘Experimental investigation of Rayleigh-Taylor instability’, Phys. Fluids 16 (1973), 1207–1210.
Sharp, D.H.: ‘An overview of Rayleigh-Taylor instability’, Physica 12D (1984), 3–18.
Shivamoggi, B.K.: ‘Nonlinear theory of Rayleigh-Taylor instability of superposed fluids’, Acta Mech. 31 (1979), 301–305.
Taylor, G.I.: ‘The stability of liquid surfaces when accelerated in a direction perpendicular to their planes’, Proc. Roy. Soc. A 201 (1950), 192–196.
Artin, E., and Schreier, O.: ‘Algebraische Konstruktion reeller Körper; Über die Zerlegung definiter Funktionen in Quadrate; Eine Kennzeichnung der reell abgeschlossenen Körper’, Abh. Math. Sem. Univ. Hamburg 5 (1927), 85–99; 100–115; 225–231.
Becker, E.: Theory of real field and sums of powers, Springer.
Becker, E., Berr, R., Delon, F., and Gondard, D.: ‘Hilbert’s 17th problem for sums of 2n-th powers’, J. Reine Angew. Math. 450 (1994), 139–157.
Bochnak, J., Coste, M., and Roy, M.-F.: Géométrie algébrique réelle, Springer, 1987.
Delzell, C.: ‘Continuous piecewise-polynomial functions which solve Hilbert’s 17th problem’, J. Reine Angew. Math. 440 (1993), 157–173.
Knebusch, M.: ‘An invitation to real spectra’: Quadratic and Hermitean forms, Conf. Hamilton/Ont. 1983, Vol. 4 of CMS Conf. Proc., Amer. Math. Soc., 1984, pp. 51–105.
Knebusch, M., and Scheiderer, C.: Einführung in die reelle Algebra, Vieweg, 1989.
Knebusch, M., and Scheiderer, C.: ‘Semi-algebraic topology in the last 10 years; Real algebra and its applications to geometry in the last 10 years: some major developments and results’, in M. Coste and M.F. Roy (eds.): Real algebraic geometry, Proc. Conf. Rennes 1991, Vol. 1524 of Lecture Notes in Mathematics, Springer, 1992, pp. 1–36; 75–96.
Lam, T. Y.: ‘The theory of ordered fields’, in B. McDonald (ed.): Ring Theory and Algebra III, Vol. 55 of Lecture Notes in Pure and Applied math., New York, 1980, pp. 1–152.
Prestel, A.: Lectures on formally real fields, Vol. 1093 of Lecture Notes in Mathematics, Springer, 1984.
Priess-Crampe, S.: Angeordnete Strukturen. Gruppen, Körper, projektive Ebenen, Vol. 98 of Ergebnisse der Mathematik und ihrer Grenzgebiete, Springer, 1983.
Tarski, A., and McKinsey, J.C.C.: A decision method for elementary algebra and geometry, Univ. California Press, 1951.
Dassow, J., and Păun, Gh.: Regulated rewriting in formal language theory, Springer, 1989.
Dassow, J., Păun, Gh., and Salomaa, A.: ‘Regulated rewriting’, in G. Rozenberg and A. Salomaa (eds.): Handbook of Formal Languages, Springer, 1997.
Rosenkrantz, D.: ‘Programmed grammars and classes of formal languages’, J. ACM 16 (1969), 107–131.
Magnen, J., in D. Iagolnitzer (ed.): XI-th Internat. Congress Math. Physics, Internat. Press, Boston, 1995, pp. 121–141.
Wilson, K.G., and Kogut, J.: ‘The renormalization group and the ε-expansion’, Phys. Rep. 12 (1974), 75–200.
Zinn-Justin, J.: Quantum field theory and critical phenomena, third ed., Oxford Univ. Press, 1996.
Asmussen, S.: Ruin probability, World Sci., to appear.
Cramér, H.: ‘On the mathematical theory of risk’, Skandia Jubilee Volume (1930).
Dassios, A., and Embrechts, P.: ‘Martingales and insurance risk’, Commun. Statist. — Stochastic models 5 (1989), 181–217.
Delbaen, F., and Haezendonck, J.: ‘Classical risk theory in an economic environment’, Insurance: Mathematics and Economics 6 (1987), 85–116.
Embrechts, P., and Veraverbeke, N.: ‘Estimates for the probability of ruin with special emphasis on the possibility of large claims’, Insurance: Mathematics and Economics 1 (1982), 55–72.
Grandell, J.: Aspects of risk theory, Springer, 1991.
Lundberg, F.: Försäkringsteknisk Riskutjämning, F. Englunds, 1926. (In Swedish.)
Sparre Andersen, E.: ‘On the collective theory of risk in the case of contagion between the claims’: Trans. XVth Internat. Congress of Actuaries, Vol. II, New York, 1957, pp. 219–229.
Thorin, O.: ‘Probabilities of ruin’, Scand. Actuarial J. (1982), 65–102.
Kopytov, V.M., and Medvedev, N.Ya.: The theory of lattice-ordered groups, Kluwer Acad. Publ., 1994. (Translated from the Russian.)
Mura, R.T.B., and Rhemtulla, A.H.: Orderable groups, M. Dekker, 1977.
Kazhdan, D., and Lusztig, G.: ‘Representations of Coxeter groups and Hecke algebras’, Invent. Math. 53 (1979), 165–184.
Knuth, D.E.: ‘Permutations, matrices and generalized Young tableaux’, Pacific J. Math. 34 (1970), 709–727.
Knuth, D.E.: The art of computer programming III. Sorting and searching, Addison-Wesley, 1975.
Lascoux, A., and Schützenberger, M.P.: ‘Le monoide plaxique’, Quad. Ricerca Scient. C.N.R. 109 (1981), 129–156.
Leclerc, B., and Thibon, J.-Y.: ‘The Robinson-Schensted correspondence, crystal bases, and the quantum straightening at q = 0’, Electronic J. Combinatorics 3, no. 2 (1996).
Robinson, G. de B.: ‘On the representations of the symmetric group’, Amer. J. Math. 60 (1938), 745–760.
Schensted, C.: ‘Longest increasing and decreasing subsequences’, Canadian J. Math. 13 (1961), 179–191.
Schützenberger, M.P.: ‘Quelques remarques sur une construction de Schensted’, Math. Scandinavica 12 (1963), 117–128.
Schützenberger, M.P.: ‘La correspondance de Robinson’, in D. Foata (ed.): Combinatoire et Représentation du Groupe Symétrique, Vol. 579 of Lecture Notes in Mathematics, Springer, 1976, pp. 59–113.
Steinberg, R.: ‘An occurrence of the Robinson-Schensted correspondence’, J. Algebra 113 (1988), 523–528.
Leeuwen, M.A.A. van: ‘The Robinson-Schensted correspondence and Schützenberger algorithms, an elementary approach’, Electronic J. Combinatorics 3, no. 2 (1996).
Zelevinsky, A.V.: ‘A generalisation of the Littlewood-Richardson rule and the Robinson-Schensted-Knuth correspondence’, J. Algebra 69 (1981), 82–94.
Anderson, I.: ‘Cyclic designs in the 1850s; the work of Rev. R.R. Anstice’, Bull. ICA 15 (1995), 41–46.
Dinitz, J.H.: ‘Room squares’, in C.J. Colbourn and J.H. Dinitz (eds.): CRC Handbook of Combinatorial Designs, CRC Press, 1996, pp. 437–442.
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.
Mullin, R.C., and Wallis, W.D.: ‘The existence of Room squares’, Aequat. Math. 13 (1975), 1–7.
Stinson, D.R.: ‘The spectrum of skew Room squares’, J. Austral. Math. Soc. A 31 (1981), 475–480.
Dekker, K., and Verwer, J.G.: Stability of Runge-Kutta methods for stiff nonlinear differential equations, North-Holland, 1984.
Hairer, E., and Wanner, G.: Solving ordinary differential equations, Vol. II: stiff and differential-algebraic problems, Springer, 1991.
Rosenbrock, H.H.: ‘Some general implicit processes for the numerical solution of differential equations’, Comput. J. 5 (1963), 329–330.
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Hazewinkel, M. (1997). R. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics. Encyclopaedia of Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1288-6_18
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