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References

  1. Abhyankar, S.S.: Algebraic geometry for scientists and engineers, Amer. Math. Soc, 1990, p. 3; 60.

    Google Scholar 

  2. Dimca, A.: Topics on real and complex singularities, Vieweg, 1987.

    Google Scholar 

  3. Griffiths, Ph., and Harris, J.: Principles of algebraic geometry, Wiley, 1978, p. 293; 507.

    Google Scholar 

  4. Walker, R.J.: Algebraic curves, Princeton Univ. Press, 1950, Reprint: Dover 1962.

    Google Scholar 

References

  1. Bonahon, F., and Siebenmann, L.: Geometric splittings of classical knots and the algebraic knots of Conway, Vol. 75 of Lecture Notes, London Math. Soc, to appear.

    Google Scholar 

  2. Conway, J.H.: ‘An enumeration of knots and links’, in J. Leech (ed.): Computational Problems in Abstract Algebra, Pergamon Press, 1969, pp. 329–358.

    Google Scholar 

  3. Lozano, M.: ‘Arcbodies’, Math. Proc. Cambridge Philos. Soc. 94 (1983), 253–260.

    Article  MATH  MathSciNet  Google Scholar 

References

  1. Habiro, K.: ‘Claspers and finite type invariants of links’, Geometry and Topology 4 (2000), 1–83.

    Article  MATH  MathSciNet  Google Scholar 

  2. Harikae, T., and Uchida, Y.: ‘Irregular dihedral branched coverings of knots’, in M. Bozhüyük (ed.): Topics in Knot Theory, Vol. 399 of NATO ASI Ser. C, Kluwer Acad. Publ., 1993, pp. 269–276.

    Google Scholar 

  3. Kirby, R.: ‘Problems in low-dimensional topology’, in W. Kazez (ed.): Geometric Topology (Proc. Georgia Internat. Topology Conf., 1993), Vol. 2 of Studies in Adv. Math., Amer. Math. Soc./IP, 1997, pp. 35–473.

    Google Scholar 

  4. Murakami, H., and Nakanishi, Y.: ‘On a certain move generating link homology’, Math. Ann. 284 (1989), 75–89.

    Article  MATH  MathSciNet  Google Scholar 

  5. Przytycki, J.H.: ‘3-coloring and other elementary invariants of knots’. Knot Theory, Vol. 42, Banach Center Publ., 1998, pp. 275–295.

    Google Scholar 

  6. Uchida, Y., in S. Suzuki (ed.): Knots ‘96, Proc. Fifth Internat. Research Inst. of MSJ, World Sci., 1997, pp. 109–113.

    Google Scholar 

References

  1. Banks, H.T., and Wade, J.G.: ‘Weak tau approximations for distributed parameter systems in inverse problems’, Numer. Fund. Anal. Optim. 12 (1991), 1–31.

    Article  MathSciNet  MATH  Google Scholar 

  2. Chaves, T., and Ortiz, E.L.: ‘On the numerical solution of two point boundary value problems for linear differential equations’, Z. Angew. Math. Mech. 48 (1968), 415–418.

    Article  MATH  MathSciNet  Google Scholar 

  3. Crisci, M.R., and Russo, E.: ‘A-stability of a class of methods for the numerical integration of certain linear systems of differential equations’, Math. Comput. 41 (1982), 431–435.

    MathSciNet  Google Scholar 

  4. Crisci, M.R., and Russo, E.: ‘An extension of Ortiz’s recursive formulation of the tau method to certain linear systems of ordinary differential equations’, Math. Comput. 41 (1983), 27–42.

    Article  MATH  MathSciNet  Google Scholar 

  5. El Daou, M., Namasivayam, S., and Ortiz, E.L.: ‘Differential equations with piecewise approximate coefficients: discrete and continuous estimation for initial and boundary value problems’, Computers Math. Appl. 24 (1992), 33–47.

    Article  MATH  Google Scholar 

  6. El Daou, M., and Ortiz, E.L.: ‘The tau method as an analytic tool in the discussion of equivalence results across numerical methods’, Computing 60 (1998), 365–376.

    Article  MATH  MathSciNet  Google Scholar 

  7. El Misiery, A.E.M., and Ortiz, E.L.: ‘Tau-lines: a new hybrid approach to the numerical treatment of crack problems based on the tau method’, Computer Methods in Applied Mechanics and Engin. 56 (1986), 265–282.

    Article  MATH  Google Scholar 

  8. Fox, L., and Parker, I.B.: Chebyshev polynomials in numerical analysis, Oxford Univ. Press, 1968.

    Google Scholar 

  9. Freilich, J.G., and Ortiz, E.L.: ‘Numerical solution of systems of differential equations: an error analysis’, Math. Comput. 39 (1982), 467–479.

    Article  MATH  MathSciNet  Google Scholar 

  10. Froes Bunchaft, M.E.: ‘Some extensions of the Lanczos-Ortiz theory of canonical polynomials in the tau method’, Math. Comput. 66,no. 218 (1997), 609–621.

    Article  MATH  Google Scholar 

  11. Gotlieb, D., and Orszag, S.A.: Numerical analysis of spectral methods: Theory and applications, Philadelphia, 1977.

    Google Scholar 

  12. Hayman, W.K., and Ortiz, E.L.: ‘An upper bound for the largest zero of Hermite’s function with applications to subharmonic functions’, Proc. Royal Soc. Edinburgh 75A (1976), 183–197.

    Google Scholar 

  13. Hosseini Ali-Abadi, M., and Ortiz, E.L.: ‘The algebraic kernel method’, Numer. Fund. Anal. Optim. 12,no. 3–4 (1991), 339–360.

    Article  MathSciNet  MATH  Google Scholar 

  14. Hosseini Ali-Abadi, M., and Ortiz, E.L.: ‘A tau method based on non-uniform space-time elements for the numerical simulation of solitons’, Computers Math. Appl. 22 (1991), 7–19.

    Article  Google Scholar 

  15. Khajah, H.G., and Ortiz, E.L.: ‘Numerical approximation of solutions of functional equations using the tau method’, Appl. Numer. Anal. 9 (1992), 461–474.

    Article  MATH  MathSciNet  Google Scholar 

  16. Khajah, H.G., and Ortiz, E.L.: ‘Ultra-high precision computations’, Computers Math. Appl. 27,no. 7 (1993), 41–57.

    Article  MathSciNet  Google Scholar 

  17. Lanczos, C.: ‘Trigonometric interpolation of empirical and analytic functions’, J. Math, and Physics 17 (1938), 123–199.

    MATH  Google Scholar 

  18. Lanczos, C.: Applied analysis, New Jersey, 1956.

    Google Scholar 

  19. Liu, K.M., and Ortiz, E.L.: ‘Tau method approximation of differential eigenvalue problems where the spectral parameter enters nonlinearly’, J. Comput. Phys. 72 (1987), 299–310.

    Article  MATH  MathSciNet  Google Scholar 

  20. Liu, K.M., and Ortiz, E.L.: ‘Numerical solution of ordinary and partial functional-differential eigenvalue problems with the tau method’, Computing 41 (1989), 205–217.

    Article  MATH  MathSciNet  Google Scholar 

  21. Luke, Y.L.: The special functions and their approximations I–II, New York, 1969.

    Google Scholar 

  22. Navasimayan, S., and Ortiz, E.L.: ‘Best approximation and the numerical solution of partial differential equations with the tau method’, Portugal. Math. 41 (1985), 97–119.

    Google Scholar 

  23. Onumanyi, P., and Ortiz, E.L.: ‘Numerical solution of stiff and singularly perturbed boundary value problems with a segmented-adaptive formulation of the tau method’, Math. Comput. 43 (1984), 189–203.

    Article  MATH  MathSciNet  Google Scholar 

  24. Ortiz, E.L.: ‘The tau method’, SIAM J. Numer. Anal. 6 (1969), 480–492.

    Article  MATH  MathSciNet  Google Scholar 

  25. Ortiz, E.L.: ‘On the numerical solution of nonlinear and functional differential equations with the tau method’, in R. Ansorge and W. Tornig (eds.): Numerical Treatment of Differential Equations in Applications, Berlin, 1978, pp. 127–139.

    Google Scholar 

  26. Ortiz, E.L., and Pham Ngoc Dinh, A.: ‘Linear recursive schemes associated with some nonlinear partial differential equations in one dimension and the tau method’, SIAM J. Math. Anal. 18 (1987), 452–464.

    Article  MATH  MathSciNet  Google Scholar 

  27. Ortiz, E.L., and Samara, H.: ‘An operational approach to the tau method for the numerical solution of nonlinear differential equations’, Computing 27 (1981), 15–25.

    Article  MATH  MathSciNet  Google Scholar 

  28. Ortiz, E.L., and Samara, H.: ‘Numerical solution of partial differential equations with variable coefficients with an operational approach to the tau method’, Computers Math. Appl. 10,no. 1 (1984), 5–13.

    Article  MATH  MathSciNet  Google Scholar 

  29. Pun, K.S., and Ortiz, E.L.: ‘A bidimensional tau-elements method for the numerical solution of nonlinear partial differential equations, with an application to Burgers equation’, Computers Math. Appl. 12B (1986), 1225–1240.

    MathSciNet  Google Scholar 

  30. Rivlin, T.J.: The Chebyshev polynomials, New York, 1974, 2nd. ed. 1990.

    Google Scholar 

  31. Wright, K.: ‘Some relationships between implicit Runge-Kutta, collocation and Lanczos tau methods’, BIT 10 (1970), 218–227.

    Article  Google Scholar 

References

  1. Albrecht, E., and Vasilescu, F.-H.: ‘Semi-Fredholm complexes’, Oper. Th. Adv. Appl. 11 (1983), 15–39.

    MathSciNet  Google Scholar 

  2. Ambrozie, C.-G., and Vasilescu, F.-H.: Banach space complexes, Kluwer Acad. Publ, 1995.

    Google Scholar 

  3. Berger, C., and Coburn, L.: ‘Wiener-Hopf operators on U 2Integral Eq. Oper. Th. 2 (1979), 139–173.

    Article  MATH  MathSciNet  Google Scholar 

  4. Berger, C., Coburn, L., and Koranyi, A.: ‘Opérateurs de Wiener-Hopf sur les spheres de Lie’, C.R. Acad. Sci. Paris Ser. A 290 (1980), 989–991.

    MATH  MathSciNet  Google Scholar 

  5. Curto, R.: ‘Spectral permanence for joint spectra’, Trans. Amer. Math. Soc. 270 (1982), 659–665.

    Article  MATH  MathSciNet  Google Scholar 

  6. Curto, R.: ‘Applications of several complex variables to multiparameter spectral theory’, in J.B. Conway and B.B. Morrel (eds.): Surveys of Some Recent Results in Operator Theory II, Vol. 192 of Pitman Res. Notes in Math., Longman Sci. Tech., 1988, pp. 25–90.

    Google Scholar 

  7. Curto, R., and Fialkow, L.: ‘The spectral picture of (L A,RB)’, J. Fund. Anal. 71 (1987), 371–392.

    Article  MATH  MathSciNet  Google Scholar 

  8. Curto, R., and Muhly, P.: ‘C*-algebras of multiplication operators on Bergman spaces’, J. Fund. Anal. 64 (1985), 315–329.

    Article  MATH  MathSciNet  Google Scholar 

  9. Curto, R., and Salinas, N.: ‘Spectral properties of cyclic subnormal m-tuples’, Amer. J. Math. 107 (1985), 113–138.

    Article  MATH  MathSciNet  Google Scholar 

  10. Curto, R., and Yan, K.: ‘The spectral picture of Reinhardt measures’, J. Fund. Anal. 131 (1995), 279–301.

    Article  MATH  MathSciNet  Google Scholar 

  11. Eschmeier, J., and Putinar, M.: Spectral decompositions and analytic sheaves, London Math. Soc. Monographs. Oxford Sci. Publ., 1996.

    Google Scholar 

  12. Laursen, K., and Neumann, M.: Introduction to local spectral theory, London Math. Soc. Monographs. Oxford Univ. Press, 2000.

    Google Scholar 

  13. Putinar, M.: ‘Uniqueness of Taylor’s functional calculus’, Proc. Amer. Math. Soc. 89 (1983), 647–650.

    Article  MATH  MathSciNet  Google Scholar 

  14. Putinar, M.: ‘Spectral inclusion for subnormal n-tuples’, Proc. Amer. Math. Soc. 90 (1984), 405–406.

    Article  MathSciNet  Google Scholar 

  15. Salinas, N.: ‘The δ-formalism and the C*-algebra of the Bergman n-tuple’, J. Oper. Th. 22 (1989), 325–343.

    MATH  MathSciNet  Google Scholar 

  16. Salinas, N., Sheu, A., and Upmeier, H.: ‘Toeplitz operators on pseudoconvex domains and foliation C*-algebras’, Ann. of Math. 130 (1989), 531–565.

    Article  MathSciNet  Google Scholar 

  17. Taylor, J.L.: ‘The analytic functional calculus for several commuting operators’, Ada Math. 125 (1970), 1–48.

    MATH  Google Scholar 

  18. Taylor, J.L.: ‘A joint spectrum for several commuting operators’, J. Fund. Anal. 6 (1970), 172–191.

    Article  MATH  Google Scholar 

  19. Upmeier, H.: ‘Toeplitz C*-algebras on bounded symmetric domains’, Ann. of Math. 119 (1984), 549–576.

    Article  MathSciNet  Google Scholar 

  20. Vasilescu, F.-H.: Analytic functional calculus and spectral decompositions, Reidel, 1982.

    Google Scholar 

  21. Venugopalkrishna, U.: ‘Fredholm operators associated with strongly pseudoconvex domains in Cn’, J. Funct. Anal. 9 (1972), 349–373.

    Article  MATH  MathSciNet  Google Scholar 

References

  1. Gaier, D.: Konstruktive Methoden der konformen Abbildung, Springer, 1964.

    Google Scholar 

  2. Gutknecht, M.H.: ‘Solving Theodorsen’s integral equation for conformal maps with the fast Fourier transform and various nonlinear iterative methods’, Numer. Math. 36 (1981), 405–429.

    Article  MATH  MathSciNet  Google Scholar 

  3. Gutknecht, M.H.: ‘Numerical experiments on solving Theodorsen’s integral equation for conformal maps with the fast Fourier transform and various nonlinear iterative methods’, SIAM J. Sci. Statist. Comput. 4 (1983), 1–30.

    Article  MATH  MathSciNet  Google Scholar 

  4. Gutknecht, M.H.: ‘Numerical conformal mapping methods based on function conjugation’, J. Comput. Appl. Math. 14 (1986), 31–77.

    Article  MATH  MathSciNet  Google Scholar 

  5. Hübner, O.: ‘The Newton method for solving the Theodorsen equation’, J. Comput. Appl. Math. 14 (1986), 19–30.

    Article  MATH  MathSciNet  Google Scholar 

  6. Kythe, P.K.: Computational conformal mapping, Birkhäuser, 1998.

    Google Scholar 

  7. Theodorsen, T.: ‘Theory of wing sections of arbitrary shape’, Kept. NACA 411 (1931).

    Google Scholar 

  8. Theodorsen, T., and Garrick, I.E.: ‘General potential theory of arbitrary wing sections’, Rept. NACA 452 (1933).

    Google Scholar 

  9. Wegmann, R.: ‘Ein Iterationsverfahren zur konformen Abbildung’, Numer. Math. 30 (1978), 453–466.

    Article  MATH  MathSciNet  Google Scholar 

  10. Wegmann, R.: ‘An iterative method for conformal mapping’, J. Comput. Appl. Math. 14 (1986), 7–18, English translation of [9]. (In German.)

    Article  MATH  MathSciNet  Google Scholar 

  11. Wegmann, R.: ‘An iterative method for the conformal mapping of doubly connected regions’, J. Comput. Appl. Math. 14 (1986), 79–98.

    Article  MATH  MathSciNet  Google Scholar 

References

  1. Berger, A.: Mathematik der Lebensversicherung, Springer Wien, 1939.

    Google Scholar 

  2. Gram, J.P.: ‘Professor Thiele som aktuar’, Dansk Forsikringsärbog (1910), 26–37.

    Google Scholar 

  3. Hald, A.: ‘T.N. Thiele’s contributions to statistics’, Internat. Statist. Rev. 49 (1981), 1–20.

    MATH  MathSciNet  Google Scholar 

  4. Hald, A.: A history of mathematical statistics from 1750 to 1930, Wiley, 1998.

    Google Scholar 

  5. Hoem, J.M.: ‘The reticent trio: Some little-known early discoveries in insurance mathematics by L.H.F. Oppermann, T.N. Thiele, and J.P. Gram’, Internat. Statist. Rev. 51 (1983), 213–221.

    Article  MATH  Google Scholar 

  6. Johnson, N.L., and Kotz, S. (eds.): Leading personalities in statistical science, Wiley, 1997.

    Google Scholar 

  7. Jørgensen, N.R.: Grundzüge einer Theorie der Lebensversicherung, G. Fischer, 1913.

    Google Scholar 

  8. Norberg, R.: ‘Reserves in life and pension insurance’, Scand. Actuarial J. (1991), 1–22.

    Google Scholar 

  9. Norberg, R.: Thorvald Nicolai Thiele, statisticians of the centuries, Internat. Statist. Inst., 2001.

    Google Scholar 

  10. Schweder, T.: ‘Scandinavian statistics, some early lines of development’, Scand. J. Statist. 7 (1980), 113–129.

    MathSciNet  MATH  Google Scholar 

  11. Thiele, T.N.: Elementœr Iagttagelseslœre, Gyldendal, Copenhagen, 1897.

    Google Scholar 

  12. Thiele, T.N.: Theory of observations, Layton, London, 1903, Reprinted in: Ann. Statist. 2 (1931), 165–308. (Translated from the Danish edition 1897.)

    MATH  Google Scholar 

  13. Thiele, T.N.: Interpolationsrechnung, Teubner, 1909.

    Google Scholar 

References

  1. Briançon, J., and Speder, J.P.: ‘La trivialité topologique n’implique pas les conditions de Whitney’, Note C.R. Acad. Sci. Paris Ser. A 280 (1975), 365.

    MATH  Google Scholar 

  2. Goresky, M., and MacPherson, R.: Stratified Morse theory, Springer, 1988.

    Google Scholar 

  3. Lê, D.T., and Teissier, B.: ‘Cycles évanescents, sections planes et conditions de Whitney II’: Proc. Symp. Pure Math., Vol. 40, Amer. Math. Soc, 1983, pp. 65–103.

    Google Scholar 

  4. Mather, J.: Notes on topological stability, Harvard Univ., 1970.

    Google Scholar 

  5. Thom, R.: ‘La stabilité topologique des applications polynomiales’, Enseign. Math. 8,no. 2 (1962), 24–33.

    MATH  MathSciNet  Google Scholar 

  6. Thom, R.: ‘Ensembles et morphismes stratifyés’, Bull. Amer. Math. Soc. 75 (1969), 240–284.

    MATH  MathSciNet  Google Scholar 

  7. Whitney, H.: ‘Local properties of analytic varieties’, in S. Cairns (ed.): Differential and Combinatorial Topology, Princeton Univ. Press, 1965, pp. 205–244.

    Google Scholar 

  8. Whitney, H.: ‘Tangents to an analytic variety’, Ann. of Math. 81 (1965), 496–549.

    Article  MathSciNet  Google Scholar 

References

  1. Assem, I.: ‘Tilting theory — an introduction’, in N. Balcerzyk et al. (eds.): Topics in Algebra, Vol. 26, Banach Center Publ., 1990, pp. 127–180.

    Google Scholar 

  2. Auslander, M., Platzeck, M.I., and Reiten, I.: ‘Coxeter functors without diagrams’, Trans. Amer. Math. Soc. 250 (1979), 1–46.

    Article  MATH  MathSciNet  Google Scholar 

  3. Bernstein, I.N., Gelfand, I.M., and Ponomarow, V.A.: ‘Coxeter functors and Gabriel’s theorem’, Russian Math. Surveys 28 (1973), 17–32.

    Article  MATH  Google Scholar 

  4. Bongartz, K.: ‘Tilted algebras’, in M. Auslander and E. Lluis (eds.): Representations of Algebras. Proc. ICRA III, Vol. 903 of Lecture Notes in Mathematics, Springer, 1981, pp. 26–38.

    Google Scholar 

  5. Brenner, S., and Butler, M.: ‘Generalizations of the Bernstein-Gelfand-Ponomarev reflection functors’, in V. Dlab and P. Gabriel (eds.): Representation Theory II. Proc. ICRA II, Vol. 832 of Lecture Notes in Mathematics, Springer, 1980, pp. 103–169.

    Google Scholar 

  6. Happel, D.: Triangulated categories in the representation theory of finite dimensional algebras, Vol. 119 of London Math. Soc. Lecture Notes, Cambridge Univ. Press, 1988.

    Google Scholar 

  7. Happel, D., Reiten, I., and Smalø, S.O.: ‘Tilting in abelian categories and quasitilted algebras’, Memoirs Amer. Math. Soc. 575 (1996).

    Google Scholar 

  8. Happel, D., and Ringel, CM.: ‘Tilted algebras’, Trans. Amer. Math. Soc. 274 (1982), 399–443.

    Article  MATH  MathSciNet  Google Scholar 

  9. Kerner, O.: ‘Tilting wild algebras’, J. London Math. Soc. 39,no. 2 (1989), 29–47.

    Article  MATH  MathSciNet  Google Scholar 

  10. Kerner, O.: ‘Wild tilted algebras revisited’, Colloq. Math. 73 (1997), 67–81.

    MATH  MathSciNet  Google Scholar 

  11. Liu, S.: ‘The connected components of the Auslander-Reiten quiver of a tilted algebra’, J. Algebra 161 (1993), 505–523.

    Article  MATH  MathSciNet  Google Scholar 

  12. Ringel, C.M.: Tame algebras and integral quadratic forms, Vol. 1099 of Lecture Notes in Mathematics, Springer, 1984.

    Google Scholar 

  13. Ringel, C.M.: ‘The regular components of the Auslander-Reiten Quiver of a tilted algebra’, Chinese Ann. Math. Ser. B. 9 (1988), 1–18.

    MATH  MathSciNet  Google Scholar 

  14. Strauss, H.: ‘On the perpendicular category of a partial tilting module’, J. Algebra 144 (1991), 43–66.

    Article  MATH  MathSciNet  Google Scholar 

References

  1. Andersen, H.H.: ‘Tensor products of quantized tilting modules’, Commun. Math. Phys. 149,no. 1 (1992), 149–159.

    Article  MATH  MathSciNet  Google Scholar 

  2. Assem, I.: ‘Tilting theory-an introduction’: Topics in Algebra, Vol. 26 of Banach Center Publ, PWN, 1990, pp. 127–180.

    Google Scholar 

  3. Auslander, M., Platzeck, M.I., and Reiten, I.: ‘Coxeter functors without diagrams’, Trans. Amer. Math. Soc. 250 (1979), 1–12.

    Article  MATH  MathSciNet  Google Scholar 

  4. Auslander, M., and Reiten, I.: ‘Applications of contravariantly finite subcategories’, Adv. Math. 86,no. 1 (1991), 111–152.

    Article  MATH  MathSciNet  Google Scholar 

  5. Bernstein, I.N., Gelpand, I.M., and Ponomarev, V.A.: ‘Coxeter functors and Gabriel’s theorem’, Russian Math. Surveys 28 (1973), 17–32. (Uspekhi Mat. Nauk. 28 (1973), 19–33.)

    Article  MATH  Google Scholar 

  6. Brenner, S., and Butler, M.C.R.: ‘Generalization of Bernstein-Gelfand-Ponomarev reflection functors’: Proc. Ottawa Conj. on Representation Theory, 1979, Vol. 832 of Lecture Notes in Mathematics, Springer, 1980, pp. 103–169.

    Google Scholar 

  7. Crawley-Boevby, W., and Kerner, O.: ‘A functor between categories of regular modules for wild hereditary algebras’, Math. Ann. 298 (1994), 481–487.

    Article  MathSciNet  Google Scholar 

  8. Donkin, S.: ‘On tilting modules for algebraic groups’, Math. Z. 212,no. 1 (1993), 39–60.

    Article  MATH  MathSciNet  Google Scholar 

  9. Geigle, W., and Lenzing, H.: ‘Perpendicular categories with applications to representations and sheaves’, J. Algebra 144 (1991), 273–343.

    Article  MATH  MathSciNet  Google Scholar 

  10. Happel, D.: ‘Triangulated categories in the representation theory of finite dimensional algebras’, London Math. Soc. Lecture Notes 119 (1988).

    Google Scholar 

  11. Happel, D.: ‘A characterization of hereditary categories with tilting object’, preprint (2000).

    Google Scholar 

  12. Happel, D., Reiten, R., and Smalø, S.O.: ‘Tilting in abelian categories and quasitilted algebras’, Memoirs Amer. Math. Soc. 575 (1996).

    Google Scholar 

  13. Happel, D., and Ringel, CM.: ‘Tilted algebras’, Trans. Amer. Math. Soc. 274 (1982), 399–443.

    Article  MATH  MathSciNet  Google Scholar 

  14. Happel, D., and Unger, L.: ‘Modules of finite projective dimension and cocovers’, Math. Ann. 306 (1996), 445–457.

    Article  MATH  MathSciNet  Google Scholar 

  15. Kerner, O.: ‘Tilting wild algebras’, J. London Math. Soc. 39,no. 2 (1989), 29–47.

    Article  MATH  MathSciNet  Google Scholar 

  16. Miyashita, Y.: ‘Tilting modules of finite projective dimension’, Math. Z. 193 (1986), 113–146.

    Article  MATH  MathSciNet  Google Scholar 

  17. Reiten, I.: ‘Tilting theory and quasitilted algebras’: Proc. Internat. Congress Math. Berlin, Vol. II, 1998, pp. 109–120.

    MathSciNet  Google Scholar 

  18. Rickard, J.: ‘Morita theory for derived categories’, J. London Math. Soc. 39,no. 2 (1989), 436–456.

    Article  MATH  MathSciNet  Google Scholar 

  19. Ringel, C.M.: ‘The canonical algebras’: Topics in Algebra, Vol. 26:1 of Banach Center Publ., PWN, 1990, pp. 407–432.

    Google Scholar 

  20. Ringel, C.M.: ‘The category of modules with good filtration over a quasi-hereditary algebra has alost split sequences’, Math. Z. 208 (1991), 209–224.

    Article  MathSciNet  Google Scholar 

  21. Unger, L.: ‘The simplicial complex of tilting modules over quiver algebras’, Proc. London Math. Soc. 73,no. 3 (1996), 27–46.

    Article  MATH  MathSciNet  Google Scholar 

  22. Unger, L.: ‘Shellability of simplicial complexes arising in representation theory’, Adv. Math. 144 (1999), 221–246.

    Article  MATH  MathSciNet  Google Scholar 

References

  1. Auslander, V.I., Reiten, I., and Smalø, S.: Representation theory of Artin algebras, Vol. 36 of Studies Adv. Math., Cambridge Univ. Press, 1995.

    Google Scholar 

  2. Bernstein, I.N., Gelfand, I.M., and Ponomarev, V.A.: ‘Coxeter functors and Gabriel’s theorem’, Russian Math. Surveys 28 (1973), 17–32. (Uspekhi Mat. Nauk. 28 (1973), 19–33.)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bongartz, K.: ‘Algebras and quadratic forms’, J. London Math. Soc. 28 (1983), 461–469.

    Article  MATH  MathSciNet  Google Scholar 

  4. Dlab, V., and Rlngel, C.M.: Indecomposable representations of graphs and algebras, Vol. 173 of Memoirs, Amer. Math. Soc, 1976.

    Google Scholar 

  5. Drozd, Yu.A.: ‘Coxeter transformations and representations of partially ordered sets’, Funkts. Anal. Prilozhen. 8 (1974), 34–42. (In Russian.)

    MathSciNet  Google Scholar 

  6. Drozd, Yu.A.: ‘On tame and wild matrix problems’: Matrix Problems, Akad. Nauk. Ukr. SSR., Inst. Mat. Kiev, 1977, pp. 104–114. (In Russian.)

    Google Scholar 

  7. Drozd, Yu.A.: ‘Tame and wild matrix problems’: Representations and Quadratic Forms, 1979, pp. 39–74. (In Russian.)

    Google Scholar 

  8. Gabriel, P.: ‘Unzerlegbare Darstellungen 1’, Manuscripta Math. 6 (1972), 71–103, Also: Berichtigungen 6 (1972), 309.

    Article  MathSciNet  Google Scholar 

  9. Gabriel, P.: ‘Représentations indécomposables’: Séminaire Bourbaki (1973/74), Vol. 431 of Lecture Notes in Mathematics, Springer, 1975, pp. 143–169.

    Google Scholar 

  10. Gabriel, P., and Roiter, A.V.: ‘Representations of finite dimensional algebras’: Algebra VIII, Vol. 73 of Encycl. Math. Stud., Springer, 1992.

    Google Scholar 

  11. Kasjan, S., and Simson, D.: ‘Tame prinjective type and Tits form of two-peak posets II’, J. Algebra 187 (1997), 71–96.

    Article  MATH  MathSciNet  Google Scholar 

  12. Nazarova, L.A.: ‘Representations of quivers of infinite type’, Izv. Akad. Nauk. SSSR 37 (1973), 752–791. (In Russian.)

    MATH  MathSciNet  Google Scholar 

  13. Peña, J.A. de la: ‘Algebras with hypercritical Tits form’: Topics in Algebra, Vol. 26: 1 of Banach Center Publ, PWN, 1990, pp. 353–369.

    Google Scholar 

  14. Peña, J.A. de la: ‘On the dimension of the module-varieties of tame and wild algebras’, Commun. Algebra 19 (1991), 1795–1807.

    Article  MATH  Google Scholar 

  15. Peña, J.A. de la, and Simson, D.: ‘Prinjective modules, reflection functors, quadratic forms and Auslander—Reiten sequences’, Trans. Amer. Math. Soc. 329 (1992), 733–753.

    Article  MATH  MathSciNet  Google Scholar 

  16. Peña, J.A. de la, and Skowroński, A.: ‘The Euler and Tits forms of a tame algebra’, Math. Ann. 315 (2000), 37–59.

    Google Scholar 

  17. Ringel, C.M.: Tame algebras and integral quadratic forms, Vol. 1099 of Lecture Notes in Mathematics, Springer, 1984.

    Google Scholar 

  18. Roiter, A.V., and Kleiner, M.M.: Representations of differential graded categories, Vol. 488 of Lecture Notes in Mathematics, Springer, 1975, pp. 316–339.

    Google Scholar 

  19. Simson, D.: Linear representations of partially ordered sets and vector space categories, Vol. 4 of Algebra, Logic Appl., Gordon & Breach, 1992.

    Google Scholar 

  20. Simson, D.: ‘Posets of finite prinjective type and a class of orders’, J. Pure Appl. Algebra 90 (1993), 77–103.

    Article  MATH  MathSciNet  Google Scholar 

  21. Simson, D.: ‘Representation types, Tits reduced quadratic forms and orbit problems for lattices over orders’, Contemp. Math. 229 (1998), 307–342.

    MathSciNet  Google Scholar 

  22. Simson, D.: ‘Coalgebras, comodules, pseudocompact algebras and tame comodule type’, Colloq. Math, in press (2001).

    Google Scholar 

References

  1. Boutet de Monvel, L.: ‘On the index of Toeplitz operators of several complex variables’, Invent. Math. 50 (1979), 249–272.

    Article  MATH  Google Scholar 

  2. Coburn, L.: ‘Singular integral operators and Toeplitz operators on odd spheres’, Indiana Univ. Math. J. 23 (1973), 433–439.

    Article  MATH  MathSciNet  Google Scholar 

  3. Douglas, R., and Howe, R.: ‘On the C*-algebra of Toeplitz operators on the quarter-plane’, Trans. Amer. Math. Soc. 158 (1971), 203–217.

    Article  MATH  MathSciNet  Google Scholar 

  4. Landstad, M., Phillips, J., Raeburn, I., and Sutherland, C: ‘Representations of crossed products by coactions and principal bundles’, Trans. Amer. Math. Soc. 299 (1987), 747–784.

    Article  MATH  MathSciNet  Google Scholar 

  5. Muhly, P., and Renault, J.: ‘C*-algebras of multivariable Wiener-Hopf operators’, Trans. Amer. Math. Soc. 274 (1982), 1–44.

    Article  MATH  MathSciNet  Google Scholar 

  6. Salinas, N., Sheu, A., and Upmeier, H.: ‘Toeplitz operators on pseudoconvex domains and foliation algebras’, Ann. Math. 130 (1989), 531–565.

    Article  MathSciNet  Google Scholar 

  7. Upmeier, H.: ‘Toeplitz C*-algebras on bounded symmetric domains’, Ann. Math. 119 (1984), 549–576.

    Article  MathSciNet  Google Scholar 

  8. Upmeier, H.: ‘Toeplitz operators on symmetric Siegel domains’, Math. Ann. 271 (1985), 401–414.

    Article  MATH  MathSciNet  Google Scholar 

  9. Upmeier, H.: Toeplitz operators and index theory in several complex variables, Birkhäuser, 1996.

    Google Scholar 

  10. Venugopalkrishna, U.: ‘Fredholm operators associated with strongly pseudoconvex domains in C n’, J. Fund. Anal. 9 (1972), 349–373.

    Article  MATH  MathSciNet  Google Scholar 

  11. Wassermann, A.: ‘Algèbres d’opérateurs de Toeplitz sur les groupes unitaires’, C.R. Acad. Sci. Paris 299 (1984), 871–874.

    MATH  MathSciNet  Google Scholar 

References

  1. Fleishnee, H.: ‘Traversing graphs: The Eulerian and Hamiltonian theme’, in M. Dror (ed.): Arc Routing: Theory, Solutions, and Applications, Kluwer Acad. Publ., 2000.

    Google Scholar 

  2. Lawler, E.L., Lenstra, J.K., Rinnoy Kan, A.H.G., and Shmoys, D.B. (eds.): The traveling salesman problem, Wiley, 1985.

    Google Scholar 

References

  1. Johnson, R.A.: Modern geometry, Houghton-Mifflin, 1929.

    Google Scholar 

  2. Kimberling, C. ‘Triangle centres and central triangles’, Congr. Numer. 129 (1998), 1–285.

    MATH  MathSciNet  Google Scholar 

References

  1. Shannon, A.: ‘Tribonacci numbers and Pascal’s pyramid’, The Fibonacci Quart. 15,no. 3 (1977), 268; 275.

    MATH  MathSciNet  Google Scholar 

  2. Spickerman, W.: ‘Binet’s formula for the Tribonacci sequence’, The Fibonacci Quart. 15,no. 3 (1977), 268; 275.

    Google Scholar 

References

  1. Atanassov, K., Hlebarova, J., and Mihov, S.: ‘Recurrent formulas of the generalized Fibonacci and Tribonacci sequences’, The Fibonacci Quart. 30,no. 1 (1992), 77–79.

    MATH  Google Scholar 

  2. Bruce, I,: ‘A modified Tribonacci sequence’, The Fibonacci Quart. 22,no. 3 (1984), 244–246.

    MATH  MathSciNet  Google Scholar 

  3. Feinberg, M.: ‘Fibonacci-Tribonacci’, The Fibonacci Quart. 1,no. 3 (1963), 71–74.

    Google Scholar 

  4. Lee, J.-Z., and Lee, J.-S.: ‘Some properties of the generalization of the Fibonacci sequence’, The Fibonacci Quart. 25,no. 2 (1987), 111–117.

    MATH  Google Scholar 

  5. Scott, A., Delaney, T., and Hoggatt Jr., V.: s‘The Tribonacci sequence’, The Fibonacci Quart. 15,no. 3 (1977), 193–200.

    MATH  Google Scholar 

  6. Shannon, A.: ‘Tribonacci numbers and Pascal’s pyramid’, The Fibonacci Quart. 15,no. 3 (1977), 268; 275.

    MathSciNet  Google Scholar 

  7. Valavigi, C.: ‘Properties of Tribonacci numbers’, The Fibonacci Quart. 10,no. 3 (1972), 231–246.

    Google Scholar 

References

  1. Boyd, J.P.: Chebyshev and Fourier spectral methods, second ed., Dover, 2000, pdf version: http://www-personal.engin.umich.edu/~jpboyd/book_spectral2000.html.

  2. Canuto, C., Hussaini, M.Y., Quarteroni, A., and Zang, T.A.: Spectral methods in fluid dynamics, Springer, 1987.

    Google Scholar 

  3. Fornberg, B.: A practical guide to pseudospectral methods, Vol. 10 of Cambridge Monographs Appl. Comput. Math., Cambridge Univ. Press, 1996.

    Google Scholar 

  4. Gottlieb, D., Hussaini, M.Y., and Orszag, S.A.: ‘Theory and application of spectral methods’, in R.G. Voigt, D. Gottlieb, and M.Y. Hussaini (eds.): Spectral Methods for Partial Differential Equations, SIAM, 1984.

    Google Scholar 

  5. Gottlieb, D., and Orszag, S.A.: Numerical analysis of spectral methods: Theory and applications, SIAM, 1977.

    Google Scholar 

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(2001). T. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics, Supplement III. Encyclopaedia of Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-0-306-48373-8_20

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