Canoni ritmici a mosaico

More documents

Recommendations

Info

BIBLIOGRAFIA [11] Moreno Andreatta, De la Conjecture de Minkowski aux Canons Rythmiques Mosaïques. L’Ouvert 114 (2007), 51-61. [12] Ethan M. Coven and Aaron Meyerowitz, Tiling the Integers with Translates of One Finite Set. J. Algebra 212 (1999), 161-174. [13] Keresztély Corrádi and Sándor Szabó, An Axiomatic Approach for the Hajós Theorem. Contribution to Algebra and Geometry 38(2) (1997), 241-248. [14] Nicolaas Govert de Bruijn, On Bases for the Set of Integers. Publicationes Mathematicae Tomus 1 (1950), 232-242. [15] Nicolaas Govert de Bruijn, On the Factorization of Finite Abelian Groups. Indag. Math. 15 (1953), 258-264. [16] Nicolaas Govert de Bruijn, On the Factorization of Cyclic Groups. Indag. Math. 17 (1955), 370-377. [17] Nicolaas Govert de Bruijn, On Number Systems. Nieuw Arch. Wisk.(3) 4 (1956), 15-17. [18] Nicolaas Govert de Bruijn, Some Direct Decomposition of the Set of Integers. Math. Comp. 18 (1964), 537-546. [19] Nicolaas Govert de Bruijn, Pólya’s theory of counting. Applied Combinatorial Mathematics, Wiley, New York (1964), 144-184. [20] Nicolaas Govert de Bruijn, On the Number of Partition Patterns of a Set. Nederl. Akad. Wetensch. Proc. Ser. A 82 = Indag. Math. 41 (1979), 229-234. [21] Harald Fripertinger, Classification of motives: a mathematical approach. (1999) Disponibile on line: http://www.uni-graz.at/˜fripert/motive.html [22] Harald Fripertinger, Enumeration of mosaics. Discrete Mathematics 199 (1999), 49-60. [23] Harald Fripertinger, Enumeration of non-isomorphic canons. Tatra Mountains Mathematical Publications 23 (2002), 47-57. [24] Harald Fripertinger, Tiling problems in music theory. Perspectives of Mathematical and Computational Music Theory, (G. Mazzola, E. Puebla et T. Noll eds.) EpOs, Universität Osnabrück (2004), 153-168. [25] Harald Fripertinger, Remarks on rhythmical canons. Colloquium on mathematical music theory 347 (2005), 73-90. [26] Laszlo Fuchs, Abelian Groups. Pergamon Press (1960). 104
BIBLIOGRAFIA [27] Bent Fuglede, Commuting self-adjoint partial differential operators and a group theoretic problem. Journal of Functional Analysis, 16 (1974), 101-121. [28] Édouard Gilbert, Polynômes cyclotomiques, canons mosaïques et rythmes kasymétriques. Mémoire de Master ATIAM, Università di Parigi VI / Ircam (2007) [29] G. Hajós, Über einfache und mehrfache Bedeckung des n-dimensionalen Raumes mit einem Würfelgitter. Math. Zeitschrift 47 (1941), 427-467. [30] G. Hajós, Sur la factorisation des groupes abéliens. Časopis Pěst. Mat. Fys. 74 (1950), 157-162. [31] G. Hajós, Sur le problème de factorisation des groupes cycliques. Acta Math. Acad. Sci. Hungar 1 (1950), 189-195. [32] Godrey H. Hardy ed Edward M. Wright, An Introduction to the Theory of Numbers (V ed.). Clarendon Press, Oxford (1979). [33] Rachel W. Hall and Paul Klinsberg, Asymmetric Rhythms and Tiling Canons. American Mathematical Monthly 113(10) (2006), 887-896. [34] Yves Hellegouarch, Gammes Naturelles. S.M.F. - Gazette des Mathmaticiens 82 (1999), 13-26. [35] Alex Iosevich, Nets Katz and Terence Tao, The Fuglede Spectral Conjecture holds for convex planar domains. Mathematical Research Letters, 10 (2003), 559-569. [36] Paul Ishiara and Michael Knapp, Basic Z12-Analysis of Musical Chords. UMAP Journal 14(4) (1993), 319-348. [37] Franck Jedrzejewski, Mathematical Theory of Music. Editions Delatour France/Ircam-Centre Pompidou (2006). [38] Palle E.T. Jorgensen and Steen Pedersen, Estimates on the Spectrum of Fractals Arising from Affine Iterations. Fractal Geometry and Stochastics, Progress in Probability 17 (1995), 191-219. [39] Mihail N. Kolountzakis and Izabella Łaba, Tiling and spectral properties of near-cubic domains. Studia Math. 160 (2004), 287-299. [40] Mihail N. Kolountzakis and Máté Matolcsi, Complex Hadamard matrices and the spectral set conjecture. Collectanea Mathematica, Vol Extra (2006), 281- 291. [41] Sergei Konyagin and Izabella Łaba, Spectra of Certain Types of Polynomials and Tiling of Integers with Translates of Finite Sets. Journal of Number Theory 103 (2004), 267-280. 105
Page 1:
Università degli Studi di Pisa FAC
Page 5 and 6:
Introduzione Matematica e musica ha
Page 7 and 8:
Introduzione congettura di Minkowsk
Page 9 and 10:
Capitolo 1 I modelli algebrici 1.1
Page 11 and 12:
1.1 Definizione musicale e definizi
Page 13 and 14:
1.1 Definizione musicale e definizi
Page 15 and 16:
1.2 Canoni ritmici e tassellazioni
Page 17 and 18:
• g + A = A, quindi g ∈ PA, e
Page 19 and 20:
1.2 Canoni ritmici e tassellazioni
Page 21 and 22:
1.3 Rappresentazioni matematiche e
Page 23 and 24:
1.3 Rappresentazioni matematiche e
Page 25 and 26:
Capitolo 2 Condizioni di esistenza
Page 27 and 28:
[⇐]: Per l’osservazione 2.1.1 (
Page 29 and 30:
2.1 Il teorema di Coven-Meyerowitz
Page 31 and 32:
da cui la tesi. 2.1 Il teorema di C
Page 33 and 34:
2.1 Il teorema di Coven-Meyerowitz
Page 35 and 36:
2.2 Esempi grado 5: 0 = a1 + a2 + a
Page 37 and 38:
1. A = {0, 1, 5} ⇒ A(x) = 1 + x +
Page 39 and 40:
Capitolo 3 Canoni di Vuza 3.1 Fatto
Page 41 and 42:
3.1 Fattorizzazioni aperiodiche Dim
Page 43 and 44:
Ritornando alla fattorizzazione ini
Page 45 and 46:
3.1 Fattorizzazioni aperiodiche In
Page 47 and 48:
3.2 La congettura di Minkowski e il
Page 49 and 50:
Page 51 and 52:
Page 53 and 54:
✻ P ❅■ w❅O Figura 3.4
Page 55 and 56:
Figura 3.8 3.2 La congettura di Min
Page 57 and 58: 3.2 La congettura di Minkowski e il
Page 59 and 60: Capitolo 4 Congettura spettrale 4.1
Page 61 and 62: 1. per ogni s, t ∈ T con s t si
Page 63 and 64: 2. | Γ |=| A | e 4.2 La congettura
Page 65 and 66: La proposizione 4.2.1 suggerisce la
Page 67 and 68: allora esiste un intero k ∈ Z tal
Page 69: • non Hajós. 4.2 La congettura s
Page 72 and 73: Capitolo 5. Trasformazione e genera
Page 86 and 87: Appendice A. Polinomi ciclotomici 3
Page 88 and 89: Appendice A. Polinomi ciclotomici i
Page 90 and 91: Appendice A. Polinomi ciclotomici c
Page 92 and 93: Appendice B. Algebra combinatoria e
Page 104 and 105: Appendice C. Nuovi canoni C.1 Defin
Page 106 and 107: Appendice C. Nuovi canoni In quest
Page 110 and 111: BIBLIOGRAFIA [42] Jeffrey C. Lagari
Page 112 and 113: BIBLIOGRAFIA [75] Terence Tao, Fugl
Page 114: INDICE ANALITICO lattice point theo
show all

Canoni ritmici a mosaico

Create successful ePaper yourself

Delete template?

Save as template?