Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
André, Y.: G-functions and geometry, Aspects of Mathematics. Vieweg, 1989.
Beukers, F.: ‘Algebraic values of G-functions’, J. Reine Angew. Math. 434 (1993), 45–65.
Beukers, F., and Wolfart, J.: ‘Algebraic values of hyperge-ometric functions’: New Advances in Transcendence Theory, Cambridge Univ. Press, 1988.
Bombieri, E.: ‘On G-functions’: Recent Progress in Analytic Number Theory, Vol. 2, Acad. Press, 1981, pp. 1–67.
Chudnovski, O., and Chudnovski, G.: ‘Applications of Padé-approximations to diophantine inequalities in values of G-functions’: Vol. 1052 of Lecture Notes in Mathematics, Springer, 1982, pp. 1–51.
Dwork, B., Gerotto, G., and Sullivan, F.J.: An introduction to G-functions, Vol. 133 of Ann. Math. Studies, Princeton Univ. Press, 1994.
Katz, N.M.: ‘On differential equations satisfied by period matrices’, IHES Publ. Math. 35 (1968).
Siegel, C.L.: ‘Über einige Anwendungen diophantischer Approximationen’: Ges. Abhandlungen, Vol. I, Springer, 1966.
Wolfart, J.: ‘Werte hypergeometrischer Funktionen’, Invent. Math. 92 (1988), 187–216.
Beth, T., Jungnickel, D., and Lenz, H.: Design theory, BI Wissenschaftsverlag & Cambridge Univ. Press, 1984.
Hirschfeld, J.W.P.: Projective geometries over finite fields, Oxford Univ. Press, 1979.
Hirschfeld, J.W.P.: Finite projective spaces in three dimensions, Oxford Univ. Press, 1985.
Hirschfeld, J.W.P., and Thas, J.A.: General Galois geometries, Oxford Sci. Publ. Clarendon Press, 1991.
Scafati, M., and Tallini, G.: Geometrie di Galois e teoria dei codici, CISU, Roma, 1995.
Scafati Tallini, M.: ‘Caratterizzazione grasfica delle forme hermitiane di un S r ,q’, Rend. Mat. Roma 26 (1967), 273–303.
Scafati Tallini, M.: ‘On k-sets of kind (m,n) of a finite projective or affine space’, Ann. Discrete Math. 14 (1982), 39–56.
Segre, B.: ‘Ovals in a finite projective plane’, Canad. J. Math. 7 (1955), 414–416.
Segre, B.: ‘Introduction to Galois geometries’, Atti Accad. Naz. Lincei, Mem. 8 (1967), 133–236.
Tallini, G.: ‘Sulle k-calotte di uno spazio lineare finito’, Ann. di Mat. (4) 42 (1956), 119–164.
Tallini, G.: ‘Le geometrie di Galois e le loro applicazioni alla statistka e alla teoria dell’informazione’, Rend. Mat. Roma 19 (1960), 379–400.
Tallini, G.: ‘On caps of kind s in a Galois r-dimensional space’, Acta Arithmetica VII (1961), 19–28.
Tallini, G.: ‘Un’applicazione delle geometrie di Galois a questioni di statistica’, Rend. Accad. Naz. Lincei 8 (1963), 479–485.
Tallini, G.: ‘Geometrie di Galois e loro applicazioni alla fisica’, Sem. Lab. Naz. CNEN F-70–63 (1970).
Tallini, G.: ‘Graphic characterization of algebraic varieties in Galois space’: Atti Conv. Int. Teorie Combinatorie, Vol. II, Accad. Naz. Lincei, 1976, pp. 153–165.
Tallini, G.: ‘General multivalued algebraic structures and geometric spaces’: Proc. 4th Int. Congress on Algebraic Hyper structures and Applications, Xanthi, Greece, 1990, pp. 197–202.
Tallini, G.: ‘Lectures on Galois geometries and Steiner systems’: Geometries, Codes and Cryptography: CIS M courses and lectures, Vol. 313, Springer, 1990, pp. 1–23.
Tallini, G., and Beutelspacher, A.: ‘Examples of essentially s-fold secure geometric authentication systems with large s’, Rend. Mat. Roma (VII) 10 (1990), 321–326.
Bonnecaze, A., Solé, P., and Calderbank, A.R.: ‘Quaternary construction of unimodular lattices’, IEEE Inform. Th. 41 (1995), 366–376.
Boztas, S., Hammons, A.R., and Kumar, P.V.: ‘4-phase sequence with near optimum correlation properties’, IEEE Inform. Th. 38 (1992), 1101–1113.
Hammons, A.R., Kumar, P.V., Calderbank, A.R., Sloane, N.J.A., and Solé, P.: ‘The Z4-linearity of Kerdock, Preparata, Goethals, and related codes’, IEEE Trans. Information Th. 40 (1994), 301–319.
Kumar, V., Helleseth, T., and Calderbank, R.A.: ‘An upper bound for Weil-type exponential sums over Galois rings and applications’, IEEE Inform. Th. 41 (1995).
Macdonald, B.R.: Finite rings with identity, M. Dekker, 1974.
Shanbag, A.G., Kumar, P.V., and Helleseth, T.: ‘An up-perbound for the extended Kloosterman sums over Galois rings’: Finite Fields and Applications, to appear.
Solé, P.: ‘A quaternary cyclic code and a family of quaternary sequences with low correlation’, in G. Cohen and J. Wolfmann (eds.): Coding Theory and Applications, Vol. 388 of Lecture Notes in Computer Science, Springer, 1989, pp. 193–201.
Spiegel, E.: ‘Codes over Zm revisited’, Inform. and Control 37 (1978), 100–104.
Udaya, P., and Siddiqui, M.U.: ‘Optimal biphase sequences with large linear complexity derived from sequences over Z4’, IEEE Inform. Th. IT-42 (1996), 202–216.
Yamada, M.: ‘Distance regular graphs of girth 4 over an extension ring of Z4’, Graphs and Combinatorics 6 (1980), 381–384
Eklof, P.C.: ‘Homological algebra and set theory’, Trans. Amer. Math. Soc. 227 (1977), 207–225.
Eklof, P.C.: ‘Methods of logic in abelian group theory’: Abelian Group Theory, Vol. 616 of Lecture Notes in Mathematics, Springer, 1977, pp. 251–269.
Eklof, P.C.: ‘Set-theoretic methods: the uses of gamma invariants’: Abelian Groups, Vol. 146 of Lecture Notes in Pure and Applied Math., M. Dekker, 1993, pp. 143–153.
Eklof, P.C., and Mekler, A.H.: Almost free modules, North-Holland, 1990.
Eklof, P.C., Mekler, A.H., and Shelah, S.: ‘Almost disjoint abelian groups’, Israel J. Math. 49 (1984), 34–54.
Mekler, A.H.: ‘How to construct almost free groups’, Canad. J. Math. 32 (1980), 1206–1228.
Shelah, S.: ‘A compactness theorem for singular cardinals, free algebras, Whitehead problem and transversals’, Israel J. Math. 21 (1975), 319–349.
Atkin, A.O.L., and Swinnerton-Dyer, H.P.P.: Modular forms on non-congruence subgroups, Vol. 19 of Proc. Symp. Pure Math., Amer. Math. Soc., 1971.
Borchereds, R.E.: ‘Sporadic groups and string theory’: First European Congress of Math., Vol. 1, 1992, pp. 411–421.
Conway, J.H., and Norton, S.P.: ‘Monstrous moonshine’, Bull. London Math. Soc. 11 (1979), 308–339.
Frenkel, I.B., Lepowsky, J., and Meurman, A.: Vertex operator algebras and the monster, Acad. Press, 1988.
Koike, M.: ‘Moonshine: a mysterious relationship between simple groups and automorphic functions’, Amer. Math. Soc. Transl. Ser. 2 160 (1994), 33–45.
Lehner, J.: Discontinuous groups and automorphic functions, Amer. Math. Soc., 1964.
Shimura, G.: Complex multiplication in terms of elliptic curves, Vol. 320 of Lecture Notes in Mathematics, Springer, 1973.
Smit, D.J.: ‘String theory and the algebraic geometry of moduli spaces’, Comm. Math. Phys. 114 (1988), 645.
Stark, H.: Complex multiplication, Vol. 320 of Lecture Notes in Mathematics, Springer, 1973.
Thompson, J.G.: ‘Finite groups and modular functions’, Bull. London Math. Soc. 11 (1979), 347–351.
Venkov, A.B.: Spectral theory of automorphic functions, Kluwer Acad. Publ., 1990.
Verlinde, E., and Verlinde, H.: ‘Chiral bosoniza-tion,determinants,and the string partition function’, Nuclear Phys. B288 (1987), 357.
Weber, H.: Lehrbuch der Algebra, Chelsea, 1961.
Witten, E.: ‘Elliptic genera and quantum field theory’, Comm. Math. Phys. 109 (1987), 525–536.
Z Agier, D.: ‘L-series and the Green functions of modular curves’: Proc. Internat. Congress Mathematicians, Berkeley, Amer. Math. Soc., 1986, pp. 689–698.
Butzer, P., and Nessel, R.: Fourier analysis and approximation, Vol. I, Birkhauser, 1971.
Courant, R., and Hilbert, D.: Methods of mathematical physics, Vol. II, Wiley, 1962.
Feller, W.: An introduction to probability theory and its applications, second ed., Vol. 2, Springer, 1976.
Titchmarsh, E.C.: Introduction to the theory of Fourier integrals, Clarendon Press, 1937.
Weierstrass, K.: ‘Ueber die analytische Darstellbarkeit sogenannter willkurlichen Functionen reeler Argumente’, Berliner Sitzungsberichte (1985), 633–639; 789–805.
Henrici, P.: Applied and computational complex analysis, Vol. I, Wiley, reprint, 1988.
Hille, E.: Analytic function theory, Vol. 1, Chelsea, reprint, 1982.
Lewin, B.J.: Nullstellenverteilung ganzer Funktionen, Akademie Verlag, 1962.
Schmidt, W.M.: Diophantine approximations and Diophantine equations, Vol. 1467 of Lecture Notes in Mathematics, Springer, 1991.
Shorey, T.N., and Tijdeman, R.: Exponential Diophantine equations, Vol. 87 of Tracts in Math., Cambridge Univ. Press, 1986.
Sprindžuk, V.G.: Classical diophantine equations, Vol. 1559 of Lecture Notes in Mathematics, Springer, 1993. (Translated from the Russian.)
Adler, S.L., and Dashen, R.: Current algebras, Benjamin, 1968.
Dashen, R., and Gell-Mann, M.: ‘Representation of local current algebra at infinite momentum’, Phys. Rev. Lett. 17 (1966), 340–343.
Hermann, R.: Lie algebras and quantum mechanics, Benjamin, 1970.
Renner, H.: Current algebras and their applications, Pergamon, 1968.
Hermann, R.d: Lie groups for physicists, Benjamin, 1966.
Weimar, E.: ‘The range of validity of the Gell-Mann formula’, Nuovo Cimento Lett. 4 (1972), 43–50.
Gell-Mann, M., and Ne’eman, Y.: The eightfold way, Benjamin, 1964.
Gell-Mann, M., and Ne’eman, Y.: The eightfold way, Benjamin, 1964.
Okubo, S.: ‘Note on unitary symmetry in strong interactions’, Prog. Theor. Phys. 27 (1962), 949–969.
De Jong, K.A.: ‘An analysis of the behavior of a class of genetic adaptive systems’, Ph.D. thesis Univ. Michigan (1975).
Goldberg, D.E.: Genetic algorithms in search, optimization and machine learning, Addison-Wesley, 1989.
Holland, J.H.: Adaptation in natural and artificial systems, Univ. Michigan Press, 1975.
Kargupta, H.: ‘The gene expression messy genetic algorithm’: Proc. IEEE Internat. Conf. on Evolutionary Computation. Nagoya University, Japan, May, 1996, 1996.
Brouwer, A.E.: ‘Block designs’, in R. Graham, M. Grötschel, and L. LovÁsz (eds.): Handbook of Combinatorics, Elsevier, 1995, p. Ch. 14.
Cameron, P.J., and Lint, J.H. van: Designs, graphs, codes and their links, Cambridge Univ. Press, 1991.
Macwilliams, F.J., and Sloane, N.J.A.: The theory of error-correcting codes, North-Holland, 1977.
Lint, J.H. Van: Introduction to coding theory, Springer, 1992.
Lint, J.H. van, and Wilson, R.M.: A course in combinatorics, Cambridge Univ. Press, 1992.
Bechlivanidis, C., and Moerbeke, P. van: ‘The Goryachev-Chaplygin top and the Toda lattice’, Comm. Math. Phys 110 (1987), 317–324.
Bobenko, A.I., and Kuznetsov, V.B.: ‘Lax representation and new formulae for the Goryachev-Chaplygin top’, J. Phys. A 21 (1988), 1999–2006.
Chaplygin, S.A.: ‘A new case of rotation of a rigid body, supported at one point’: Collected works, Vol. I, Gostekhizdat, 1948, pp. 118–124. (In Russian.)
Goryachev, D.: ‘On the motion of a rigid material body about a fixed point in the case A — B = C’, Mat. Sb. 21 (1900). (In Russian.)
Piovan, L.: ‘Cyclic coverings of Abelian varieties and the Goryachev-Chaplygin top’, Math. Ann. 294 (1992), 755–764.
Cremers, A.B., and Ginsburg, S.: ‘Context-free grammar forms’, J. Comput. System Sci. 11 (1975), 86–116.
Maurer, H.A., Penttonen, M., Salomaa, A., and Wood, D.: ‘On non context-free grammar forms’, Math. Systems Th. 12 (1979), 297–324.
Niemi, V.: ‘Density of grammar forms, I; II’, Internat. J. Comput. Math. 20 (1986), 3–21;
Niemi, V.: ‘Density of grammar forms, I; II’, Internat. J. Comput. Math. 20 (1986), 91–114.
Pǎun, Gh., and Salomaa, A.: ‘Families generated by grammars and L systems’, in G. Rozenberg and A. Salomaa (eds.): Handbook of Formal Languages, Vol. 1, Springer, 1997, pp. 811–861.
Salomaa, A.: ‘On color-families of graphs’, Ann. Acad. Sci. Fennicae AI6 (1981), 135–148.
Salomaa, A., Maurer, H.A., and Wood, D.: ‘Dense hierarchies of grammatical families’, J. Assoc. Comput. Mach. 29 (1982), 118–126.
Csuhaj-Varju, E., and Dassow, J.: ‘On cooperating distributed grammar systems’, J. Inform. Process. Cybern., EIK 26 (1990), 49–63.
Csuhaj-Varju, E., Dassow, J., Kelemen, J., and Pǎun, Gh.: Grammar systems. A grammatical approach to distribution and cooperation, Gordon&Breach, 1994.
Csuhaj-Varju, E., Kelemen, J., Kelemenova, A., and Paun, GH.: ‘Eco-grammar systems: a framework for studying life-like interactions’, Artificial Life 3, no. 1 (1997), 1–28.
Csuhaj-Varju, E., Kelemen, J., and Pǎun, GH.: ‘Grammar systems with WAVE-like communication’, Computers and AI 15, no. 4 (1996), 419–436.
Dassow, J., Pǎun, GH., and Rozenberg, G.: ‘Grammar systems’, in G. Rozenberg and A. Salomaa (eds.): Handbook of Formal Languages, Springer, 1996.
Pǎun, G.: ‘Five (plus two) universal DNA computing models based on the splicing operation’: Second Ann. Meeting on DNA Based Computers, Princeton Univ. Press, 1996, pp. 67–86.
Pǎun, GH., and Salomaa, A.: ‘DNA computing based on the splicing operation’, Math. Japon. 43 (1996), 607–632.
Paun, GH., and Sântean(now Kari), L.: ‘Parallel communicating grammar systems: the regular case’, Ann. Univ. Buc, Mat-Inform. Series 38 (1989), 55–63.
Heath, F.G.: ‘Origins of the binary code’, Scientific American 227 (1972), 76–83.
Nijenhuis, A., and Wilf, H.S.: Combinatorial algorithms, second ed., Acad. Press, 1978.
Pruesse, G., and Ruskey, F.: ‘Generating linear extensions fast’, SIAM J. Computing 23 (1994), 373–386.
Reingold, E.M., Nievergelt, J., and Deo, N.: Combinatorial algorithms: Theory and practice, Prentice-Hall, 1977.
Savage, C.D.: ‘Gray code sequences of partitions’, J. Algorithms 10 (1989), 577–595.
Savage, C.D., and Winkler, P.: ‘Monotone Gray codes and the middle two levels problem’, J. Combinatorial Th. A 70 (1995).
Witte, D., and Gallian, J.A.: ‘A survey: Hamiltonian cycles in Cayley graphs’, Discrete Math. 51 (1984), 293–304.
Korte, B., Lovász, L., and Schruder, R.: Greedoids, Springer, 1991.
Papadimitriou, C.H., and Steiglitz, K.: Combinatorial optimization, Prentice-Hall, 1982.
Walukiewicz, S.: Integer programming, Kluwer Acad. Publ., 1991.
Dilworth, R.P.: ‘A decomposition theorem for partially ordered sets’, Ann. of Math. 51 (1950), 161–166.
Frank, A.: ‘On chain and antichain families of a partially ordered set’, J. Combin. Th. Ser. B 29 (1980), 176–184.
Greene, C.: ‘Some partitions associated with a partially ordered set’, J. Combin. Th. Ser. A 20 (1976), 69–79.
Greene, C., and Kleitman, D.J.: ‘The structure of Sperner k-families’, J. Combin. Th. Ser. A 20 (1976), 41–68.
Becker, TH., Weispfenning, V., and Kredel, H.: Gröbner bases: a computational approach to commutative algebra, Springer, 1993.
Buchberger, B.: ‘An algorithmic criterion for the solvability of algebraic systems of equations’, Aequationes Math. 4 (1965), 374–383, This paper is a published version of the author’s PhD Thesis (Innsbruck, 1965) under the advice of Prof. W. Gröbner.
Buchberger, B.: ‘Gröbner bases: an algorithmic method in polynomial ideal theory’, in N.K. Bose (ed.): Recent Trends in Multidimensional Systems Theory, Reidel, 1985, pp. 184–232.
Cannon, J.: ‘The combinatorial structure of cocompact discrete hyperbolic groups’, Geom. Dedicata 16 (1984), 123–148.
Cannon, J.: ‘The theory of negatively curved spaces and groups’, in T. Bedford, M. Keane, and C. Series (eds.): Ergodic Theory, Symbolic Dynamics and Hyperbolic Spaces, Oxford Univ. Press, 1991, pp. 315–369.
Coornaert, M., Delzant, T., and Papadopoulos, A.: Géométrie et théorie des groupes, Vol. 1441 of Lecture Notes in Mathematics, Springer, 1990.
Ghys, E., and Harpe, P. De La(eds.): Sur les groupes hyperboliques d’après Mikhael Gromov, Vol. 83 of Progress in Maths., Birkhäuser, 1990.
Gromov, M.: ‘Infinite groups as geometric objects’: Proc. Int. Congress Math. Warszawa, 1983, Vol. 1, 1984, pp. 385–391.
Gromov, M.: ‘Hyperbolic groups’, in S.M. Gersten (ed.): Essays in Group Theory, Vol. 8 of MSRI Publ., Springer, 1987, pp. 75–263.
Kaimanovich, V.A.: ‘Ergodicity of harmonic invariant measures for the geodesic flow on hyperbolic spaces’, J. Reine Angew. Math. 455 (1994), 57–103.
Rips, E.: ‘Subgroups of small cancellation groups’, Bull. London Math. Soc. 14 (1982), 45–47
Ando, T.: ‘Convergent sequences of finitely additive measures’, Pacific J. Math. 11 (1961), 395–404.
Bourgain, J.: ‘H ∞ is a Grothendieck space’, Studia Math. 75 (1983), 193–216.
Coulhon, TH.: ‘Suites d’operateurs sur un espace C(K) de Grothendieck’, C.R 298 (1984), 13–15.
Diestel, J.: ‘Grothendieck spaces and vector measures’: Vector and Operator Valued Measures and Applications, Acad. Press, 1973, pp. 97–108.
Diestel, J., and Uhl, Jr., J.J.: Vector measures, Vol. 15 of Math. Surveys, Amer. Math. Soc, 1977.
Grothendieck, A.: ‘Sur les applications linéaires faiblement compactes d’espaces du type C(K)’, Canadian J. Math. 5 (1953), 129–173.
Lotz, H.P.: ‘Uniform convergence of operators on L ∞ and similar spaces’, Math. Z. 190 (1985), 207–220.
Pfitzner, H.: ‘Weak compactness in the dual of a C*-algebra is determined commutatively’, Math. Ann. 298 (1994), 349–371.
Rábiger, F.: ‘Beiträge zur Strukturtheorie der Grothendieck-Räume’, Sitzungsber. Heidelberger Akad. Wissenschaft. Math.-Naturwiss. Kl. Abh. 4 (1985).
Seever, G. L.: ‘Measures on F-spaces’, Trans. Amer. Math. Soc. 133 (1968), 267–280.
Shaw, S.-Y.: ‘Ergodic theorems for semigroups of operators on a Grothendieck space’, Proc. Japan Acad. 59 (A) (1983), 132–135.
Barrat, M.B., and Priddy, S.B.: ‘On the homology of non-connected monoids and their associated groups’, Comm. Math. Helvetici 47 (1972), 1–14.
Jardine, J.F.: ‘The homotopical foundations of algebraic K-theory’: Algebraic K-Theory and Algebraic Number Theory, Vol. 83 of Contemp. Math., Amer. Math. Soc., 1989, pp. 57–82.
May, J.P.: Classifying spaces and fibrations, Vol. 155 of Memoirs, Amer. Math. Soc., 1975.
McDuff, D., and Segal, G.: ‘Homology fibrations and the group completion theorem’, Invent. Math. 31 (1976), 279–287.
Moerduk, I.: ‘Bisimplicial sets and the group-completion theorem’: Algebraic K-Theory: Connections with Geometry and Topology, Kluwer Acad. Publ., 1989, pp. 225–240.
Borovik, A., and Nesin, A.: Groups of finite Morley rank, Oxford Univ. Press, 1994.
Cherlin, G.: ‘Groups of small Morley rank’, Ann. Math. Logic 17 (1979), 1–28.
Poizat, B.: Groupes stables, Nur Al-Mantiq Wal-Ma’rifah, Villeurbanne, 1987.
Zil’ber, B.I.: ‘Groups and rings whose theory is categorical’, Fund. Math. 55 (1977), 1730188.
Editor information
Rights and permissions
Copyright information
© 1997 Kluwer Academic Publishers
About this chapter
Cite this chapter
Hazewinkel, M. (1997). G. In: Hazewinkel, M. (eds) Encyclopaedia of Mathematics. Encyclopaedia of Mathematics. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-1288-6_7
Download citation
DOI: https://doi.org/10.1007/978-94-015-1288-6_7
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-4896-7
Online ISBN: 978-94-015-1288-6
eBook Packages: Springer Book Archive